(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 619980, 21159]*) (*NotebookOutlinePosition[ 621025, 21194]*) (* CellTagsIndexPosition[ 620934, 21188]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " kasutamine" }], "Title"], Cell["1. Sissejuhatus", "Subtitle"], Cell[TextData[{ StyleBox["Programmi ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["Mathematica", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" avanemisel pole programmi tuum - ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["Kernel", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" - vaikimisi k\[ADoubleDot]ivitatud. ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["Kernel", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" on programmi see osa, mis tegelikult teostab arvutusi. ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["Mathematica", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" abil v\[OTilde]ib mitte ainult arvutada, vaid ka kujundada \ dokumente. Peale selle, programmi tuum v\[OTilde]ib t\[ODoubleDot]\ \[ODoubleDot]tada hoopis teises arvutis, mis asub samas arvutiv\[OTilde]rgus. \ Seda k\[OTilde]ike on v\[OTilde]imalik konfigureerida, vaikimisi k\ \[ADoubleDot]ivitatakse tuum siiski samas arvutis esimese arvutuse k\ \[ADoubleDot]ivitamisel.", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["\n", CharacterEncoding->"WindowsANSI"], StyleBox["Arvutuse teostamiseks tuleb p\[ADoubleDot]rast arvutuse \ sisestamist vajutada ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["Shift+Enter", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[". N\[ADoubleDot]iteks:", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["\n", CharacterEncoding->"WindowsANSI"], StyleBox["2+4", FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox[" Shift+Enter.", FontFamily->"Courier New", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["\n", CharacterEncoding->"WindowsANSI"], StyleBox["Ekraanile ilmub:", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"] }], "Text", TextAlignment->Left, TextJustification->1], Cell[CellGroupData[{ Cell[BoxData[ \(2 + 4\)], "Input"], Cell[BoxData[ \(6\)], "Output"] }, Open ]], Cell["\<\ In ja Out n\[ADoubleDot]itavad, mitmenda arvutusega on tegemist, antud juhul \ on esimene sisestus 2 + 4 ja esimene v\[ADoubleDot]ljund 6. Edasistes \ arvutustes saab viidata tagasi eelmistele sisestustele ja \ v\[ADoubleDot]ljunditele ning neid arvutustes kasutada. Seda vaatame hiljem. \ Arvutustes saab kasutada nii tekstip\[OTilde]hist arvutust - k\[OTilde]ik \ tehted tr\[UDoubleDot]kitakse sisse k\[ADoubleDot]sitsi, ei mingit hiirega \ edasi-tagasi s\[OTilde]elumist. (kes on proovinud hiire abil Wordis valemeid \ sisestada, teab, kui aega n\[OTilde]udev see on). Mathematica 4 ja 5 \ versioonides saab kasutada ka graafilist kasutajaliidest. Shift-Enteri asemel \ v\[OTilde]ib vajutada ka Enter-klahvi, mis asetseb klaviatuuri paremas \ servas. \tVihje: tihedalt valemeid t\[ADoubleDot]is tekstis kasutatakse TeX-i - \ tulemus on ilusam, valemite sisestamine \tv\[OTilde]tab tunduvalt v\[ADoubleDot]hem aega. Teisalt - TeX-i \ \[OTilde]ppimine v\[OTilde]tab natuke aega, kuid kes teadusega \ttahab tegelda, selle jaoks on see enam-v\[ADoubleDot]hem kohustuslik. \ Matemaatika ja f\[UDoubleDot]\[UDoubleDot]sika ajakirjad \tv\[OTilde]tavad vastu \[UDoubleDot]ldjuhul vaid TeX-s v\[OTilde]i LaTeX-s \ esitatud tekste), kuigi viimastel aastatel siiski ka \tn\[ADoubleDot]iteks MS Wordis kirjutatut.\ \>", "Text", TextAlignment->Left, TextJustification->1], Cell[CellGroupData[{ Cell["2. Aritmeetika, algebra.", "Subtitle"], Cell["2.1. Aritmeetika. T\[ADoubleDot]psed ja ligikaudsed tehted.", \ "Subsubtitle"], Cell["Tavalistes arvutustes kasutatavad tehted:", "Text"], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"\t\t ", StyleBox[" ", FontFamily->"Courier New"], StyleBox[" ", FontFamily->"Courier New", FontSlant->"Italic"]}]], RowBox[{ RowBox[{ StyleBox["x", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["+", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["y", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["+", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], RowBox[{ StyleBox["z", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["\t\t ", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["liitmine", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"]}]}], StyleBox["\n", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[ RowBox[{ StyleBox["\t", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], "\t"}]], RowBox[{ RowBox[{ StyleBox[\(-x\), FormatType->StandardForm, FontFamily->"Courier New", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[ RowBox[{ StyleBox["\t ", FormatType->StandardForm, FontFamily->"Courier New", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"]}]], StyleBox["lahutamine", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"]}], StyleBox[",", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["miinus", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[",", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[\(neg . \ arv\), FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"]}], StyleBox[" ", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["\n", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[ RowBox[{ StyleBox["\t", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], "\t"}]], RowBox[{ RowBox[{ StyleBox["x", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["y", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["z", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["v\[OTilde]i", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["x", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["*", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["y", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["*", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["z", FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["\t ", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["korrutamine", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"]}], StyleBox[",", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[\(korrutusm\[ADoubleDot]rk\ v\[OTilde]i\ t\[UDoubleDot]hik\ \ selle\ asemel\), FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"]}], StyleBox["\n", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[ RowBox[{ StyleBox["\t", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], "\t"}]], RowBox[{ StyleBox[\(x/y\), FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox[ RowBox[{ StyleBox[" ", FormatType->StandardForm, FontFamily->"Courier New", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"]}]], StyleBox["jagamine", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"]}], StyleBox["\n", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[ RowBox[{ StyleBox["\t", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], "\t"}]], StyleBox[\(x^y\), FormatType->StandardForm, FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Courier New", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["ehk", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], \(x\^y\), StyleBox[ RowBox[{ StyleBox[" ", FormatType->StandardForm, FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"]}]], StyleBox["astendamine", FormatType->StandardForm, FontFamily->"Times New Roman", FontWeight->"Plain", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"]}]}]], "Text", Background->GrayLevel[0.900008]], Cell["\<\ ASCII koodis on astendamism\[ADoubleDot]rk 94, selle saab k\[ADoubleDot]tte \ kui vajutada Alt+94 (94 klaviatuuri paremalt poolelt). N\[ADoubleDot]ited:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(2.3 + 5.6*2\)], "Input"], Cell[BoxData[ \(13.5`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(2\ 4\ 6\)], "Input"], Cell[BoxData[ \(48\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(2.4\^32\)], "Input"], Cell[BoxData[ \(1.4681138466456628`*^12\)], "Output"] }, Open ]], Cell[TextData[{ "Viimane avaldis on antud juba nn teaduslikus t\[ADoubleDot]histuses (", StyleBox["scientific notation", FontSlant->"Italic"], "). Samamoodi saab arve ka sisestada. Kolm j\[ADoubleDot]rgmist kirjutist \ on samav\[ADoubleDot]\[ADoubleDot]rsed:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(3.5\ 10\^34\)], "Input"], Cell[BoxData[ \(3.5`*^34\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(3.5\ 10^34\)], "Input"], Cell[BoxData[ \(3.5`*^34\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(3.5*^34\)], "Input"], Cell[BoxData[ \(3.5`*^34\)], "Output"] }, Open ]], Cell["\<\ Kuigi Mathematica v\[OTilde]ib leida v\[ADoubleDot]ga pikki arvutustulemusi t\ \[ADoubleDot]pselt, on tavaliselt soovitav need esitada siiski n\[ODoubleDot] \ \[UDoubleDot]mmardatud kujul, k\[UDoubleDot]mne astmete kaudu. \ K\[UDoubleDot]mne astmete kaudu (ligikaudsel kujul) saab arve esitada \ kasutades funktsiooni N[ ]:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(3\^32\)], "Input"], Cell[BoxData[ \(1853020188851841\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(3\^32\ // N\)], "Input"], Cell[BoxData[ \(1.853020188851841`*^15\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[3\^32]\)], "Input"], Cell[BoxData[ \(1.853020188851841`*^15\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[2\^40]\)], "Input"], Cell[BoxData[ \(1.099511627776`*^12\)], "Output"] }, Open ]], Cell["\<\ Mathematica eristab t\[ADoubleDot]isarve ning reaalarve. Kui sisestate \ arvutuses k\[OTilde]ik arvud t\[ADoubleDot]isarvudena, siis antakse ka l\ \[OTilde]pptulemus t\[ADoubleDot]isarvude kaudu. N\[ADoubleDot]iteks 34 on \ antud programmi jaoks t\[ADoubleDot]isarv, 34.0 ehk ka 34. reaalarv. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(1/2 + 4/7\)], "Input"], Cell[BoxData[ \(15\/14\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(452/62\)], "Input"], Cell[BoxData[ \(226\/31\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(452.0/62\)], "Input"], Cell[BoxData[ \(7.290322580645161`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(1.0 + 452/62\)], "Input"], Cell[BoxData[ \(8.29032258064516`\)], "Output"] }, Open ]], Cell["\<\ Seega, kui arvutuses on antud v\[ADoubleDot]hemalt \[UDoubleDot]ks reaalarv, \ antakse vastus reaalarvuna.\ \>", "Text"], Cell["M\[OTilde]ned matemaatilised funktsioonid.", "Text", FontWeight->"Bold", FontSlant->"Italic"], Cell[TextData[{ StyleBox["Sqrt[x] ", FontFamily->"Courier"], StyleBox["ehk", FontSlant->"Italic"], " ", Cell[BoxData[ \(TraditionalForm\`\@x\)]], "\t\t\t\truutjuur x-st\n", StyleBox["Sqrt[x,n]", FontFamily->"Courier New"], " ", StyleBox["ehk ", FontSlant->"Italic"], " ", Cell[BoxData[ \(TraditionalForm\`\@x\%n\)]], "\t\t\tn-s juur x-st\n", StyleBox["Log[x]", FontFamily->"Courier New"], "\t\t\t\t\tnaturaallogaritm - ln x\n", StyleBox["Log[a,x]", FontFamily->"Courier New"], "\t\t\t\t\tlogaritm alusel a - ", Cell[BoxData[ \(TraditionalForm\`\(log\_a\) x\)]], "\nSin[x], Cos[x], Tan[x], Cot[x]\t\t\ttrigonomeetrilised funktsioonid, \ argument on radiaanides!\nArcSin[x], ArcCos[x], ArcTan[x], ArcCot[x]\t\ trigonomeetrilised p\[ODoubleDot]\[ODoubleDot]rdfunktsioonid \ (arkusfunktsioonid),\n \t\t\t\t\t\tannavad vastuse radiaanides\nn!\t\t\t\t\t\t\ faktoriaal\nAbs[x]\t\t\t\t\t\tabsoluutv\[ADoubleDot]\[ADoubleDot]rtus\n\ Round[x]\t\t\t\t\t\[UDoubleDot]mmardamine\nMod[n,m]\t\t\t\t\tj\[ADoubleDot]\ \[ADoubleDot]k, mis saadakse jagamisel ", Cell[BoxData[ \(TraditionalForm\`n\/m\)]], "\nQuotient[n,m]\t\t\t\t\tjagatise ", Cell[BoxData[ \(TraditionalForm\`n\/m\)]], " t\[ADoubleDot]isosa\nRandom[]\t\t\t\t\tpseudojuhuslik arv 0 ja 1 vahel\n\ Max[x,y,...], Min[x,y,...]\t\t\tarvude (avaldiste) x,y,... maksimum, miinimum\ \nFactorInteger[n]\t\t\t\tt\[ADoubleDot]isarvu n lahutamine algarvude \ korrutiseks\n", StyleBox["avaldis // ", FontSlant->"Italic"], "N ", StyleBox["ehk", FontSlant->"Italic"], " N[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t", StyleBox["avaldise", FontSlant->"Italic"], " ligikaudne v\[ADoubleDot]\[ADoubleDot]rtus; esitaminek\[UDoubleDot]mne \ astmete kaudu\nN[", StyleBox["avaldis,", FontSlant->"Italic"], "n]\t\t\t\t\t", StyleBox["avaldise", FontSlant->"Italic"], " v\[ADoubleDot]\[ADoubleDot]rtus n numbrikoha (mitte komakoha!) t\ \[ADoubleDot]psusega" }], "Text", Background->GrayLevel[0.900008]], Cell[TextData[{ StyleBox["NB! ", FontSlant->"Italic"], StyleBox["Mathematica's on k\[OTilde]igi funktsioonide argumendid antud \ alati kandilistes sulgudes. Funktsioonide ja protseduuride nimed algavad \ alati suure t\[ADoubleDot]hega. Seet\[OTilde]ttu on m\[OTilde]istlik enda \ defineeritud suurused ja funktsioonid anda v\[ADoubleDot]ikeste algust\ \[ADoubleDot]htedega.", FontWeight->"Plain", FontSlant->"Italic"] }], "Text", FontWeight->"Bold"], Cell[TextData[StyleBox["Konstandid.", FontWeight->"Bold"]], "Text", FontWeight->"Plain", FontSlant->"Italic"], Cell[TextData[{ StyleBox["Pi ", FontWeight->"Bold"], StyleBox["v\[OTilde]i", FontSlant->"Italic"], " \[Pi]\t\t\t\t\t\[Pi] \[TildeTilde] 3,14159\nE ", StyleBox["v\[OTilde]i", FontSlant->"Italic"], " \[ExponentialE]\t\t\t\t\te \[TildeTilde] 2,71828\nDegree ", StyleBox["v\[OTilde]i ", FontSlant->"Italic"], "\[Degree]\t\t\t\tnurgakraadi t\[ADoubleDot]his\nI ", StyleBox["v\[OTilde]i", FontSlant->"Italic"], " \[ImaginaryI]\t\t\t\t\timmaginaar\[UDoubleDot]hik, ", Cell[BoxData[ \(TraditionalForm\`\[ImaginaryI] = \@\(-1\)\)]], "\nInfinity ", StyleBox["v\[OTilde]i \[Infinity]\t\t\t\t ", FontSlant->"Italic"], "l\[OTilde]pmatus" }], "Text", Background->GrayLevel[0.900008]], Cell["\<\ \[Pi] ja e v\[OTilde]etakse arvuti poolt vaikimisi samuti kui \ t\[ADoubleDot]psed arvud. Seet\[OTilde]ttu ei anna arvuti selliste avaldiste \ ligikaudseid v\[ADoubleDot]\[ADoubleDot]rtusi. M\[OTilde]ned \ n\[ADoubleDot]ited:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Pi]/4\)], "Input"], Cell[BoxData[ \(\[Pi]\/4\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Pi/4. \)], "Input"], Cell[BoxData[ \(0.7853981633974483`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Sin[20 \[Degree]]\ // \ N\)], "Input"], Cell[BoxData[ \(0.3420201433256687`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[ExponentialE]\^20. \)], "Input"], Cell[BoxData[ \(4.851651954097903`*^8\)], "Output"] }, Open ]], Cell[TextData[{ "Ilma ligikaudset vastust n\[OTilde]udva funktsioonita N antakse vatuseks \ lihtsalt ", StyleBox["Sin[20\[Degree]]", FontWeight->"Bold"], ", mis ongi t\[ADoubleDot]pne vastus." }], "Text"], Cell[TextData[StyleBox["Kompleksarvud.", FontSlant->"Italic"]], "Text", FontWeight->"Bold"], Cell[TextData[{ "x + I y\t\t\t\t\t\tkompleksarv kujul ", StyleBox["x+i y\n", FontSlant->"Italic"], "Re[z]\t\t\t\t\t\tkompleksarvu reaalosa - x\nIm[z]\t\t\t\t\t\tkompleksarvu \ immaginaarosa - y\nAbs[z] \t\t\t\t\tabsoluutv\[ADoubleDot]\[ADoubleDot]rus \ |z|\nArg[z]\t\t\t\t\t\tkompleksarvu ", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(z\)\(|\)\(e\^i\[CurlyPhi]\)\)\)]], " argument \[CurlyPhi]\nConjugate[z]\t\t\t\t\tarvu ", StyleBox["z", FontSlant->"Italic"], " kaaskompleks ", Cell[BoxData[ \(TraditionalForm\`z\&_\)]], " ehk ", Cell[BoxData[ \(TraditionalForm\`\(z\^*\)\)]] }], "Text", Background->GrayLevel[0.900008]], Cell["N\[ADoubleDot]ited:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\((3 + 2 I)\) \((7 - I)\)\)], "Input"], Cell[BoxData[ \(23 + 11\ \[ImaginaryI]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(3 + 2 I\)\/\(7 - I\) // N\)], "Input"], Cell[BoxData[ \(\(\(0.38`\)\(\[InvisibleSpace]\)\) + 0.34`\ \[ImaginaryI]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Exp[2.0 - 7 I]\)], "Input"], Cell[BoxData[ \(\(\(5.570626050452962`\)\(\[InvisibleSpace]\)\) - 4.854510834178772`\ \[ImaginaryI]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["2.2. Algebralised teisendused", "Subsubtitle"], Cell[TextData[{ StyleBox["Mathematica", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" v\[OTilde]imaldab ka tehteid suure arvu muutujate ja arvudega, \ sisaldab erinevaid teisendusreegleid, v\[OTilde]imaldab taandada ja murdudes \ koondada, tuua mingeid liikmeid sulgude ette jne. \[CapitalUDoubleDot]ht omap\ \[ADoubleDot]ra tuleb k\[UDoubleDot]ll enne mainida. ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["\n", CharacterEncoding->"WindowsANSI"], StyleBox["\[CapitalUDoubleDot]lalpool on \[ODoubleDot]eldud, et korrutusm\ \[ADoubleDot]rgina v\[OTilde]ib kasutada ka t\[UDoubleDot]hikut. Kuid n\ \[ADoubleDot]iteks juhul ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["2(x-3) ", FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox["pole t\[UDoubleDot]hikut vaja. Samuti", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FontFamily->"Courier New", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["2x", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["on sama, mis", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FontFamily->"Courier New", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["2*x;", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FontFamily->"Times New Roman", FontSize->10, CharacterEncoding->"WindowsANSI"], StyleBox["kuid", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FontFamily->"Courier New", FontSize->10, FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["x2", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["on uus muutuja, mida v\[OTilde]iks t\[ADoubleDot]histada ka x", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["2", FontFamily->"Times New Roman", FontVariations->{"CompatibilityType"->"Subscript"}, CharacterEncoding->"WindowsANSI"], StyleBox[". ", FontFamily->"Times New Roman", FontSize->10, CharacterEncoding->"WindowsANSI"], StyleBox["Seega - arvu korrutamisel muutujaga, kui arv asub eespool, pole \ t\[UDoubleDot]hikut v\[OTilde]i korrutusm\[ADoubleDot]rki vaja. Kuid muutuja \ korrutamisel arvuga (muutuja on enne arvu),", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox[" ", FontFamily->"Times New Roman", FontSize->10, CharacterEncoding->"WindowsANSI"], StyleBox["peab see olemas olema -", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox[" x*2", FontFamily->"Courier New", CharacterEncoding->"WindowsANSI"], StyleBox[". ", FontFamily->"Courier New", FontSize->10, CharacterEncoding->"WindowsANSI"], StyleBox["Ka", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox[" xy ", FontFamily->"Courier New", FontSize->10, CharacterEncoding->"WindowsANSI"], StyleBox["t\[ADoubleDot]hendab lihtsalt \[UDoubleDot]ht uut muutujat, \ mitte", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox[" x ", FontFamily->"Courier New", FontSize->10, CharacterEncoding->"WindowsANSI"], StyleBox["ja", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox[" y ", FontFamily->"Courier New", FontSize->10, CharacterEncoding->"WindowsANSI"], StyleBox["korrutist.\n", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"] }], "Text"], Cell[TextData[{ "Expand[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\t\tkorrutab lahti k\[OTilde]ik korrutised ja astmed \n\t\t\t\t\t\t\ kirjutades saadud tulemuse summana\nExpandAll[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\t\trakendab Expand'i k\[OTilde]ikjal (v\[OTilde]tab kauem aega)\n\ PowerExpand[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\tkirjutab lahti ka astmete korrutised ja jagatised \ (n\[ADoubleDot]iteks ruutjuur ruudust)\nFactor[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\t\tkirjutab ", StyleBox["avaldise", FontSlant->"Italic"], " v\[ADoubleDot]hima arvu tegurite korrutisena\nSimplify[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\t\t\[UDoubleDot]ritab leida ", StyleBox["avaldise", FontSlant->"Italic"], " lihtsaimat kuju kasutades \n\t\t\t\t\t\terinevaid algebralisi teisendusi\n\ FullSimplify[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\t\t\[UDoubleDot]ritab leida ", StyleBox["avaldise", FontSlant->"Italic"], " lihtsaimat kuju kasutades \n\t\t\t\t\t\terinevaid algebralisi teisendusi, \ v\[OTilde]imaldab rohkem aega kulutada, \n\t\t\t\t\t\tresultaat v\[OTilde]ib \ v\[ADoubleDot]ga pikkade avaldiste korral olla l\[UDoubleDot]hem\nTogether[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\t\tviib murdude summa k\[OTilde]ik liikmed \[UDoubleDot]hisele \ nimetajale\nApart[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\t\tkirjutab murru lahti, tulemuseks on murrud, millede nimetajad\n\t\ \t\t\t\t\ton v\[OTilde]imalikult lihtsamal kujul\nCancel[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\t\ttaandab murru nimetaja ja lugeja \[UDoubleDot]hised tegurid\n\ Collect[", StyleBox["avaldis,x", FontSlant->"Italic"], "]\t\t\t\tr\[UDoubleDot]hmitab ", StyleBox["avaldise", FontSlant->"Italic"], " liidetavad ", StyleBox["x", FontSlant->"Italic"], " astmete j\[ADoubleDot]rgi\nFactorTerms[", StyleBox["avaldis,x", FontSlant->"Italic"], "]\t\t\ttoob sulgude ette liikmed, mis ei s\[OTilde]ltu ", StyleBox["x", FontSlant->"Italic"], "-st" }], "Text", Background->GrayLevel[0.900008]], Cell[BoxData[ \(\($Line = 0;\)\)], "Input"], Cell["N\[ADoubleDot]ited:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(f = \(\(\((x - 1)\)\^2\) \((2 + x)\)\)\/\(\((1 + x)\) \((x - \ 3)\)\^2\)\)], "Input"], Cell[BoxData[ \(\(\((\(-1\) + x)\)\^2\ \((2 + x)\)\)\/\(\((\(-3\) + x)\)\^2\ \((1 + \ x)\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[f]\)], "Input"], Cell[BoxData[ \(2\/\(\((\(-3\) + x)\)\^2\ \((1 + x)\)\) - \(3\ x\)\/\(\((\(-3\) + \ x)\)\^2\ \((1 + x)\)\) + x\^3\/\(\((\(-3\) + x)\)\^2\ \((1 + x)\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s = ExpandAll[f]\)], "Input"], Cell[BoxData[ \(2\/\(9 + 3\ x - 5\ x\^2 + x\^3\) - \(3\ x\)\/\(9 + 3\ x - 5\ x\^2 + \ x\^3\) + x\^3\/\(9 + 3\ x - 5\ x\^2 + x\^3\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Together[s]\)], "Input"], Cell[BoxData[ \(\(2 - 3\ x + x\^3\)\/\(9 + 3\ x - 5\ x\^2 + x\^3\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Apart[%]\)], "Input"], Cell[BoxData[ \(1 + 5\/\((\(-3\) + x)\)\^2 + 19\/\(4\ \((\(-3\) + x)\)\) + 1\/\(4\ \((1 + x)\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Factor[%]\)], "Input"], Cell[BoxData[ \(\(\((\(-1\) + x)\)\^2\ \((2 + x)\)\)\/\(\((\(-3\) + x)\)\^2\ \((1 + \ x)\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[%]\)], "Input"], Cell[BoxData[ \(\(\((\(-1\) + x)\)\^2\ \((2 + x)\)\)\/\(\((\(-3\) + x)\)\^2\ \((1 + \ x)\)\)\)], "Output"] }, Open ]], Cell[TextData[StyleBox["St, Factor k\[ADoubleDot]suga leitud avaldis ongi \ juba lihtsaimal kujul", "Text"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(v = \(\((3 + 2 x)\)\^2\) \((x + 2 y)\)\^2\)], "Input"], Cell[BoxData[ \(\((3 + 2\ x)\)\^2\ \((x + 2\ y)\)\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[v]\)], "Input"], Cell[BoxData[ \(9\ x\^2 + 12\ x\^3 + 4\ x\^4 + 36\ x\ y + 48\ x\^2\ y + 16\ x\^3\ y + 36\ y\^2 + 48\ x\ y\^2 + 16\ x\^2\ y\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Collect[v, x]\)], "Input"], Cell[BoxData[ \(4\ x\^4 + 36\ y\^2 + x\^3\ \((12 + 16\ y)\) + x\^2\ \((9 + 48\ y + 16\ y\^2)\) + x\ \((36\ y + 48\ y\^2)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(FactorTerms[v, y]\)], "Input"], Cell[BoxData[ \(\((9 + 12\ x + 4\ x\^2)\)\ \((x\^2 + 4\ x\ y + 4\ y\^2)\)\)], "Output"] }, Open ]], Cell[TextData[{ "TrigExpand[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\tkorrutab trigonomeetrilised avaldised summana lahti\nTrigFactor[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\tkirjutab trigonomeetrilise avaldise lahti tegurite korrutisena\n\ TrigReduce[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\tteisendab, koondab ja taandab avaldise kasutades nurkade \n\t\t\t\t\ \ttrigonomeetriliste funktsioonide vahelisi seoseid\nTrigToExp[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\tteisendab trigonomeetrilised funktsioonid eksponentideks\n\ ExpToTrig[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\tteisendab eksponendid trigonomeetrilisteks avaldisteks\n\ FunctionExpand[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\tkorrutab (eraldab v\[ADoubleDot]lja) spetsiaalfunktsioonid\n\ ComplexExpand[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\tkorrutab kompleksarvudega avaldised lahti" }], "Text", Background->GrayLevel[0.900008]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ 2.3. Muutujatele, avaldistele v\[ADoubleDot]\[ADoubleDot]rtuse omistamine, tehted eelnevate arvutustulemustega\ \>", "Subsubtitle"], Cell[TextData[{ "x = v\[ADoubleDot]\[ADoubleDot]rtus\t\t\t", StyleBox["\t\tx-le antakse mingi v\[ADoubleDot]\[ADoubleDot]rtus, see v\ \[OTilde]ib olla arvuline v\[ADoubleDot]\[ADoubleDot]rtus, \n\t\t\t\t\t\ algebraline avaldis v\[OTilde]i mingi pikem funktsioon, arvutus, \ v\[OTilde]rrand jne\n", FontSlant->"Plain"], "x = . v\[OTilde]i ", StyleBox["Clear[x]\t\t\tx-i v\[ADoubleDot]\[ADoubleDot]rtus \ t\[UDoubleDot]histatakse\n", FontSlant->"Plain"], "x := v\[ADoubleDot]\[ADoubleDot]rtus\t", StyleBox["\t\t\t\tx-le antakse mingi v\[ADoubleDot]\[ADoubleDot]rtus, \ sarnane esimese omistamisega\n", FontSlant->"Plain"], "avaldis /. x-> v\[ADoubleDot]\[ADoubleDot]rtus", StyleBox["\t\tannab avaldises ", FontSlant->"Plain"], "x", StyleBox["-le v\[ADoubleDot]\[ADoubleDot]rtuse\n", FontSlant->"Plain"], "avaldis /. ", Cell[BoxData[ \(TraditionalForm\`{x -> x\_v\[ADoubleDot]\[ADoubleDot]rt\)]], ", ", Cell[BoxData[ \(TraditionalForm\`y -> y\_v\[ADoubleDot]\[ADoubleDot]rt\)]], StyleBox["}\tavaldises antakse v\[ADoubleDot]\[ADoubleDot]rtused nii x-le \ kui ka y-le", FontSlant->"Plain"], StyleBox["\t\t\t\t\t", FontSlant->"Plain"] }], "Text", FontSlant->"Italic", Background->GrayLevel[0.900008]], Cell["Defineerime avaldise s j\[ADoubleDot]rgmiselt:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(s = x\^2 + 4.5 x - y\)], "Input"], Cell[BoxData[ \(4.5`\ x + x\^2 - y\)], "Output"] }, Open ]], Cell["\<\ J\[ADoubleDot]rgnevalt n\[ADoubleDot]itame mitmeid erinevaid \ v\[OTilde]imalusi avaldises s sisalduvatele muutujatele v\[ADoubleDot]\ \[ADoubleDot]rtuste omistamiseks.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(s /. \ x \[Rule] 4\)], "Input"], Cell[BoxData[ \(\(\(34.`\)\(\[InvisibleSpace]\)\) - y\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s /. {x \[Rule] 2.3, \ y -> 3}\)], "Input"], Cell[BoxData[ \(12.639999999999999`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s /. {x \[Rule] y, \ y \[Rule] t}\)], "Input"], Cell[BoxData[ \(\(-t\) + 4.5`\ y + y\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s /. {x \[Rule] x\^2, y \[Rule] y\^3}\)], "Input"], Cell[BoxData[ \(4.5`\ x\^2 + x\^4 - y\^3\)], "Output"] }, Open ]], Cell[TextData[{ "Viimane on nn rekursiivne v\[ADoubleDot]\[ADoubleDot]rtustamine ", StyleBox["Mathematica's", FontSlant->"Italic"], " ja peaks v\[ADoubleDot]ga tuttav olema neile, kes on programmeerimisega \ kokku puutunud. /. abil v\[ADoubleDot]\[ADoubleDot]rtuste omistamine ja \ arvutus toimib j\[ADoubleDot]rgmiselt: ", StyleBox["esmalt teostatakse arvutus avaldises olevate muutujatega, seej\ \[ADoubleDot]rel omistatakse muutujatele uus v\[ADoubleDot]\[ADoubleDot]rtus \ ning antakse l\[OTilde]plik arvutustulemus. Seda demonstreerib ka j\ \[ADoubleDot]rgmine n\[ADoubleDot]ide.", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(s\^2 + 3\ /. \ x \[Rule] 2\)], "Input"], Cell[BoxData[ \(3 + \((\(\(13.`\)\(\[InvisibleSpace]\)\) - y)\)\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[%]\)], "Input"], Cell[BoxData[ \(\(\(172.`\)\(\[InvisibleSpace]\)\) - 26.`\ y + y\^2\)], "Output"] }, Open ]], Cell[TextData[{ "Viimases arvutuses rakendati protseduuri Expand eelmisele (eelviimasele).\n\ Teine ", StyleBox["v\[OTilde]imalus avaldises v\[OTilde]i arvutuses olevatele \ muutujatele v\[ADoubleDot]\[ADoubleDot]rtuse omistamine on toodud j\ \[ADoubleDot]rgnevas n\[ADoubleDot]ites.", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(a = 3. ;\)\), "\[IndentingNewLine]", \(\(b = 2.5;\)\), "\[IndentingNewLine]", \(\(c = x - y;\)\), "\[IndentingNewLine]", \(a\^2 + b\^3 - c\/2. \)}], "Input"], Cell[BoxData[ \(\(\(24.625`\)\(\[InvisibleSpace]\)\) - 0.5`\ \((x - y)\)\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["Viimases n\[ADoubleDot]ites oleme enne arvutust omistanud v\ \[ADoubleDot]\[ADoubleDot]rtused muutujatele a, b, c. Semikoolon rea l\ \[OTilde]pus eristab erinevaid sisestusi; semikooloniga l\[OTilde]ppeva rea \ arvutuse tulemust ei kuvata ekraanile (ka lihtne \ v\[ADoubleDot]\[ADoubleDot]rtuse omistamine a=3. on siin m\[OTilde]istetud \ arvutusena), samas on iga sellise arvutuse tulemus ikkagi hiljem kasutatav. \ Semikoolonit on vahel m\[OTilde]tekas kasutada ka siis, kui on tegemist \ pikkade arvutustega ning mingi vahetulemus on v\[ADoubleDot]ga pikk, sel \ juhul v\[OTilde]ib kasutada pidevalt viimast arvutust (vahepeal lihtsustades \ ning taandades/koondades erinevaid liikmeid) iga kord semikooloniga sisestuse \ l\[OTilde]pus ning alles viimase sisestus on ilma semikoolonita. Semikooloni \ kasutamine on m\[OTilde]istlik ka arvutim\[ADoubleDot]lu s\[ADoubleDot]\ \[ADoubleDot]stmise seisukohalt. ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["\n", CharacterEncoding->"WindowsANSI"], StyleBox["Veel \[UDoubleDot]ks omap\[ADoubleDot]ra on toodud \ j\[ADoubleDot]rgmises n\[ADoubleDot]ites:", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(23 x\ + \ 14 y - 23 x*y\), "\[IndentingNewLine]", \(2 y\^2 - 11 x\)}], "Input"], Cell[BoxData[ \(23\ x + 14\ y - 23\ x\ y\)], "Output"], Cell[BoxData[ \(\(-11\)\ x + 2\ y\^2\)], "Output"] }, Open ]], Cell[TextData[StyleBox["Esimeses sisestuses on teisele reale mindud \ \[UDoubleDot]le reavahetuse klahvi abil. Nagu n\[ADoubleDot]ha on arvuti \ eeldanud, et tegemist on kahe erineva sisestusega, mitte \[UDoubleDot]he ja \ sama avaldisega. Juhul, kui avaldis ei mahu \[UDoubleDot]hte ritta \ \[ADoubleDot]ra ja peaks ilmtingimata just korrutusm\[ADoubleDot]rgi koha \ pealt avaldist t\[UDoubleDot]heldama, peaks esimese rea l\[OTilde]ppu \ kirjutama korrutusm\[ADoubleDot]rgi:", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(23 x + 14 y - 23 x*y*\[IndentingNewLine]2 y\^2 - 11 x\)], "Input"], Cell[BoxData[ \(12\ x + 14\ y - 46\ x\ y\^3\)], "Output"] }, Open ]], Cell["\<\ Mathematica vanemad versioonid eeldavad vaikimisi siiski, et tegemist oli \ korrutamisega. Nagu mainitud, on antud programmis mitmeid v\[OTilde]imalusi eelmistele v\ \[ADoubleDot]ljunditele.\ \>", "Text"], Cell["\<\ %\t\t\t\t\t\teelmise arvutuse v\[ADoubleDot]ljund (resultaat) %%\t\t\t\t\t\t\[UDoubleDot]le-eelmise arvutuse v\[ADoubleDot]ljund %n\t\t\t\t\t\tn-nda arvutuse v\[ADoubleDot]ljund Out[n]\t\t\t\t\t\tn-nda arvutuse v\[ADoubleDot]ljund\ \>", "Text", Background->GrayLevel[0.900008]], Cell["\<\ Veel m\[OTilde]ned n\[ADoubleDot]ited. Pidage silmas, et kui teie sisestate \ avaldised t\[ADoubleDot]pselt nii nagu alltoodud n\[ADoubleDot]ites, v\ \[OTilde]ite saada t\[ADoubleDot]iesti erineva tulemuse, kui teie arvutuste \ numeratsioon erineb antud n\[ADoubleDot]idete omast:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(%14\^2\)], "Input"], Cell[BoxData[ \(159.76959999999997`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[%14 - y\^2]\)], "Input"], Cell[BoxData[ \(\(\(12.639999999999999`\)\(\[InvisibleSpace]\)\) - y\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Out[16] - Out[17]\)], "Input"], Cell[BoxData[ \(\(-3\) + 4.5`\ x\^2 + x\^4 - \((\(\(13.`\)\(\[InvisibleSpace]\)\) - y)\)\^2 - y\^3\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[%]\)], "Input"], Cell[BoxData[ \(\(-172.`\) + 4.5`\ x\^2 + x\^4 + 26.`\ y - y\^2 - y\^3\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[%]\)], "Input"], Cell[BoxData[ \(4.5`\ x\^2 + x\^4 - 1.`\ \((\(\(7.510743773335052`\)\(\[InvisibleSpace]\)\) + y)\)\ \((\(\(22.9005282553562`\)\(\[InvisibleSpace]\)\) - 6.510743773335052`\ y + y\^2)\)\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["2.4.", FontFamily->"Verdana", FontSize->11.5], StyleBox["Avaldiste l\[UDoubleDot]hendamine, avaldise\nosade eraldamine, \ avaldise lihtsustamine eeldustel", FontFamily->"Verdana", FontSize->11.5, CharacterEncoding->"WindowsANSI"] }], "Subsubtitle"], Cell["\<\ Esmalt vaatame m\[OTilde]ningaid lihtsustamisi lisaeeldustel. \ N\[ADoubleDot]iteks \ \>", "Text"], Cell[BoxData[{ \(\($Line = 0;\)\), "\[IndentingNewLine]", \(\(Clear[s, a, b, c];\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[\@x\^2]\)], "Input"], Cell[BoxData[ \(\@x\^2\)], "Output"] }, Open ]], Cell[TextData[{ "Selline on vastus t\[ADoubleDot]nu sellele, et ", Cell[BoxData[ \(TraditionalForm\`\@x\^2 = x\)]], " vaid siis, kui x>0. Kui eeldame, et see tingimus on t\[ADoubleDot]idetud, \ peaksime kirjutama:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[\@x\^2, x > 0]\)], "Input"], Cell[BoxData[ \(x\)], "Output"] }, Open ]], Cell[TextData[{ "St lihtsustamine toimub eeldusel, mis on avaldisest eraldatud komaga.\n\ Veel ", StyleBox["\[UDoubleDot]ks n\[ADoubleDot]ide sellisest eeldusest on juhul, \ kui eeldame, et mingi suurus kuulub kindlasse hulka. Eeldame, et ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["n\[Element]N", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[", st n on t\[ADoubleDot]isarv.", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[Sin[x + 2 \[Pi]\ n], Element[n, Integers]]\)], "Input"], Cell[BoxData[ \(Sin[x]\)], "Output"] }, Open ]], Cell[TextData[{ "Simplify[", StyleBox["avaldis, eeldus", FontSlant->"Italic"], "]\t\t\t\tlihtsustab avaldist antud eeldusel\nSimplify[", StyleBox["avaldis, ", FontSlant->"Italic"], Cell[BoxData[ \(TraditionalForm\`{eeldus\_1, \ eeldus\_2}\)]], "]\t\t\tlihtsustab avaldist antud eeldustel (mis ei tohi olla \n\t\t\t\t\t\t\ \t\[UDoubleDot]ksteisega vastuolus\nElement[", StyleBox["x, hulk", FontSlant->"Italic"], "]\t\t\t\t\tdefineerib ", StyleBox["x", FontSlant->"Italic"], " kui ", StyleBox["hulga", FontSlant->"Italic"], " liikme\n", Cell[BoxData[ \(TraditionalForm\`\(\(Element\)\([\)\({x\_1, \ x\_2, \ x\_3 ... \)\)\)]], "}, ", StyleBox["hulk", FontSlant->"Italic"], "]\t\t\tdefineerib k\[OTilde]ik ", Cell[BoxData[ \(TraditionalForm\`x\_i\)]], StyleBox["hulga", FontSlant->"Italic"], " liikmetena\nReals\t\t\t\t\t\t\treaalarvud\nIntegers\t\t\t\t\t\tt\ \[ADoubleDot]isarvud\nComplexes\t\t\t\t\t\tkompleksarvud\nPrimes\t\t\t\t\t\t\t\ algarvud" }], "Text", Background->GrayLevel[0.900008]], Cell["\<\ Hulga v\[OTilde]ib ka ise defineerida ja siis lihtsustada tingimusel, et \ mingi suurus kuulub defineeritud hulka Algebralisetest avaldistest v\[OTilde]ib k\[ADoubleDot]tte saada ka vaid \ nende osasid, vastavad k\[ADoubleDot]sud on j\[ADoubleDot]rgmised:\ \>", "Text"], Cell[TextData[{ "Coefficient[", StyleBox["avaldis", FontSlant->"Italic"], ", ", StyleBox["vorm", FontSlant->"Italic"], "]\t\t\t\tannab avaldise ", StyleBox["vorm'i ", FontSlant->"Italic"], "kordaja\nExponent[", StyleBox["avaldis, vorm", FontSlant->"Italic"], "]\t\t\t\tannab ", StyleBox["vormi", FontSlant->"Italic"], " maksimaalse astme\nPart[", StyleBox["avaldis", FontSlant->"Italic"], "] v\[OTilde]i ", StyleBox["avaldis", FontSlant->"Italic"], "[[n]]\t\t\tannab ", StyleBox["avaldise", FontSlant->"Italic"], " n-nda liikme\nNumenator[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\t\t\tannab murdavaldise lugeja\nDenominator[", StyleBox["avaldis", FontSlant->"Italic"], "]\t\t\t\t\tannab murdavaldise nimetaja" }], "Text", Background->GrayLevel[0.900008]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ 3. S\[UDoubleDot]mbolarvutus. Tuletised, integraalid. Funktsioonid.\ \>", "Subtitle"], Cell["\<\ 3.1. Tuletis, diferentsiaal, integraal, piirv\[ADoubleDot]\[ADoubleDot]rtus, summa.\ \>", "Subsubtitle"], Cell[BoxData[ \(Clear[f]; $Line = 0;\)], "Input"], Cell[TextData[{ "D[f,x] ", StyleBox["v\[OTilde]i", FontSlant->"Italic"], " ", Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_x\ f\)]], "\t\t\t\t(osa)tuletis funktsioonist f x j\[ADoubleDot]rgi: ", Cell[BoxData[ \(TraditionalForm\`df\/dx\)]], "ehk ", Cell[BoxData[ \(TraditionalForm\`\[PartialD]f\/\[PartialD]x\)]], "\nD[f,x,y,...] ", StyleBox["v\[OTilde]i ", FontSlant->"Italic"], " ", Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_\(x, y, z, ... \)f\)]], "\t\t\tmitmekordne (osa)tuletis funktsioonist v\[OTilde]i avaldisest f: ", Cell[BoxData[ \(TraditionalForm\`\[PartialD]\^3 f\/\(\[PartialD]x \[PartialD]y \ \[PartialD]z\)\)]], ".\nD[f,{x,n}]\t\t\t\t\tn-kordne tuletis avaldisest f x j\[ADoubleDot]rgi: \ ", Cell[BoxData[ \(TraditionalForm\`\(\(d\^n\) f\)\/dx\^n\)]], "\n", Cell[BoxData[ \(TraditionalForm\`Limit[f, x -> x\_0]\)]], "\t\t\t\tpiirv\[ADoubleDot]\[ADoubleDot]rtus ", Cell[BoxData[ \(TraditionalForm\`lim\_\(x \[Rule] x\_0\)\ f\)]], "\nDt[f]\t\t\t\t\t\tt\[ADoubleDot]isdiferentsiaal\nDt[f,x]\t\t\t\t\t\tt\ \[ADoubleDot]istuletisavaldisest f muutuja x j\[ADoubleDot]rgi\n", Cell[BoxData[ \(TraditionalForm\`\[Integral]f \[DifferentialD]x\)]], " ", StyleBox["v\[OTilde]i", FontSlant->"Italic"], " Integrate[f,x]\t\t\tm\[ADoubleDot]\[ADoubleDot]ramata integraal\n", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_a\%b\( f(x)\) \[DifferentialD]x\)]], " ", StyleBox["v\[OTilde]i", FontSlant->"Italic"], " Integrate[f,{x,a,b}]\t\tm\[ADoubleDot]\[ADoubleDot]ratud integraal\n", Cell[BoxData[ \(TraditionalForm\`\[Integral]\(\[Integral]\(f(x, y)\) \[DifferentialD]x \[DifferentialD]y\)\)]], " ", StyleBox["v\[OTilde]i", FontSlant->"Italic"], " Integrate[f,x,y]\tmitmekordne m\[ADoubleDot]\[ADoubleDot]ramata integraal \ muutujate x ja y j\[ADoubleDot]rgi\n", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_a\%b\(\[Integral]\_c\%d\( f(x, y)\) \[DifferentialD]x \[DifferentialD]y\)\)]], "\t", StyleBox["v\[OTilde]i", FontSlant->"Italic"], " ", "\t\t\tmitmekordne m\[ADoubleDot]\[ADoubleDot]ratud integraal\n\ Integrate[f,{x,a,b},{y,c,d}]\n", Cell[BoxData[ \(TraditionalForm\`Series[f, {x, x\_0, j\[ADoubleDot]rk}]\)]], "\t\t\tTaylori astmerida funktsioonist (avaldisest) f punkti ", Cell[BoxData[ \(TraditionalForm\`x = x\_0\)]], " juures\nNormal[", StyleBox["rida", FontSlant->"Italic"], "]\t\t\t\t\tjuhul, kui ", StyleBox["rida", FontSlant->"Italic"], " on Taylori astemrida, siis see protseduur annab\n\t\t\t\t\t\ttulemuseks \ Taylori rea ilma viimase liikmeta\n", Cell[BoxData[ \(TraditionalForm\`\[Sum]\+\(i = i\_min\)\%\(i\_max\)f\)]], " ", StyleBox["v\[OTilde]i", FontSlant->"Italic"], " ", Cell[BoxData[ \(TraditionalForm\`Sum[f, {i, i\_min, i\_max}]\)]], "\tsumma\n", Cell[BoxData[ \(TraditionalForm\`Sum[ f, {i, \ i\_min, \ i\_max}, {j, j\_min, j\_max}]\)]], "\tmitmekordne summa\n", Cell[BoxData[ \(TraditionalForm\`\[Product]\+\(i = i\_min\)\%\(i\_max\)f\)]], " ", StyleBox["ehk", FontSlant->"Italic"], " ", Cell[BoxData[ \(TraditionalForm\`Product[f, {i, i\_min, i\_max}]\)]], "\tkorrutis" }], "Text", Background->GrayLevel[0.900008]], Cell["Tuletised, diferentsiaalid", "Text", FontWeight->"Bold"], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_x\ x\^3\)], "Input"], Cell[BoxData[ \(3\ x\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(D[x\^n, x]\)], "Input"], Cell[BoxData[ \(n\ x\^\(\(-1\) + n\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(D[x\^n, n]\)], "Input"], Cell[BoxData[ \(x\^n\ Log[x]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_x\ x\^2 Log[x + a]\)], "Input"], Cell[BoxData[ \(2\ x\ Log[a + x]\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["Esimene avaldis on tavaline tuletis. Teine n\[ADoubleDot]itab, et \ kui tuletist v\[OTilde]etakse ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["x", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" j\[ADoubleDot]rgi, on ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["n", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" lihtsalt konstant (tegemist on osatuletisega x \ j\[ADoubleDot]rgi).. Kolmandas arvutuses oleme leidnud osatuletise muutuja n \ j\[ADoubleDot]rgi, Ka viimases arvutuses leitakse osatuletis x \ j\[ADoubleDot]rgi v\[OTilde]ttes a konstandiks.", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_\(x, y\)\((3\ \(x\^2\) y\^5)\)\)], "Input"], Cell[BoxData[ \(30\ x\ y\^4\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_\(x, y\)\ 3 \( x\^2\) y\^5\)], "Input"], Cell[BoxData[ \(0\)], "Output"] }, Open ]], Cell["\<\ Eelviimane avaldis n\[ADoubleDot]itab, kuidas k\[ADoubleDot]ib mitmekordse \ osatuletise leidmine. Sellise kirjutusviisi korral peab avaldis paiknema \ kindlasti \[UDoubleDot]marsulgudes. Vastasel juhul leitakse tuletis vaid \ avaldise esimesest tegurist, mida n\[ADoubleDot]itab viimane \ n\[ADoubleDot]ide, kus tuletis on leitud arvust 3 (mis on loomulikult 0). \ Samast avaldisest v\[OTilde]ime leida ka kahekordse tuletise muutuja x j\ \[ADoubleDot]rgi:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_\(x, x\)\((3 \( x\^2\) y\^5)\)\)], "Input"], Cell[BoxData[ \(6\ y\^5\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(D[3 \( x\^2\) y\^5, {x, 2}]\)], "Input"], Cell[BoxData[ \(6\ y\^5\)], "Output"] }, Open ]], Cell["\<\ Tuletise v\[OTilde]ime leida ka tundmatul kujul antud funktsioonist, kus on n\ \[ADoubleDot]idatud, et see funktsioon s\[OTilde]ltub muutujast x:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_x\ \((3\ f[x])\)\)], "Input"], Cell[BoxData[ RowBox[{"3", " ", RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "x", "]"}]}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(D[Sin[x]\ f[3 x], x]\)], "Input"], Cell[BoxData[ RowBox[{\(Cos[x]\ f[3\ x]\), "+", RowBox[{"3", " ", \(Sin[x]\), " ", RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", \(3\ x\), "]"}]}]}]], "Output"] }, Open ]], Cell["\<\ Niinimetatud t\[ADoubleDot]istuletise Dt[f,x] korral eeldatakse, et \ k\[OTilde]ik muutujad (st mitte-arvud) s\[OTilde]ltuvad muutujast x.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Dt[n\ Sin[x], x]\)], "Input"], Cell[BoxData[ \(n\ Cos[x] + Dt[n, x]\ Sin[x]\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["Seega, viimases avaldises t\[ADoubleDot]hendab Dt[", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["n,x", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["] tuletist ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["n", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox["-st muutuja ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"], StyleBox["x", FontFamily->"Times New Roman", FontSlant->"Italic", CharacterEncoding->"WindowsANSI"], StyleBox[" j\[ADoubleDot]rgi. ", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"] }], "Text"], Cell["Integreerimine.", "Text", FontWeight->"Bold"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\(\(3 y\)\/\(x\^2 + y\^2\)\) \[DifferentialD]x\)], "Input"], Cell[BoxData[ \(3\ ArcTan[x\/y]\)], "Output"] }, Open ]], Cell["\<\ Antud integraali leidmisel arvestati loomulikult, et y ei s\[OTilde]ltu x-st, \ y on konstant.Koolimatemaatikast on meil teada, et \ m\[ADoubleDot]\[ADoubleDot]ramata integraali leidmisel liidetakse alati otsa \ konstant. Antud programm j\[ADoubleDot]tab selle kasutajate hooleks.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\_0\%5 2 \( x\^3\) \[DifferentialD]x\)], "Input"], Cell[BoxData[ \(625\/2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Integrate[\(2 y\)\/\(x\^2 + y\^2\), x, y]\)], "Input"], Cell[BoxData[ \(\(-2\)\ x + 2\ y\ ArcTan[x\/y] + x\ Log[x\^2 + y\^2]\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["J\[ADoubleDot]rgmisena vaatame kahekordset m\[ADoubleDot]\ \[ADoubleDot]ratud integraali, kus integreerimispiirkond on \ n\[ADoubleDot]idatud allpool toodud joonisel. See t\[ADoubleDot]hendab, et v\ \[OTilde]ime integreerida funktsiooni ", FontFamily->"Times New Roman", FontColor->GrayLevel[0], CharacterEncoding->"WindowsANSI"], StyleBox["f(x,y", FontFamily->"Times New Roman", FontSlant->"Italic", FontColor->GrayLevel[0], CharacterEncoding->"WindowsANSI"], StyleBox[") esmalt ", FontFamily->"Times New Roman", FontColor->GrayLevel[0], CharacterEncoding->"WindowsANSI"], StyleBox["y", FontFamily->"Times New Roman", FontSlant->"Italic", FontColor->GrayLevel[0], CharacterEncoding->"WindowsANSI"], StyleBox[" j\[ADoubleDot]rgi 0-st kuni ", FontFamily->"Times New Roman", FontColor->GrayLevel[0], CharacterEncoding->"WindowsANSI"], Cell[BoxData[ \(TraditionalForm\`\(2 x\)\/3\)]], StyleBox["-ni ja siis ", FontFamily->"Times New Roman", FontColor->GrayLevel[0], CharacterEncoding->"WindowsANSI"], StyleBox["x", FontFamily->"Times New Roman", FontSlant->"Italic", FontColor->GrayLevel[0], CharacterEncoding->"WindowsANSI"], StyleBox[" j\[ADoubleDot]rgi 0-st 3-ni:", FontFamily->"Times New Roman", FontColor->GrayLevel[0], CharacterEncoding->"WindowsANSI"] }], "Text"], Cell[GraphicsData["Metafile", "\<\ CF5dJ6E]HGAYHf4PEfU^I6mgLb15CDHPAVmbKF5d0@0003SP0@0006@000000000000005@1003A0000 0000000000188`00^aD00215CDH00040h3P004/2000400000000000000000000E@400=80001J0000 =`00000000000000000000X0000@00000000000000090000400005D1003B0000500000`0000=0000 4P0000`0000100008@0000P0000Q0000200001@0000<00003@0002L0000H00000@000000003oool0 000002D0000<00000@0002H0000L00000P0000000000000000000000000U000030000080000[0000 6000000000000000E@400=80000D0000300000d0000R000030000?oooolD0000300000d0000Q0000 200002D0000<00001`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U0000 3000008000040000;0000840002a0000P@000;<000020000P@000;<000210000/@0002D0000<0000 1`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U000030000080000?0000 50000840002a000000000580001<0@000`000?Coool0000000000000002@0@0000000000009306l0 M@1b06T0I@1b0200CP1U07L000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000005P0000`0000H0000 600000`0000000009@0000`000030000E00005@0001n0000``0008D0003B00000@00000000000000 OP000<<000010000C0000080000000000000000000000000D0000340000600009@0000`000070020 :00000`0000200009P0001`0000200000000000000000000000002D0000<00000P0000@0000/0000 dP000;40003B0000/`000080003B0000/`000=80002a00009@0000`000070020:00000`000020000 9P0001`0000200000000000000000000000002D0000<00000P0000l0000D0000dP000;4000000000 9@0000`0000:0020:00000`000030000DP0004`100030000m?ooo`00000000000000090100000000 00000T<0K`1e0780J@1U0780801>06D0M`0000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000F0000 300001P0000H000030000000000U0000300000<0001D0000E00000000``000040001<00000P0000000000000000000000001@000080002b0000 hP000;<000020000hP000;<0003R0000/P0002D0000<00001`00P2P0000<00000P0002H0000L0000 0P0000000000000000000000000U000030000080000?000050000>80002b0000000002D0000<0000 1`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U00003000008000040000 ;0000?80002b0000lP000;<000020000lP000;<0003b0000/P0002D0000<00001`00P2P0000<0000 0P0002H0000L00000P0000000000000000000000000U000030000080000?000050000?80002b0000 000002D0000<00001`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U0000 3000008000040000;0000081002b00000P400;<0000200000P400;<000020@00/P0002D0000<0000 1`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U000030000080000?0000 50000081002b0000000002D0000<00001`00P2P0000<00000P0002H0000L00000P00000000000000 00000000000U00003000008000040000;00001<1002b00004`400;<0000200004`400;<0000C0@00 /P0002D0000<00001`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U0000 30000080000?0000500001<1002b0000000002D0000<00001`00P2P0000<00000P0002H0000L0000 0P0000000000000000000000000U00003000008000040000;0000200002b000080000;<000020000 80000;<0000P0000/P0002D0000<00001`00P2P0000<00000P0002H0000L00000P00000000000000 00000000000U000030000080000?000050000200002b0000000002D0000<00001`00P2P0000<0000 0P0002H0000L00000P0000000000000000000000000U00003000008000040000;00000l0002b0000 3`000;<0000200003`000;<0000?0000/P0002D0000<00001`00P2P0000<00000P0002H0000L0000 0P0000000000000000000000000U000030000080000?0000500000l0002b0000000002D0000<0000 1`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U00003000008000040000 ;00003<1002b0000<`400;<000020000<`400;<0000c0@00/P0002D0000<00001`00P2P0000<0000 0P0002H0000L00000P0000000000000000000000000U000030000080000?0000500003<1002b0000 000002D0000<00001`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U0000 3000008000040000;00004<1002b0000@`400;<000020000@`400;<000130@00/P0002D0000<0000 1`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U000030000080000?0000 500004<1002b0000000002D0000<00001`00P2P0000<00000P0002H0000L00000P00000000000000 00000000000U00003000008000040000;0000000002c0000D`400;<00002000000000;<0001C0@00 /`0002D0000<00001`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U0000 30000080000?0000500005<1002c0000000002D0000<00001`00P2P0000<00000P0002H0000L0000 0P0000000000000000000000000U00003000008000040000;0000340002>0000<`0008h000020000 <@0008h0000c0000SP0002D0000<00001`00P2P0000<00000P0002H0000L00000P00000000000000 00000000000U000030000080000?0000500003<0002>0000000002D0000<00002P00P2P0000<0000 0`000580001<0@000`000?Coool0000000000000002@0@0000000000009306l0M@1b06T0I@1b0200 CP1U07L0000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000005P0000`0000H0000600000`000000000 9@0000`000030000E0000600000G0000TP0002T0002Q00000@000000000000005`00098000030000 C0000080000000000000000000000000E0000300;P0e00001P0000H0000600009@0000`000070020 :00000`0000200009P0001`0000200000000000000000000000002D0000<00000P0000@0000/0000 <@0006P0000c0000J0000080000a0000J00003<0001X00009@0000`000070020:00000`000020000 9P0001`0000200000000000000000000000002D0000<00000P0000l0000D0000<`0006P000000000 9@0000`0000:0020:00000`000030000DP0004`100030000m?ooo`00000000000000090100000000 00000T<0K`1e0780J@1U0780801>06D0M`0000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000F0000 300001P0000H000030000000000U0000300000<0001D0000E00002D0001/0000;00007/000010000 00000000000U0000K0000040001<00000P0000000000000000000000001@0000<@0000H0000U0000 300000L0080X000030000080000V0000700000800000000000000000000000009@0000`000020000 100002`0000a0000@P0003<0001200000P00034000120000<`000480000U0000300000L0080X0000 30000080000V0000700000800000000000000000000000009@0000`0000200003`0001@0000c0000 @P000000000U0000300000X0080X0000300000<0001B0000C04000<0003doooo0000000000000000 T040000000000002@`1_07D0LP1Y06D0LP0P04h0I@1g000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 000001H0000<0000600001P0000<0000000002D0000<00000`0005@0001P00005`0004H0000Y0000 E@00004000000000000001L0001600000`0004`0000200000000000000000000000005@0000a02h0 =@0000H0000600001P0002D0000<00001`00P2P0000<00000P0002H0000L00000P00000000000000 00000000000U00003000008000040000;0000340000N0000<`0001h000020000<@0001h0000c0000 7P0002D0000<00001`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U0000 30000080000?0000500003<0000N0000000002D0000<00002P00P2P0000<00000`000580001<0@00 0`000?Coool0000000000000002@0@0000000000009306l0M@1b06T0I@1b0200CP1U07L000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000005P0000`0000H0000600000`0000000009@0000`000030000 E00005@0000U00008@0002`0000`00000@000000000000009@00024000010000C000008000000000 0000000000000000D0000380000600009@0000`000070020:00000`0000200009P0001`000020000 0000000000000000000002D0000<00000P0000@0000/0000<@000:`0000b0000[0000080000a0000 [0000380002/00009@0000`000070020:00000`0000200009P0001`0000200000000000000000000 000002D0000<00000P0000l0000D0000`000080000a0000>`000380000k00009@0000`000070020:00000`000020000 9P0001`0000200000000000000000000000002D0000<00000P0000l0000D000000009@0000`000070020:00000`0000200009P0001`0000200000000000000000000 000002D0000<00000P0000l0000D00000000170000k@0003l0003j0000 =`0000L1000^00005@4002H0000S0@0070000301000E0000?`4000`0001;0@001@0002D0000<0000 1`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U000030000080000?0000 500004/10005000000000280000<0000oooooa@0000<00003@000280000<0000oooooa@0000<0000 3@0002D0000<00001`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U0000 3000008000040000;0000281000O00008P400;<0000200008P400;<0000R0@007`00024000080000 9@0000`0000:0020:00000`000030000DP0004`100030000kOooo`00000000000000090100000000 00004U@0J@1]06D0L`0P04h0I@1g0200DP1_06d0H@1^000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000F0000 300001P0000H000030000000000U0000300000<0001D0000E00004<100350000C0400=X000010000 0000000000130@00a@000040001<00000P0000000000000000000000001@0000N00000T0000R0000 30000?oooolD0000300000d0000Q0000200002D0000<00002P00P2P0000<00000`000580001<0@00 0`000>goool0000000000000002@0@0000000000019D06T0K@1U07<0801>06D0M`0P0580K`1]0640 KP000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000005P0000`0000H0000600000`0000000009@0000`000030000 E00005@0000N00005@0002L0000Z00000@000000000000007P0001D000010000C000008000000000 0000000000000000D00007T0000900008P0000`0003ooooo500000`0000=00009@0000`000010020 :00000`0000100009`0001P00001000000000>KViP0000009@0000`0000100009@0000`000070020 :00000`0000200009P0001`0000200001@00000000000000oooo02D0000<00000P0000<0000l0000 <00001h0000R0@00/`0000@0000`0000/`000281000N00008P400;<0000`0000/`0002D0000<0000 1`00P2P0000<00000P0002H0000L00000P0000000000000000000000000U00003000008000040000 ?0000300000N00008P400;<000040000<0000;<0000R0@007P000281002c0000<0000;<0000>0000 50000000000F00005000 \>"], "Graphics", ImageSize->{340, 209}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\_0\%3\(\[Integral]\_0\%\(\(2 x\)\/3\)\((x\^2 + y\^2)\) \[DifferentialD]y \[DifferentialD]x\)\)], "Input"], Cell[BoxData[ \(31\/2\)], "Output"] }, Open ]], Cell[TextData[StyleBox["Sama integraal teiste t\[ADoubleDot]histustega:", \ "Text"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Integrate[x\^2 + y\^2, {x, 0, 3}, {y, 0, \(2 x\)\/3}]\)], "Input"], Cell[BoxData[ \(31\/2\)], "Output"] }, Open ]], Cell["\<\ Viimasest arvutusest on n\[ADoubleDot]ha, et sellisel juhul integreeritakse \ esimesena viimasena antud muutuja j\[ADoubleDot]rgi erinevalt tavap\ \[ADoubleDot]rasest esitusviisist, kus esmalt leitakse sisemine integraal.\ \>", "Text"], Cell["Piirv\[ADoubleDot]\[ADoubleDot]rtused. Taylori rida.", "Text", FontWeight->"Bold"], Cell[TextData[{ "Taylori rida on astmerida kujul:\n\n", Cell[BoxData[{ \(TraditionalForm\`f( x) = \(\(f(x\_0) + f' \((x)\)\)\( | \_\(x = x\_0\)\)\(\ \)\(\((x - x\_0)\)\ + \(1\/2\) f'' \((x)\)\)\( | \_\(x = x\_0\)\)\(\ \)\(\(\(\((x - x\_0)\)\^2\)\(+\)\)\ ... \)\(\ \)\)\), "\[IndentingNewLine]", \(TraditionalForm\`\(+\ \(1\/\(n!\)\)\) \(\(f\^\((n)\)\)( x)\)\( | \_\(x = x\_0\)\)\ \(\(\((x - x\_0)\)\^n\)\(+\)\)\ ... \)}]], "\nJ\[ADoubleDot]rgmises n\[ADoubleDot]ites arendame Taylori ritta \ funktsiooni ", Cell[BoxData[ \(TraditionalForm\`f(x) = \(e\^x\)(1 + x)\)]], " punkti ", Cell[BoxData[ \(TraditionalForm\`x\_0 = 0\)]], " juures." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Series[\(\[ExponentialE]\^x\) \((1 + x)\), {x, 0, 4}]\)], "Input"], Cell[BoxData[ InterpretationBox[ RowBox[{ "1", "+", \(2\ x\), "+", \(\(3\ x\^2\)\/2\), "+", \(\(2\ x\^3\)\/3\), "+", \(\(5\ x\^4\)\/24\), "+", InterpretationBox[\(O[x]\^5\), SeriesData[ x, 0, {}, 0, 5, 1]]}], SeriesData[ x, 0, {1, 2, Rational[ 3, 2], Rational[ 2, 3], Rational[ 5, 24]}, 0, 5, 1]]], "Output"] }, Open ]], Cell[TextData[{ "Viimane liige - ", Cell[BoxData[ \(TraditionalForm\`O[x]\^5\)]], " v\[OTilde]tab kokku k\[OTilde]ik liikmed, milles x aste on 5 v\[OTilde]i \ sellest suurem. Et sellest vabaneda, tuleks kasutada k\[ADoubleDot]sku \ Normal:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Normal[%]\)], "Input"], Cell[BoxData[ \(1 + 2\ x + \(3\ x\^2\)\/2 + \(2\ x\^3\)\/3 + \(5\ x\^4\)\/24\)], "Output"] }, Open ]], Cell[TextData[{ "J\[ADoubleDot]rgmised paar n\[ADoubleDot]idet on piirv\[ADoubleDot]\ \[ADoubleDot]rtuste kohta. Esmalt defineerime avaldise, siis leiame piirv\ \[ADoubleDot]\[ADoubleDot]rtuse ning vaatama ka seda, kuidas ", StyleBox["Mathematica", FontSlant->"Italic"], " otsese arvutusega \[UDoubleDot]ritab avaldise \ v\[ADoubleDot]\[ADoubleDot]rtust leida." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(s = Sin[x]\/x\)], "Input"], Cell[BoxData[ \(Sin[x]\/x\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Limit[s, x \[Rule] 0]\)], "Input"], Cell[BoxData[ \(1\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s /. x \[Rule] 0\)], "Input"], Cell[BoxData[ \(Power::"infy" \(\(:\)\(\ \)\) "Infinite expression \!\(1\/0\) encountered."\)], "Message"], Cell[BoxData[ RowBox[{\(\[Infinity]::"indet"\), \(\(:\)\(\ \)\), "\<\"Indeterminate \ expression \\!\\(0\\\\ \\*InterpretationBox[\\\"ComplexInfinity\\\", \ DirectedInfinity[]]\\) encountered.\"\>"}]], "Message"], Cell[BoxData[ \(Indeterminate\)], "Output"] }, Open ]], Cell["\<\ Seega, avaldisel leidus l\[OTilde]plik piirv\[ADoubleDot]\[ADoubleDot]rtus - \ 1, kuid otsesel arvutusel oleks tulnud jagada nulliga ning tulemus j\ \[ADoubleDot]\[ADoubleDot]nud leidmata.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(t = \(\((9 - x\^2)\) 2 x\^3\)\/\((3 x - 9)\)\)], "Input"], Cell[BoxData[ \(\(2\ x\^3\ \((9 - x\^2)\)\)\/\(\(-9\) + 3\ x\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Limit[t, x \[Rule] 3]\)], "Input"], Cell[BoxData[ \(\(-108\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t /. x \[Rule] 3\)], "Input"], Cell[BoxData[ \(Power::"infy" \(\(:\)\(\ \)\) "Infinite expression \!\(1\/0\) encountered."\)], "Message"], Cell[BoxData[ RowBox[{\(\[Infinity]::"indet"\), \(\(:\)\(\ \)\), "\<\"Indeterminate \ expression \\!\\(0\\\\ \\*InterpretationBox[\\\"ComplexInfinity\\\", \ DirectedInfinity[]]\\) encountered.\"\>"}]], "Message"], Cell[BoxData[ \(Indeterminate\)], "Output"] }, Open ]], Cell["Veel m\[OTilde]ned n\[ADoubleDot]ited:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Limit[\[ExponentialE]\^\(-x\) - 1, x \[Rule] \[Infinity]]\)], "Input"], Cell[BoxData[ \(\(-1\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Limit[Tan[x], x \[Rule] \[Pi]\/2]\)], "Input"], Cell[BoxData[ InterpretationBox[\(-\[Infinity]\), DirectedInfinity[ -1]]], "Output"] }, Open ]], Cell["Summad ja korrutised.", "Text", FontWeight->"Bold"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sum]\+\(i = 0\)\%5 2\^i\/\(i!\)\)], "Input"], Cell[BoxData[ \(109\/15\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[%]\)], "Input"], Cell[BoxData[ \(7.266666666666667`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sum]\+\(i = 1\)\%\[Infinity] 1\/i\^2\)], "Input"], Cell[BoxData[ \(\[Pi]\^2\/6\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sum]\+\(i = 1\)\%\[Infinity] 1\/\(\(i!\) + \(\((2 i)\)!\)\)\)], \ "Input"], Cell[BoxData[ \(\[Sum]\+\(i = 1\)\%\[Infinity] 1\/\(\(i!\) + \(\((2\ i)\)!\)\)\)], \ "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[%]\)], "Input"], Cell[BoxData[ \(0.37319734675969646`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sum]\+\(i = 1\)\%3\(\[Sum]\+\(j = 1\)\%i\( x\^i\) y\^j\)\)], "Input"], Cell[BoxData[ \(x\ y + x\^2\ y + x\^3\ y + x\^2\ y\^2 + x\^3\ y\^2 + x\^3\ y\^3\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Product[x + i, {i, 1, 5}]\)], "Input"], Cell[BoxData[ \(\((1 + x)\)\ \((2 + x)\)\ \((3 + x)\)\ \((4 + x)\)\ \((5 + x)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["3.2. Funktsioonide defineerimine.", "Subsubtitle"], Cell[BoxData[{ \(\(Clear[s, f];\)\), "\[IndentingNewLine]", \(\($Line = 0;\)\)}], "Input"], Cell[TextData[{ "Lisaks ", StyleBox["Mathematica", FontSlant->"Italic"], "'s defineeritud funktsioonidele ja protseduuridele v\[OTilde]ib neid ka \ ise teha. Defineerime j\[ADoubleDot]rgmise ruutfunktsiooni:" }], "Text"], Cell[BoxData[ \(f[x_] := 3 x\^2 + 2 x + 1\)], "Input"], Cell["\<\ Siin alakriips ('blank') t\[ADoubleDot]hendab, et see funktsioon ehk reegel \ antud funktsiooni leidmiseks kehtib ka siis, kui me edaspidi asendama muutuja \ x muutujaga y:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(f[y]\)], "Input"], Cell[BoxData[ \(1 + 2\ y + 3\ y\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(f[2.5]\)], "Input"], Cell[BoxData[ \(24.75`\)], "Output"] }, Open ]], Cell["V\[OTilde]rdluseks m\[OTilde]ned vastupidised n\[ADoubleDot]ited:", \ "Text"], Cell[BoxData[ \(g[x] := 3 x\^2 + 2 x + 1\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(g[y]\)], "Input"], Cell[BoxData[ \(g[y]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(g[3]\)], "Input"], Cell[BoxData[ \(g[3]\)], "Output"] }, Open ]], Cell["\<\ St, antud reegel (g[x]) ei \[UDoubleDot]tle midagi selle kohta, kui x asemel \ on y. Me saame k\[UDoubleDot]ll leida m\[OTilde]ningate avaldiste v\ \[ADoubleDot]\[ADoubleDot]rtusi, kuid enamus v\[OTilde]imalusi j\[ADoubleDot]\ \[ADoubleDot]b kasutamata.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(g[x] /. x \[Rule] y\)], "Input"], Cell[BoxData[ \(1 + 2\ y + 3\ y\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(g[x] /. x \[Rule] 3\)], "Input"], Cell[BoxData[ \(34\)], "Output"] }, Open ]], Cell["\<\ Seega, sellisel, ilma alakriipusta definitsioonil 'kui funktsioon x-st' \ puudub m\[OTilde]te. Selliselt v\[OTilde]ime m\[ADoubleDot]\[ADoubleDot]rata \ ka lihtsa avaldisena (v\[ADoubleDot]hem vaeva edasistes arvutustes). Esmalt t\ \[UDoubleDot]histame g[x] definitsiooni:\ \>", "Text"], Cell[BoxData[ \(Clear[g]\)], "Input"], Cell[BoxData[ \(g := 3 x\^2 + 2 x + 1\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(g /. x \[Rule] 4\)], "Input"], Cell[BoxData[ \(57\)], "Output"] }, Open ]], Cell[TextData[{ "Analoogiliselt v\[OTilde]ib defineerida ka mitme muutuja funktsioone. \ Allpool toome n\[ADoubleDot]itena f\[UDoubleDot]\[UDoubleDot]sikast tuntud \ avaldise teepikkuse m\[ADoubleDot]\[ADoubleDot]ramiseks mingil ajahetkel kui \ funktsiooni ajast t, algkiirusest ", Cell[BoxData[ \(TraditionalForm\`v\_0\)]], " ja kiirendusest a.\nM\[ADoubleDot]rkus: alaindeksite kasutamine \ arvutustes ei ole alati v\[ADoubleDot]ga hea idee!" }], "Text"], Cell[BoxData[ \(Clear[s]\)], "Input"], Cell[BoxData[ \(s[t_, v0_, a_] := v0*t + \(1\/2\) a*t\^2\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(s[4, 0.5, 1]\)], "Input"], Cell[BoxData[ \(10.`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s[4, 1, 0.5]\)], "Input"], Cell[BoxData[ \(8.`\)], "Output"] }, Open ]], Cell["\<\ Funktsioone saab defineerida ka kui mingit funktsioonide jada - \ protseduuri:\ \>", "Text"], Cell[BoxData[ \(avald[n_] := Expand[\[Product]\+\(i = 1\)\%n\((x + i)\)]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(avald[4]\)], "Input"], Cell[BoxData[ \(24 + 50\ x + 35\ x\^2 + 10\ x\^3 + x\^4\)], "Output"] }, Open ]], Cell[TextData[{ "Siin defineerisime funktsiooni (x+1)(x+2)(x+3)...(x+n), mis korrutab selle \ avaldise ka lahti (vaikimisi ", StyleBox["Mathematica", FontSlant->"Italic"], " seda ei tee)." }], "Text"], Cell[BoxData[ \(ava[x_, n_] := Expand[\[Product]\+\(i = 1\)\%n\((x + i\^2)\)]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(ava[3, 4]\)], "Input"], Cell[BoxData[ \(6384\)], "Output"] }, Open ]], Cell["\<\ Mis juhtub, kui n asemele sisetada negatiivne arv v\[OTilde]i mitte-t\ \[ADoubleDot]isarv?\ \>", "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`f[x_] := x\^3\)]], "\t\t\t\tfunktsiooni f(x) defineerimine\n", Cell[BoxData[ \(TraditionalForm\`f[x_, y_] := x\^3 + Sin[2 x + 3]\)]], "\t\tmitme muutuja funktsiooni defineerimine\nClear[f]\t\t\t\tfunktsiooni f \ definitsiooni t\[UDoubleDot]histamine\n?f\t\t\t\t\tfunktsiooni f kuju n\ \[ADoubleDot]itamine (kehtib ka arvuti \n\t\t\t\t\tpoolt defineeritud \n\t\t\t\ \t\tfunktsioonide ja protseduuride kohta\n??f\t\t\t\t\tkogu funktsiooni v\ \[OTilde]i protseduuri f kohta k\[ADoubleDot]iva \n\t\t\t\t\tinfo n\ \[ADoubleDot]itamine\n", Cell[BoxData[ \(TraditionalForm\`f[x] = x\^3\)]], "\t\t\t\tavaldise (ja mitte funktsiooni) f defineerimine" }], "Text", Background->GrayLevel[0.900008]] }, Open ]], Cell[CellGroupData[{ Cell["3.3. V\[OTilde]rrandid.", "Subsubtitle"], Cell[TextData[{ "Alapunktis 2.3 n\[ADoubleDot]itasime, kuidas omistada v\[ADoubleDot]\ \[ADoubleDot]rtusi muutujatele. N\[ADoubleDot]iteks ", StyleBox["x = y", FontSlant->"Italic"], " on lihtsalt muutujale ", StyleBox["x", FontSlant->"Italic"], " muutuja ", StyleBox["y", FontSlant->"Italic"], " v\[ADoubleDot]\[ADoubleDot]rtuse omistamine. Selline omistamine \ deklareerib m\[OTilde]lemad suurused v\[OTilde]rdseks, kuid \[UDoubleDot]he t\ \[ADoubleDot]psustusega. Kui anname ", StyleBox["y", FontSlant->"Italic"], "-le mingi v\[ADoubleDot]\[ADoubleDot]rtuse, saab ka muutuja ", StyleBox["x", FontSlant->"Italic"], " automaatselt sama v\[ADoubleDot]\[ADoubleDot]rtuse, kuid muutujale ", StyleBox["x", FontSlant->"Italic"], " v\[ADoubleDot]\[ADoubleDot]rtuse omistamisega, \ j\[ADoubleDot]\[ADoubleDot]b ", StyleBox["y", FontSlant->"Italic"], " v\[ADoubleDot]\[ADoubleDot]rtus muutumatuks ning sellest hetkest alates \ ei olen enam ", StyleBox["x", FontSlant->"Italic"], " ", StyleBox["y", FontSlant->"Italic"], "-ga v\[OTilde]rdne. ", StyleBox["x == y", FontSlant->"Italic"], " aga kontrollib, kas ", StyleBox["x", FontSlant->"Italic"], " on ", StyleBox["y", FontSlant->"Italic"], "-ga v\[OTilde]rdne. Kahte v\[OTilde]rdusm\[ADoubleDot]rki kasutatakse ka v\ \[OTilde]rrandite lahendamisel (v\[OTilde]rrandite defineerimisel samuti)." }], "Text", TextAlignment->Left, TextJustification->1], Cell[CellGroupData[{ Cell[BoxData[ \(x = y\)], "Input"], Cell[BoxData[ \(y\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(x \[Equal] y\)], "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(2 + 4 \[Equal] 6\)], "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(2*5 \[Equal] 11\)], "Input"], Cell[BoxData[ \(False\)], "Output"] }, Open ]], Cell[BoxData[ \(x =. \)], "Input"], Cell[TextData[{ "Viimase v\[OTilde]rdusega t\[UDoubleDot]histasime ", StyleBox["x", FontSlant->"Italic"], " v\[ADoubleDot]\[ADoubleDot]rtuse." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(x \[Equal] 5\)], "Input"], Cell[BoxData[ \(x == 5\)], "Output"] }, Open ]], Cell[TextData[{ "Kuiv\[OTilde]rd ", StyleBox["x", FontSlant->"Italic"], "-l v\[ADoubleDot]\[ADoubleDot]rtus puudub, ei oska ka programm \ \[ODoubleDot]elda, kas v\[OTilde]rdus on t\[OTilde]ene v\[OTilde]i v\ \[ADoubleDot]\[ADoubleDot]r. \nAvaldis x==5 on tegelikult juba \ v\[OTilde]rrand (mille lahendiks on ilmselt x=5), sest ", StyleBox["x", FontSlant->"Italic"], " v\[ADoubleDot]\[ADoubleDot]rtus on defineerimata.\nProgrammis ", StyleBox["Mathematica ", FontSlant->"Italic"], "(ja ka n\[ADoubleDot]iteks Maple's) on tihti tavaks anda mingile \ avaldisele v\[ADoubleDot]\[ADoubleDot]rtuseks v\[OTilde]rrand ise." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(eq = x\^2 - 4 x - 7 \[Equal] 0\)], "Input"], Cell[BoxData[ \(\(-7\) - 4\ x + x\^2 == 0\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["x = y", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox[" \t\t\t\t\tomistab x-le v\[ADoubleDot]\[ADoubleDot]rtuse y\n", Background->GrayLevel[0.900008]], StyleBox["x == y", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox[" \t\t\t\t\tkontrollib, kas ", Background->GrayLevel[0.900008]], StyleBox["x", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox[" ja ", Background->GrayLevel[0.900008]], StyleBox["y", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox[" on v\[OTilde]rdsed\n", Background->GrayLevel[0.900008]], StyleBox["x != y", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["\t\t\t\t\tkontrollib, kas ", Background->GrayLevel[0.900008]], StyleBox["x", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox[" ei v\[OTilde]rdu ", Background->GrayLevel[0.900008]], StyleBox["y-", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["ga (kui x ja y ei ole v\[OTilde]rdsed, \n\t\t\t\t\ton vastus \ True)\n", Background->GrayLevel[0.900008]], StyleBox["x > y", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["\t\t\t\t\tkontrollib, kas ", Background->GrayLevel[0.900008]], StyleBox["x", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox[" on suurem, kui ", Background->GrayLevel[0.900008]], StyleBox["y", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["\n", Background->GrayLevel[0.900008]], StyleBox["x < y", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["\t\t\t\t\tkontrollib, kas ", Background->GrayLevel[0.900008]], StyleBox["x", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox[" on v\[ADoubleDot]iksem kui ", Background->GrayLevel[0.900008]], StyleBox["y", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["\n", Background->GrayLevel[0.900008]], StyleBox["x <= y", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["\t\t\t\t\tv\[ADoubleDot]iksem v\[OTilde]i v\[OTilde]rdne\n", Background->GrayLevel[0.900008]], StyleBox["x >= y", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["\t\t\t\t\tsuurem v\[OTilde]i v\[OTilde]rdne\n", Background->GrayLevel[0.900008]], StyleBox["x == y == z", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["\t\t\t\tkas k\[OTilde]ik on omavahel v\[OTilde]rdsed\n", Background->GrayLevel[0.900008]], StyleBox["x != y != z", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["\t\t\t\tkas k\[OTilde]ik on omavahel mittev\[OTilde]rdsed", Background->GrayLevel[0.900008]] }], "Text", Background->GrayLevel[0.900008]], Cell[TextData[{ "\[CapitalUDoubleDot]laltoodud avaldisi saab eriti h\[ADoubleDot]sti \ kasutada keerulisemata \[UDoubleDot]lesannet lahendamisel, \ n\[ADoubleDot]iteks programmeerimisel ", StyleBox["Mathematica", FontSlant->"Italic"], "s, kasutades laused While-, Do, For, If." }], "Text"], Cell[TextData[StyleBox["V\[OTilde]rrandite lahendamine.", FontWeight->"Bold", FontSlant->"Italic"]], "Text"], Cell[TextData[{ "Solve[v", StyleBox["asak pool == parem pool, x", FontSlant->"Italic"], "]\tv\[OTilde]rrandi lahendamine ", StyleBox["x", FontSlant->"Italic"], " suhtes, tulemuseks on \n\t\t\t\t\t\ton reegilite hulk (list)\nx /. lahend\ \t\t\t\t\treeglite listi kasutatakse x v\[ADoubleDot]\[ADoubleDot]rtuste \ saamiseks\navaldis /. lahend\t\t\t\treeglite listi kasutatakse avaldisele v\ \[ADoubleDot]\[ADoubleDot]rtuse andmiseks" }], "Text", Background->GrayLevel[0.900008]], Cell["\<\ Solve abil saab lahendada algebralisi v\[OTilde]rrandeid, milles muutuja aste \ on maksimaalselt 4. Kui k\[OTilde]rgeim aste on \[UDoubleDot]le nelja, ei \ pruugi t\[ADoubleDot]pset lahendit antud protseduur leida.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[eq, x]\)], "Input"], Cell[BoxData[ \({{x \[Rule] 2 - \@11}, {x \[Rule] 2 + \@11}}\)], "Output"] }, Open ]], Cell["\<\ Kuiv\[OTilde]rd v\[OTilde]rrandis olid k\[OTilde]ik arvud \ t\[ADoubleDot]isarvud, siis antakse tulemus t\[ADoubleDot]pselt. Ligikaudse \ lahendi saamiseks oleks kordajatest v\[ADoubleDot]hemalt \[UDoubleDot]ks \ tulnud ette anda reaalarvuna (nt 7.0) v\[OTilde]i teha nii nagu \ j\[ADoubleDot]rgnevas n\[ADoubleDot]ites:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(N[%]\)], "Input"], Cell[BoxData[ \({{x \[Rule] \(-1.3166247903553998`\)}, {x \[Rule] 5.3166247903554`}}\)], "Output"] }, Open ]], Cell["\<\ Viimane avaldis on reeglite hulk (list). Ainult arvude hulga saame j\ \[ADoubleDot]rgmiselt:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(lahendid = x\ /. \ %28\)], "Input"], Cell[BoxData[ \({\(-1.3166247903553998`\), 5.3166247903554`}\)], "Output"] }, Open ]], Cell[TextData[{ "Kui n\[UDoubleDot]\[UDoubleDot]d soovime omistada esimese v\[ADoubleDot]\ \[ADoubleDot]rtuse ", Cell[BoxData[ \(TraditionalForm\`x\_0\)]], "-le, teise ", Cell[BoxData[ \(TraditionalForm\`x\_1\)]], "-le, tuleks teha j\[ADoubleDot]rgmiselt:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(x\_0 = lahendid[\([1]\)]\)], "Input"], Cell[BoxData[ \(\(-1.3166247903553998`\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(x\_1 = lahendid[\([2]\)]\)], "Input"], Cell[BoxData[ \(5.3166247903554`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\@x\ /. \ %28\)], "Input"], Cell[BoxData[ \({\(\(0.`\)\(\[InvisibleSpace]\)\) + 1.1474427176793618`\ \[ImaginaryI], 2.3057807333646014`}\)], "Output"] }, Open ]], Cell[TextData[{ "Kuiv\[OTilde]rd Out[9] oli meil list, milles x-l oli kaks v\[ADoubleDot]\ \[ADoubleDot]rtust, siis ka ", Cell[BoxData[ \(TraditionalForm\`\@x\)]], " protseduuri rakendamine andis tulemuseks listi, milles on kaks liiget. Ja \ kuiv\[OTilde]rd esimene v\[ADoubleDot]\[ADoubleDot]rtus oli negatiivne, siis \ sellest ruutjuure v\[OTilde]tmisel saame tulemuseks loomulikult \ kompleksarvu." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[x\^5 - 4 x\^4 + 9 \[Equal] 0, x]\)], "Input"], Cell[BoxData[ \({{x \[Rule] Root[9 - 4\ #1\^4 + #1\^5 &, 1]}, {x \[Rule] Root[9 - 4\ #1\^4 + #1\^5 &, 2]}, {x \[Rule] Root[9 - 4\ #1\^4 + #1\^5 &, 3]}, {x \[Rule] Root[9 - 4\ #1\^4 + #1\^5 &, 4]}, {x \[Rule] Root[9 - 4\ #1\^4 + #1\^5 &, 5]}}\)], "Output"] }, Open ]], Cell["\<\ Nagu n\[ADoubleDot]he, ei suutnud antud juhul Solve-protseduur anda t\ \[ADoubleDot]pset lahendit. K\[UDoubleDot]ll saame ligikaudse: \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[x\^5 - 4 x\^4 + 9.0 \[Equal] 0, x]\)], "Input"], Cell[BoxData[ \({{x \[Rule] \(-1.1497767610903715`\)}, {x \[Rule] \ \(-0.08619637221601012`\) - 1.2025654913272121`\ \[ImaginaryI]}, {x \[Rule] \ \(-0.08619637221601012`\) + 1.2025654913272121`\ \[ImaginaryI]}, {x \[Rule] 1.3586376003599896`}, {x \[Rule] 3.9635319051624025`}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[Sin[x] \[Equal] a, x]\)], "Input"], Cell[BoxData[ \(Solve::"ifun" \(\(:\)\(\ \)\) "Inverse functions are being used by \!\(Solve\), so some solutions may \ not be found."\)], "Message"], Cell[BoxData[ \({{x \[Rule] ArcSin[a]}}\)], "Output"] }, Open ]], Cell["\<\ Antud juhul kasutatakse siinuse p\[ODoubleDot]\[ODoubleDot]rdfunktsiooni \ arcsin, seet\[OTilde]ttu on siin ka hoiatus,et et m\[OTilde]ned lahendid v\ \[OTilde]ivad j\[ADoubleDot]\[ADoubleDot]da leidmata. Antud v\[OTilde]rrandil \ on tegelikult l\[OTilde]pmata hulk lahendeid, mis erinevad \ \[UDoubleDot]ksteisest 2 \[Pi] n v\[OTilde]rra, n on siin \ t\[ADoubleDot]isarv. \ \>", "Text", TextAlignment->Left, TextJustification->1], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[Sin[x] \[Equal] x, x]\)], "Input"], Cell[BoxData[ \(Solve::"tdep" \(\(:\)\(\ \)\) "The equations appear to involve the variables to be solved for in an \ essentially non-algebraic way."\)], "Message"], Cell[BoxData[ \(Solve[Sin[x] == x, x]\)], "Output"] }, Open ]], Cell[TextData[StyleBox["See t\[ADoubleDot]hendab, et \[UDoubleDot]laltoodud v\ \[OTilde]rrand sisaldab transendentseid funktsioone ning algebraliselt on \ seda v\[OTilde]rrandit v\[OTilde]imatu lahendada. Selliste transendetnsete v\ \[OTilde]rrandeid lahendatakse numbriliselt ning nende lahendamiseks on \ funktsioon FindRoot, mida k\[ADoubleDot]sitleme hiljem.", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"]], "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`Solve[{vp\_1 \[Equal] pp\_1, vp\_2 \[Equal] pp\_2, ... }, {x\_1, x\_2, \ ... }]\)]], "\t\tv\[OTilde]rrandis\[UDoubleDot]steemi \n\t\t\t\t\t\t\t\tlahendamine ", Cell[BoxData[ \(TraditionalForm\`x\_1\)]], ", ", Cell[BoxData[ \(TraditionalForm\`x\_2\)]], ", ..suhtes\n", Cell[BoxData[ \(TraditionalForm\`NSolve[{vp\_1 \[Equal] pp\_1, \ vp\_2 \[Equal] pp\_2, \ ... }, {x\_1, x\_2, \ ... }]\)]], " \t\tv\[OTilde]rrandis\[UDoubleDot]steemi numbriline \t\n\t\t\t\t\t\t\t\t\ lahendamine ", Cell[BoxData[ \(TraditionalForm\`x\_1\)]], ", ", Cell[BoxData[ \(TraditionalForm\`x\_2\)]], " ..suhtes\n", Cell[BoxData[ \(TraditionalForm\`\(\(Eliminate[{vp\_1 \[Equal] pp\_1, \ vp\_2 \[Equal] pp\_2, \ ... }, {x\_1, x\_2, \ ... }]\)\(\ \)\)\)]], " \tv\[OTilde]rrandis\[UDoubleDot]steemist muutujate ", Cell[BoxData[ \(TraditionalForm\`x\_1\)]], ", ", Cell[BoxData[ \(TraditionalForm\`x\_2\)]], " \n\t\t\t\t\t\t\t\tellimineerimine\nReduce[{", Cell[BoxData[ \(TraditionalForm\`{vp\_1 \[Equal] pp\_1, \ vp\_2 \[Equal] pp\_2, \ ... }, {x\_1, x\_2, \ ... }\)]], "] \tannab lihtsustatud v\[OTilde]rrandite s\[UDoubleDot]steemi koos\n\t\t\t\ \t\t\t\t\tv\[OTilde]imalike lahendustega\n", Cell[BoxData[ \(TraditionalForm\`FindRoot[vp \[Equal] pp, \ {x, x\_0}]\)]], "\t\t\t\t\tleiab numbriliselt lahendi v\[OTilde]rrandile, alustades ", Cell[BoxData[ \(TraditionalForm\`x\_0\)]], "-st" }], "Text", Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[{2 x - 4 y + 3 z \[Equal] 0, x - 3 y - z \[Equal] 0, x - 3 z \[Equal] \(-9\)}, {x, y, z}]\)], "Input"], Cell[BoxData[ \({{x \[Rule] \(-\(117\/19\)\), y \[Rule] \(-\(45\/19\)\), z \[Rule] 18\/19}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(NSolve[{2 x - 4 y + 3 z \[Equal] 0, x - 3 y - z \[Equal] 0, x - 3 z \[Equal] \(-9\)}, {x, y, z}]\)], "Input"], Cell[BoxData[ \({{x \[Rule] \(-6.157894736842104`\), y \[Rule] \(-2.3684210526315788`\), z \[Rule] 0.9473684210526315`}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Eliminate[{2 x + 4 y + 3 z \[Equal] 0, x - 3 y \[Equal] z - 2}, z]\)], "Input"], Cell[BoxData[ \(\(-6\) + 5\ y == 5\ x\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Reduce[{2 x + 4 y + 3 z \[Equal] 0, x - 3 y \[Equal] z - 2}, {x, y}]\)], "Input"], Cell[BoxData[ \(x == 1\/10\ \((\(-8\) - 5\ z)\) && y == 1\/10\ \((4 - 5\ z)\)\)], "Output"] }, Open ]], Cell[TextData[StyleBox["Eliminate k\[ADoubleDot]suga saime kahest kolme \ muutujaga v\[OTilde]rrandist \[UDoubleDot]he kahe muutujaga v\[OTilde]rrandi. \ Reduce abiga antud juhul saime kaks v\[OTilde]imalikku uut v\[OTilde]rrandit \ - esimesel juhul elimineerisime y, teisel juhul x. \nKuigi NSolve leiab v\ \[OTilde]rrandite lahendeid numbriliselt, sobib see protseduur siiski vaid v\ \[OTilde]rrandite jaoks, kus muutujad on mingites astmetes \ (pol\[UDoubleDot]noomv\[OTilde]rrandid). Vastasel juhul tuleb kasutada ikkagi \ protseduuri FindRoot, mis leiab nullkohad Newtoni iteratsioonimeetodil, kuid \ selleks tuleb anda piisavalt hea l\[ADoubleDot]htepunkt, st ligikaudne \ nullkoht. Viimast on \[UDoubleDot]sna hea leida joonise abil.\n\ J\[ADoubleDot]rgnevas n\[ADoubleDot]ites defineerime uue funktsiooni, teeme \ selle kohta joonise ja siis leiame nullkohad.", FontFamily->"Times New Roman", CharacterEncoding->"WindowsANSI"]], "Text"], Cell[BoxData[ \(\(Clear[f, g];\)\)], "Input"], Cell[BoxData[ \(g[x_] := 2 x*E\^\(0.1 x\) - x\^2\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[g[x], {x, \(-2\), 4}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.15873 0.515768 0.068874 [ [.02381 .50327 -6 -9 ] [.02381 .50327 6 0 ] [.18254 .50327 -6 -9 ] [.18254 .50327 6 0 ] [.5 .50327 -3 -9 ] [.5 .50327 3 0 ] [.65873 .50327 -3 -9 ] [.65873 .50327 3 0 ] [.81746 .50327 -3 -9 ] [.81746 .50327 3 0 ] [.97619 .50327 -3 -9 ] [.97619 .50327 3 0 ] [.32877 .10252 -12 -4.5 ] [.32877 .10252 0 4.5 ] [.32877 .24027 -12 -4.5 ] [.32877 .24027 0 4.5 ] [.32877 .37802 -12 -4.5 ] [.32877 .37802 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 .51577 m .02381 .52202 L s [(-2)] .02381 .50327 0 1 Mshowa .18254 .51577 m .18254 .52202 L s [(-1)] .18254 .50327 0 1 Mshowa .5 .51577 m .5 .52202 L s [(1)] .5 .50327 0 1 Mshowa .65873 .51577 m .65873 .52202 L s [(2)] .65873 .50327 0 1 Mshowa .81746 .51577 m .81746 .52202 L s [(3)] .81746 .50327 0 1 Mshowa .97619 .51577 m .97619 .52202 L s [(4)] .97619 .50327 0 1 Mshowa .125 Mabswid .05556 .51577 m .05556 .51952 L s .0873 .51577 m .0873 .51952 L s .11905 .51577 m .11905 .51952 L s .15079 .51577 m .15079 .51952 L s .21429 .51577 m .21429 .51952 L s .24603 .51577 m .24603 .51952 L s .27778 .51577 m .27778 .51952 L s .30952 .51577 m .30952 .51952 L s .37302 .51577 m .37302 .51952 L s .40476 .51577 m .40476 .51952 L s .43651 .51577 m .43651 .51952 L s .46825 .51577 m .46825 .51952 L s .53175 .51577 m .53175 .51952 L s .56349 .51577 m .56349 .51952 L s .59524 .51577 m .59524 .51952 L s .62698 .51577 m .62698 .51952 L s .69048 .51577 m .69048 .51952 L s .72222 .51577 m .72222 .51952 L s .75397 .51577 m .75397 .51952 L s .78571 .51577 m .78571 .51952 L s .84921 .51577 m .84921 .51952 L s .88095 .51577 m .88095 .51952 L s .9127 .51577 m .9127 .51952 L s .94444 .51577 m .94444 .51952 L s .25 Mabswid 0 .51577 m 1 .51577 L s .34127 .10252 m .34752 .10252 L s [(-6)] .32877 .10252 1 0 Mshowa .34127 .24027 m .34752 .24027 L s [(-4)] .32877 .24027 1 0 Mshowa .34127 .37802 m .34752 .37802 L s [(-2)] .32877 .37802 1 0 Mshowa .125 Mabswid .34127 .13696 m .34502 .13696 L s .34127 .1714 m .34502 .1714 L s .34127 .20584 m .34502 .20584 L s .34127 .27471 m .34502 .27471 L s .34127 .30915 m .34502 .30915 L s .34127 .34358 m .34502 .34358 L s .34127 .41246 m .34502 .41246 L s .34127 .44689 m .34502 .44689 L s .34127 .48133 m .34502 .48133 L s .34127 .06809 m .34502 .06809 L s .34127 .03365 m .34502 .03365 L s .34127 .5502 m .34502 .5502 L s .34127 .58464 m .34502 .58464 L s .25 Mabswid .34127 0 m .34127 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .06244 .10026 L .10458 .18568 L .14415 .25847 L .18221 .32173 L .22272 .38187 L .26171 .4328 L .30316 .47951 L .34309 .51734 L .3815 .54715 L .42237 .57186 L .44268 .58147 L .46172 .58888 L .47994 .59453 L .49955 .59904 L .50966 .60074 L .51499 .60146 L .52069 .6021 L .52615 .60259 L .5311 .60293 L .5335 .60305 L .53608 .60316 L .53727 .6032 L .53853 .60324 L .5397 .60326 L .54078 .60328 L .542 .6033 L .54264 .60331 L .54332 .60331 L .54447 .60332 L .54573 .60332 L .54686 .60331 L .54806 .6033 L .54921 .60328 L .55025 .60326 L .55262 .60319 L .5552 .6031 L .5579 .60297 L .56041 .60282 L .56928 .60209 L .57424 .60154 L .57875 .60095 L .59793 .59752 L .60875 .59492 L .61873 .5921 L .65813 .57704 L .69602 .5567 L .73636 .52883 L .77518 .49602 L .81646 .4548 L Mistroke .85622 .40902 L .89447 .35945 L .93516 .30085 L .97435 .23882 L .97619 .23577 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ Jooniselt on n\[ADoubleDot]ha, et \[UDoubleDot]ks nullkoht on umbes kohal 0, \ teine kohal 2,5. Tuleb kasutada kaks korda protseduuri FindRoot\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(FindRoot[g[x] \[Equal] 0, {x, 0}]\)], "Input"], Cell[BoxData[ \({x \[Rule] 0.`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(FindRoot[g[x] \[Equal] 0, {x, 2.5}]\)], "Input"], Cell[BoxData[ \({x \[Rule] 2.5917110181968916`}\)], "Output"] }, Open ]], Cell[TextData[{ "Seega on kaks nullkohta: ", Cell[BoxData[ \(TraditionalForm\`x\_1 = 0, \ x\_2 \[TildeTilde] 2, 59\)]], "." }], "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["4. Joonised", "Subtitle"], Cell["4.1. Joonised tasandil", "Subsubtitle"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`Plot[f, {x, x\_min, \ x\_max}]\)]], "\t\t\tjoonistab funktsiooni f graafiku ", Cell[BoxData[ \(TraditionalForm\`x\_min\)]], "-st \n\t\t\t\t\t\tkuni ", Cell[BoxData[ \(TraditionalForm\`x\_max\)]], "-ni\n", Cell[BoxData[ \(TraditionalForm\`Plot[{f, g, ... }, {x, x\_min, \ x\_max}]\)]], "\t\tjoonistab mitme funktsiooni graafikud\nShow[joonis1, joonis2]\t\t\t\t\ joonistab erinevad joonised \[UDoubleDot]hele kokku" }], "Text", Background->GrayLevel[0.900008]], Cell[BoxData[ \(\($Line = 0;\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[E\^\(\(-0.5\) x\)\ Sin[x], {x, 0, 2 \[Pi]}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.151576 0.116016 0.947695 [ [.17539 .10352 -3 -9 ] [.17539 .10352 3 0 ] [.32696 .10352 -3 -9 ] [.32696 .10352 3 0 ] [.47854 .10352 -3 -9 ] [.47854 .10352 3 0 ] [.63011 .10352 -3 -9 ] [.63011 .10352 3 0 ] [.78169 .10352 -3 -9 ] [.78169 .10352 3 0 ] [.93327 .10352 -3 -9 ] [.93327 .10352 3 0 ] [.01131 .02125 -24 -4.5 ] [.01131 .02125 0 4.5 ] [.01131 .21079 -18 -4.5 ] [.01131 .21079 0 4.5 ] [.01131 .30555 -18 -4.5 ] [.01131 .30555 0 4.5 ] [.01131 .40032 -18 -4.5 ] [.01131 .40032 0 4.5 ] [.01131 .49509 -18 -4.5 ] [.01131 .49509 0 4.5 ] [.01131 .58986 -18 -4.5 ] [.01131 .58986 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .11602 m .17539 .12227 L s [(1)] .17539 .10352 0 1 Mshowa .32696 .11602 m .32696 .12227 L s [(2)] .32696 .10352 0 1 Mshowa .47854 .11602 m .47854 .12227 L s [(3)] .47854 .10352 0 1 Mshowa .63011 .11602 m .63011 .12227 L s [(4)] .63011 .10352 0 1 Mshowa .78169 .11602 m .78169 .12227 L s [(5)] .78169 .10352 0 1 Mshowa .93327 .11602 m .93327 .12227 L s [(6)] .93327 .10352 0 1 Mshowa .125 Mabswid .05412 .11602 m .05412 .11977 L s .08444 .11602 m .08444 .11977 L s .11476 .11602 m .11476 .11977 L s .14507 .11602 m .14507 .11977 L s .2057 .11602 m .2057 .11977 L s .23602 .11602 m .23602 .11977 L s .26633 .11602 m .26633 .11977 L s .29665 .11602 m .29665 .11977 L s .35728 .11602 m .35728 .11977 L s .38759 .11602 m .38759 .11977 L s .41791 .11602 m .41791 .11977 L s .44822 .11602 m .44822 .11977 L s .50885 .11602 m .50885 .11977 L s .53917 .11602 m .53917 .11977 L s .56948 .11602 m .56948 .11977 L s .5998 .11602 m .5998 .11977 L s .66043 .11602 m .66043 .11977 L s .69074 .11602 m .69074 .11977 L s .72106 .11602 m .72106 .11977 L s .75138 .11602 m .75138 .11977 L s .81201 .11602 m .81201 .11977 L s .84232 .11602 m .84232 .11977 L s .87264 .11602 m .87264 .11977 L s .90295 .11602 m .90295 .11977 L s .96358 .11602 m .96358 .11977 L s .9939 .11602 m .9939 .11977 L s .25 Mabswid 0 .11602 m 1 .11602 L s .02381 .02125 m .03006 .02125 L s [(-0.1)] .01131 .02125 1 0 Mshowa .02381 .21079 m .03006 .21079 L s [(0.1)] .01131 .21079 1 0 Mshowa .02381 .30555 m .03006 .30555 L s [(0.2)] .01131 .30555 1 0 Mshowa .02381 .40032 m .03006 .40032 L s [(0.3)] .01131 .40032 1 0 Mshowa .02381 .49509 m .03006 .49509 L s [(0.4)] .01131 .49509 1 0 Mshowa .02381 .58986 m .03006 .58986 L s [(0.5)] .01131 .58986 1 0 Mshowa .125 Mabswid .02381 .0402 m .02756 .0402 L s .02381 .05915 m .02756 .05915 L s .02381 .07811 m .02756 .07811 L s .02381 .09706 m .02756 .09706 L s .02381 .13497 m .02756 .13497 L s .02381 .15392 m .02756 .15392 L s .02381 .17288 m .02756 .17288 L s .02381 .19183 m .02756 .19183 L s .02381 .22974 m .02756 .22974 L s .02381 .24869 m .02756 .24869 L s .02381 .26765 m .02756 .26765 L s .02381 .2866 m .02756 .2866 L s .02381 .32451 m .02756 .32451 L s .02381 .34346 m .02756 .34346 L s .02381 .36242 m .02756 .36242 L s .02381 .38137 m .02756 .38137 L s .02381 .41928 m .02756 .41928 L s .02381 .43823 m .02756 .43823 L s .02381 .45719 m .02756 .45719 L s .02381 .47614 m .02756 .47614 L s .02381 .51405 m .02756 .51405 L s .02381 .533 m .02756 .533 L s .02381 .55196 m .02756 .55196 L s .02381 .57091 m .02756 .57091 L s .02381 .00229 m .02756 .00229 L s .02381 .60882 m .02756 .60882 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .11602 m .04262 .22625 L .06244 .32637 L .08426 .41749 L .10458 .48485 L .12297 .53181 L .14264 .56817 L .15285 .58172 L .15824 .58747 L .16394 .59255 L .16892 .59615 L .17441 .59924 L .17682 .60032 L .17941 .60129 L .18186 .60203 L .18408 .60255 L .1853 .60278 L .18662 .60298 L .18734 .60307 L .18801 .60314 L .18932 .60325 L .19045 .6033 L .19169 .60332 L .19298 .60329 L .19419 .60323 L .19487 .60318 L .19562 .60311 L .19697 .60294 L .19951 .60251 L .20247 .6018 L .20522 .60094 L .20985 .5991 L .21496 .59648 L .22531 .58941 L .2354 .58039 L .24465 .57045 L .26551 .54288 L .30513 .47555 L .34324 .39998 L .3838 .31651 L .42285 .23984 L .46435 .16766 L .50433 .11047 L .54279 .06836 L .56267 .05165 L .58371 .0376 L .60329 .02775 L .6216 .02118 L .63201 .01852 L .63713 .01748 L Mistroke .64189 .01667 L .64654 .01602 L .65076 .01555 L .65544 .01515 L .65801 .01499 L .66042 .01487 L .66159 .01482 L .66284 .01478 L .66402 .01476 L .66509 .01474 L .66635 .01472 L .66707 .01472 L .66772 .01472 L .66893 .01472 L .67021 .01473 L .67143 .01475 L .67275 .01478 L .67399 .01482 L .67513 .01486 L .67777 .01498 L .68054 .01515 L .68512 .01551 L .68938 .01593 L .69903 .01721 L .70958 .01907 L .71952 .02123 L .73812 .0262 L .77664 .03946 L .81761 .05621 L .85707 .0731 L .89501 .0887 L .9354 .10356 L .97428 .1155 L .97619 .11602 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[{2 x\^2 - 4 x, 2 x}, {x, \(-2\), 4}, AxesLabel \[Rule] {x, y}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.15873 0.132436 0.0294302 [ [.02381 .11994 -6 -9 ] [.02381 .11994 6 0 ] [.18254 .11994 -6 -9 ] [.18254 .11994 6 0 ] [.5 .11994 -3 -9 ] [.5 .11994 3 0 ] [.65873 .11994 -3 -9 ] [.65873 .11994 3 0 ] [.81746 .11994 -3 -9 ] [.81746 .11994 3 0 ] [.97619 .11994 -3 -9 ] [.97619 .11994 3 0 ] [1.025 .13244 0 -6.28125 ] [1.025 .13244 10 6.28125 ] [.32877 .27959 -6 -4.5 ] [.32877 .27959 0 4.5 ] [.32877 .42674 -12 -4.5 ] [.32877 .42674 0 4.5 ] [.32877 .57389 -12 -4.5 ] [.32877 .57389 0 4.5 ] [.34127 .64303 -5 0 ] [.34127 .64303 5 12.5625 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 .13244 m .02381 .13869 L s [(-2)] .02381 .11994 0 1 Mshowa .18254 .13244 m .18254 .13869 L s [(-1)] .18254 .11994 0 1 Mshowa .5 .13244 m .5 .13869 L s [(1)] .5 .11994 0 1 Mshowa .65873 .13244 m .65873 .13869 L s [(2)] .65873 .11994 0 1 Mshowa .81746 .13244 m .81746 .13869 L s [(3)] .81746 .11994 0 1 Mshowa .97619 .13244 m .97619 .13869 L s [(4)] .97619 .11994 0 1 Mshowa .125 Mabswid .05556 .13244 m .05556 .13619 L s .0873 .13244 m .0873 .13619 L s .11905 .13244 m .11905 .13619 L s .15079 .13244 m .15079 .13619 L s .21429 .13244 m .21429 .13619 L s .24603 .13244 m .24603 .13619 L s .27778 .13244 m .27778 .13619 L s .30952 .13244 m .30952 .13619 L s .37302 .13244 m .37302 .13619 L s .40476 .13244 m .40476 .13619 L s .43651 .13244 m .43651 .13619 L s .46825 .13244 m .46825 .13619 L s .53175 .13244 m .53175 .13619 L s .56349 .13244 m .56349 .13619 L s .59524 .13244 m .59524 .13619 L s .62698 .13244 m .62698 .13619 L s .69048 .13244 m .69048 .13619 L s .72222 .13244 m .72222 .13619 L s .75397 .13244 m .75397 .13619 L s .78571 .13244 m .78571 .13619 L s .84921 .13244 m .84921 .13619 L s .88095 .13244 m .88095 .13619 L s .9127 .13244 m .9127 .13619 L s .94444 .13244 m .94444 .13619 L s .25 Mabswid 0 .13244 m 1 .13244 L s gsave 1.025 .13244 -61 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 1.000 setlinewidth grestore .34127 .27959 m .34752 .27959 L s [(5)] .32877 .27959 1 0 Mshowa .34127 .42674 m .34752 .42674 L s [(10)] .32877 .42674 1 0 Mshowa .34127 .57389 m .34752 .57389 L s [(15)] .32877 .57389 1 0 Mshowa .125 Mabswid .34127 .16187 m .34502 .16187 L s .34127 .1913 m .34502 .1913 L s .34127 .22073 m .34502 .22073 L s .34127 .25016 m .34502 .25016 L s .34127 .30902 m .34502 .30902 L s .34127 .33845 m .34502 .33845 L s .34127 .36788 m .34502 .36788 L s .34127 .39731 m .34502 .39731 L s .34127 .45617 m .34502 .45617 L s .34127 .4856 m .34502 .4856 L s .34127 .51503 m .34502 .51503 L s .34127 .54446 m .34502 .54446 L s .34127 .10301 m .34502 .10301 L s .34127 .07358 m .34502 .07358 L s .34127 .04415 m .34502 .04415 L s .34127 .01472 m .34502 .01472 L s .34127 .60332 m .34502 .60332 L s .25 Mabswid .34127 0 m .34127 .61803 L s gsave .34127 .64303 -66 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (y) show 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .60332 m .06244 .52085 L .10458 .43885 L .14415 .3694 L .18221 .30951 L .22272 .25319 L .26171 .20623 L .30316 .1641 L .34309 .1311 L .3815 .10638 L .40095 .0965 L .42237 .08766 L .44268 .08125 L .45178 .07901 L .46172 .077 L .4671 .0761 L .4721 .07539 L .47727 .07478 L .48196 .07434 L .48658 .074 L .4887 .07387 L .49093 .07377 L .49332 .07368 L .49438 .07365 L .49552 .07362 L .49675 .0736 L .49789 .07359 L .49859 .07358 L .49925 .07358 L .50049 .07358 L .50163 .07358 L .50286 .07359 L .50401 .07361 L .50508 .07364 L .50754 .07371 L .51014 .07382 L .51268 .07395 L .51504 .0741 L .5204 .07455 L .5293 .07558 L .53882 .0771 L .54906 .0792 L .56016 .08203 L .58032 .08865 L .60019 .09703 L .62123 .10791 L .65912 .13273 L .69946 .16652 L .73829 .20622 L .77956 .25616 L Mistroke .81932 .31179 L .85757 .37227 L .89827 .44413 L .93745 .52063 L .97619 .60332 L Mfstroke .02381 .01472 m .06244 .02904 L .10458 .04467 L .14415 .05934 L .18221 .07345 L .22272 .08847 L .26171 .10293 L .30316 .1183 L .34309 .13311 L .3815 .14735 L .42237 .16251 L .46172 .1771 L .49955 .19113 L .53984 .20607 L .57861 .22045 L .61984 .23573 L .65954 .25046 L .69774 .26462 L .73838 .27969 L .77751 .2942 L .81909 .30962 L .85916 .32448 L .89771 .33878 L .93871 .35398 L .97619 .36788 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Show[%1, %2]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.253765 0.114978 0.255132 0.0601041 [ [.02381 .24263 -6 -9 ] [.02381 .24263 6 0 ] [.48372 .24263 -3 -9 ] [.48372 .24263 3 0 ] [.71368 .24263 -3 -9 ] [.71368 .24263 3 0 ] [.94363 .24263 -3 -9 ] [.94363 .24263 3 0 ] [.24126 .01472 -12 -4.5 ] [.24126 .01472 0 4.5 ] [.24126 .13492 -12 -4.5 ] [.24126 .13492 0 4.5 ] [.24126 .37534 -6 -4.5 ] [.24126 .37534 0 4.5 ] [.24126 .49555 -6 -4.5 ] [.24126 .49555 0 4.5 ] [.24126 .61576 -6 -4.5 ] [.24126 .61576 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 .25513 m .02381 .26138 L s [(-2)] .02381 .24263 0 1 Mshowa .48372 .25513 m .48372 .26138 L s [(2)] .48372 .24263 0 1 Mshowa .71368 .25513 m .71368 .26138 L s [(4)] .71368 .24263 0 1 Mshowa .94363 .25513 m .94363 .26138 L s [(6)] .94363 .24263 0 1 Mshowa .125 Mabswid .0813 .25513 m .0813 .25888 L s .13879 .25513 m .13879 .25888 L s .19628 .25513 m .19628 .25888 L s .31125 .25513 m .31125 .25888 L s .36874 .25513 m .36874 .25888 L s .42623 .25513 m .42623 .25888 L s .54121 .25513 m .54121 .25888 L s .5987 .25513 m .5987 .25888 L s .65619 .25513 m .65619 .25888 L s .77116 .25513 m .77116 .25888 L s .82865 .25513 m .82865 .25888 L s .88614 .25513 m .88614 .25888 L s .25 Mabswid 0 .25513 m 1 .25513 L s .25376 .01472 m .26001 .01472 L s [(-4)] .24126 .01472 1 0 Mshowa .25376 .13492 m .26001 .13492 L s [(-2)] .24126 .13492 1 0 Mshowa .25376 .37534 m .26001 .37534 L s [(2)] .24126 .37534 1 0 Mshowa .25376 .49555 m .26001 .49555 L s [(4)] .24126 .49555 1 0 Mshowa .25376 .61576 m .26001 .61576 L s [(6)] .24126 .61576 1 0 Mshowa .125 Mabswid .25376 .04477 m .25751 .04477 L s .25376 .07482 m .25751 .07482 L s .25376 .10487 m .25751 .10487 L s .25376 .16498 m .25751 .16498 L s .25376 .19503 m .25751 .19503 L s .25376 .22508 m .25751 .22508 L s .25376 .28518 m .25751 .28518 L s .25376 .31524 m .25751 .31524 L s .25376 .34529 m .25751 .34529 L s .25376 .40539 m .25751 .40539 L s .25376 .43544 m .25751 .43544 L s .25376 .4655 m .25751 .4655 L s .25376 .5256 m .25751 .5256 L s .25376 .55565 m .25751 .55565 L s .25376 .5857 m .25751 .5857 L s .25 Mabswid .25376 0 m .25376 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .25376 .25513 m .26803 .26212 L .28307 .26847 L .29962 .27425 L .31503 .27852 L .32898 .2815 L .3439 .28381 L .35165 .28467 L .35573 .28503 L .36006 .28535 L .36384 .28558 L .368 .28578 L .36983 .28585 L .37179 .28591 L .37365 .28596 L .37534 .28599 L .37626 .286 L .37726 .28602 L .37781 .28602 L .37832 .28603 L .37931 .28603 L .38017 .28604 L .38111 .28604 L .38209 .28604 L .383 .28603 L .38352 .28603 L .38409 .28602 L .38512 .28601 L .38704 .28599 L .38929 .28594 L .39137 .28589 L .39488 .28577 L .39876 .2856 L .40661 .28515 L .41427 .28458 L .42128 .28395 L .43711 .2822 L .46716 .27793 L .49607 .27314 L .52684 .26785 L .55645 .26298 L .58793 .25841 L .61826 .25478 L .64744 .25211 L .66252 .25105 L .67848 .25016 L .69333 .24953 L .70722 .24912 L .71511 .24895 L .719 .24888 L Mistroke .72261 .24883 L .72614 .24879 L .72933 .24876 L .73289 .24873 L .73483 .24872 L .73667 .24872 L .73755 .24871 L .7385 .24871 L .73939 .24871 L .74021 .24871 L .74117 .24871 L .74171 .24871 L .7422 .24871 L .74312 .24871 L .74409 .24871 L .74502 .24871 L .74602 .24871 L .74696 .24871 L .74782 .24872 L .74982 .24872 L .75193 .24873 L .7554 .24876 L .75863 .24878 L .76595 .24887 L .77395 .24898 L .7815 .24912 L .79561 .24944 L .82482 .25028 L .8559 .25134 L .88583 .25241 L .91461 .2534 L .94525 .25434 L .97474 .2551 L .97619 .25513 L Mfstroke .13826 .61803 m .13855 .61676 L .16789 .50175 L .19613 .40584 L .22616 .31979 L .25508 .2524 L .28291 .20192 L .29699 .18174 L .31251 .16368 L .32722 .1506 L .33382 .14602 L .34101 .14192 L .34491 .14009 L .34853 .13864 L .35228 .13739 L .35568 .13648 L .35902 .13578 L .36055 .13553 L .36217 .13532 L .3639 .13514 L .36467 .13507 L .3655 .13502 L .36639 .13497 L .36721 .13494 L .36772 .13493 L .3682 .13493 L .3691 .13492 L .36992 .13494 L .37081 .13496 L .37165 .135 L .37242 .13505 L .37421 .13519 L .37609 .13541 L .37793 .13569 L .37964 .136 L .38352 .13691 L .38997 .13902 L .39686 .14211 L .40428 .14641 L .41232 .15219 L .42692 .1657 L .44132 .18282 L .45656 .20505 L .484 .25573 L .51322 .32474 L .54135 .40582 L .57125 .50781 L s .57125 .50781 m .59919 .61803 L s .02381 .01472 m .0518 .04397 L .08232 .07588 L .11098 .10585 L .13855 .13467 L .16789 .16535 L .19613 .19488 L .22616 .22627 L .25508 .25651 L .28291 .2856 L .31251 .31655 L .34101 .34635 L .36842 .375 L .3976 .40551 L .42569 .43487 L .45555 .46609 L .48431 .49616 L .51197 .52509 L .54142 .55587 L .56976 .5855 L .59988 .61699 L s .59988 .61699 m .60088 .61803 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "Nagu teisest arvutusest n\[ADoubleDot]ha, v\[OTilde]ib Plot-protseduurile \ anda erinevaid lisav\[OTilde]imalusi. T\[ADoubleDot]ieliku info \ v\[OTilde]imalustest saab Help-st v\[OTilde]i kasutades \ Help-k\[ADoubleDot]sku (kehtib k\[OTilde]igi ", StyleBox["Mathematica", FontSlant->"Italic"], " funktsioonide ja protseduuride kohta)." }], "Text"], Cell["M\[OTilde]ned n\[ADoubleDot]ited erinevate v\[OTilde]imaluste \ kasutamise kohta.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[{E\^x, x, Log[x]}, {x, \(-3\), 3}, PlotStyle \[Rule] {RGBColor[1, 0, 0], RGBColor[0.5, 0.5, 0], RGBColor[0, 0.5, 1]}, AxesLabel \[Rule] {"\", "\"}, PlotRange \[Rule] {{\(-3\), 3}, {\(-3\), 4}}, AspectRatio \[Rule] Automatic]\)], "Input"], Cell[BoxData[ \(Plot::"plnr" \(\(:\)\(\ \)\) "\!\(Log[x]\) is not a machine-size real number at \!\(x\) = \ \!\(-2.99999975`\)."\)], "Message"], Cell[BoxData[ \(Plot::"plnr" \(\(:\)\(\ \)\) "\!\(Log[x]\) is not a machine-size real number at \!\(x\) = \ \!\(-2.7565980505625056`\)."\)], "Message"], Cell[BoxData[ \(Plot::"plnr" \(\(:\)\(\ \)\) "\!\(Log[x]\) is not a machine-size real number at \!\(x\) = \ \!\(-2.491147200843758`\)."\)], "Message"], Cell[BoxData[ \(General::"stop" \(\(:\)\(\ \)\) "Further output of \!\(Plot :: \"plnr\"\) will be suppressed during \ this calculation."\)], "Message"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.16667 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.166667 0.5 0.166667 [ [0 .4875 -6 -9 ] [0 .4875 6 0 ] [.16667 .4875 -6 -9 ] [.16667 .4875 6 0 ] [.33333 .4875 -6 -9 ] [.33333 .4875 6 0 ] [.66667 .4875 -3 -9 ] [.66667 .4875 3 0 ] [.83333 .4875 -3 -9 ] [.83333 .4875 3 0 ] [1 .4875 -3 -9 ] [1 .4875 3 0 ] [1.025 .5 0 -6.28125 ] [1.025 .5 10 6.28125 ] [.4875 0 -12 -4.5 ] [.4875 0 0 4.5 ] [.4875 .16667 -12 -4.5 ] [.4875 .16667 0 4.5 ] [.4875 .33333 -12 -4.5 ] [.4875 .33333 0 4.5 ] [.4875 .66667 -6 -4.5 ] [.4875 .66667 0 4.5 ] [.4875 .83333 -6 -4.5 ] [.4875 .83333 0 4.5 ] [.4875 1 -6 -4.5 ] [.4875 1 0 4.5 ] [.4875 1.16667 -6 -4.5 ] [.4875 1.16667 0 4.5 ] [.5 1.19167 -5 0 ] [.5 1.19167 5 12.5625 ] [ 0 0 0 0 ] [ 1 1.16667 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .5 m 0 .50625 L s [(-3)] 0 .4875 0 1 Mshowa .16667 .5 m .16667 .50625 L s [(-2)] .16667 .4875 0 1 Mshowa .33333 .5 m .33333 .50625 L s [(-1)] .33333 .4875 0 1 Mshowa .66667 .5 m .66667 .50625 L s [(1)] .66667 .4875 0 1 Mshowa .83333 .5 m .83333 .50625 L s [(2)] .83333 .4875 0 1 Mshowa 1 .5 m 1 .50625 L s [(3)] 1 .4875 0 1 Mshowa .125 Mabswid .03333 .5 m .03333 .50375 L s .06667 .5 m .06667 .50375 L s .1 .5 m .1 .50375 L s .13333 .5 m .13333 .50375 L s .2 .5 m .2 .50375 L s .23333 .5 m .23333 .50375 L s .26667 .5 m .26667 .50375 L s .3 .5 m .3 .50375 L s .36667 .5 m .36667 .50375 L s .4 .5 m .4 .50375 L s .43333 .5 m .43333 .50375 L s .46667 .5 m .46667 .50375 L s .53333 .5 m .53333 .50375 L s .56667 .5 m .56667 .50375 L s .6 .5 m .6 .50375 L s .63333 .5 m .63333 .50375 L s .7 .5 m .7 .50375 L s .73333 .5 m .73333 .50375 L s .76667 .5 m .76667 .50375 L s .8 .5 m .8 .50375 L s .86667 .5 m .86667 .50375 L s .9 .5 m .9 .50375 L s .93333 .5 m .93333 .50375 L s .96667 .5 m .96667 .50375 L s .25 Mabswid 0 .5 m 1 .5 L s gsave 1.025 .5 -61 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .5 0 m .50625 0 L s [(-3)] .4875 0 1 0 Mshowa .5 .16667 m .50625 .16667 L s [(-2)] .4875 .16667 1 0 Mshowa .5 .33333 m .50625 .33333 L s [(-1)] .4875 .33333 1 0 Mshowa .5 .66667 m .50625 .66667 L s [(1)] .4875 .66667 1 0 Mshowa .5 .83333 m .50625 .83333 L s [(2)] .4875 .83333 1 0 Mshowa .5 1 m .50625 1 L s [(3)] .4875 1 1 0 Mshowa .5 1.16667 m .50625 1.16667 L s [(4)] .4875 1.16667 1 0 Mshowa .125 Mabswid .5 .03333 m .50375 .03333 L s .5 .06667 m .50375 .06667 L s .5 .1 m .50375 .1 L s .5 .13333 m .50375 .13333 L s .5 .2 m .50375 .2 L s .5 .23333 m .50375 .23333 L s .5 .26667 m .50375 .26667 L s .5 .3 m .50375 .3 L s .5 .36667 m .50375 .36667 L s .5 .4 m .50375 .4 L s .5 .43333 m .50375 .43333 L s .5 .46667 m .50375 .46667 L s .5 .53333 m .50375 .53333 L s .5 .56667 m .50375 .56667 L s .5 .6 m .50375 .6 L s .5 .63333 m .50375 .63333 L s .5 .7 m .50375 .7 L s .5 .73333 m .50375 .73333 L s .5 .76667 m .50375 .76667 L s .5 .8 m .50375 .8 L s .5 .86667 m .50375 .86667 L s .5 .9 m .50375 .9 L s .5 .93333 m .50375 .93333 L s .5 .96667 m .50375 .96667 L s .5 1.03333 m .50375 1.03333 L s .5 1.06667 m .50375 1.06667 L s .5 1.1 m .50375 1.1 L s .5 1.13333 m .50375 1.13333 L s .25 Mabswid .5 0 m .5 1.16667 L s gsave .5 1.19167 -66 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (y) show 69.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 1.16667 L 0 1.16667 L closepath clip newpath 1 0 0 r .5 Mabswid 0 .5083 m .04057 .51058 L .08481 .5138 L .12636 .51771 L .16632 .52251 L .20885 .52905 L .2498 .53714 L .29331 .54822 L .33524 .56202 L .37557 .579 L .41848 .6022 L .4598 .63095 L .49953 .6662 L .54183 .71422 L .58254 .77348 L .62583 .85459 L .66752 .95538 L .70762 1.07925 L s .70762 1.07925 m .72969 1.16667 L s .5 .5 0 r 0 0 m .04057 .04057 L .08481 .08481 L .12636 .12636 L .16632 .16632 L .20885 .20885 L .2498 .2498 L .29331 .29331 L .33524 .33524 L .37557 .37557 L .41848 .41848 L .4598 .4598 L .49953 .49953 L .54183 .54183 L .58254 .58254 L .62583 .62583 L .66752 .66752 L .70762 .70762 L .7503 .7503 L .79139 .79139 L .83505 .83505 L .87712 .87712 L .9176 .9176 L .96065 .96065 L 1 1 L s 0 .5 1 r .50834 0 m .51085 .04476 L .51599 .10929 L .52162 .1596 L .53207 .22533 L .54183 .26961 L .56148 .33378 L .58254 .38288 L .60484 .42275 L .62597 .45334 L .66622 .49955 L .70904 .53775 L .75027 .56776 L .78991 .59226 L .83212 .61492 L .87274 .63415 L .91594 .65242 L .95754 .66831 L .99756 .68229 L 1 .6831 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{246.813, 287.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ Nagu n\[ADoubleDot]ha, andis programm ka teada, et funktsiooni ln(x) (Log[x]) \ ei saa negatiivsete v\[ADoubleDot]\[ADoubleDot]rtuste ja nulli kohal leida. \ Kuiv\[OTilde]rd tegemist on kolme funktsiooni graafikuga, siis on ka \ PlotStyle-s iga funktsiooni jaoks v\[ADoubleDot]rv \[ADoubleDot]ra m\ \[ADoubleDot]\[ADoubleDot]ratud, st PlotStyle's on tegemist listiga.\ \>", "Text"], Cell[BoxData[ \(funkt[x_] := 2*Sin[2 x]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[funkt[x], {x, 0, 12}, TextStyle \[Rule] {FontSlant -> "\", \ FontSize \[Rule] 12}, \[IndentingNewLine]Ticks \[Rule] {{{1.5, "\"}, {3, "\<2a\ \>"}, 8}, Automatic}, Epilog \[Rule] {Text["\", {8.7, 0.8}, {0, 0}]}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0793651 0.309015 0.147152 [ [.14286 .29652 -5.59375 -15.1875 ] [.14286 .29652 5.59375 0 ] [.2619 .29652 -9.1875 -15.1875 ] [.2619 .29652 9.1875 0 ] [.65873 .29652 -5.59375 -15.1875 ] [.65873 .29652 5.59375 0 ] [.01131 .01471 -19.125 -7.59375 ] [.01131 .01471 0 7.59375 ] [.01131 .16186 -19.125 -7.59375 ] [.01131 .16186 0 7.59375 ] [.01131 .45617 -11.1875 -7.59375 ] [.01131 .45617 0 7.59375 ] [.01131 .60332 -11.1875 -7.59375 ] [.01131 .60332 0 7.59375 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .14286 .30902 m .14286 .31527 L s gsave .14286 .29652 -66.5938 -19.1875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.1875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (a) show 70.188 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .2619 .30902 m .2619 .31527 L s gsave .2619 .29652 -70.1875 -19.1875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.1875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 70.188 14.938 moveto (a) show 77.375 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .65873 .30902 m .65873 .31527 L s gsave .65873 .29652 -66.5938 -19.1875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.1875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (8) show 1.000 setlinewidth grestore 0 .30902 m 1 .30902 L s .02381 .01471 m .03006 .01471 L s gsave .01131 .01471 -80.125 -11.5938 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.1875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.938 moveto %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 70.938 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 1.000 setlinewidth grestore .02381 .16186 m .03006 .16186 L s gsave .01131 .16186 -80.125 -11.5938 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.1875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.938 moveto %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 70.938 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 1.000 setlinewidth grestore .02381 .45617 m .03006 .45617 L s gsave .01131 .45617 -72.1875 -11.5938 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.1875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 1.000 setlinewidth grestore .02381 .60332 m .03006 .60332 L s gsave .01131 .60332 -72.1875 -11.5938 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.1875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 1.000 setlinewidth grestore .125 Mabswid .02381 .04414 m .02756 .04414 L s .02381 .07357 m .02756 .07357 L s .02381 .103 m .02756 .103 L s .02381 .13243 m .02756 .13243 L s .02381 .19129 m .02756 .19129 L s .02381 .22072 m .02756 .22072 L s .02381 .25015 m .02756 .25015 L s .02381 .27958 m .02756 .27958 L s .02381 .33845 m .02756 .33845 L s .02381 .36788 m .02756 .36788 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .4856 m .02756 .4856 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .30902 m .04262 .44334 L .0522 .50205 L .06244 .55238 L .0679 .57275 L .07286 .58697 L .07525 .59229 L .07784 .5969 L .07903 .5986 L .08029 .60013 L .08145 .60126 L .08255 .60212 L .0832 .60251 L .08392 .60286 L .08516 .60323 L .08586 .60331 L .08662 .6033 L .08732 .60319 L .08797 .60301 L .08922 .60243 L .08993 .60198 L .09058 .60148 L .09304 .59889 L .09442 .59694 L .09571 .5948 L .09865 .58882 L .10458 .57212 L .10959 .55344 L .11503 .52872 L .12493 .47356 L .14349 .34591 L .16287 .20457 L .17317 .13746 L .18427 .07811 L .18942 .05645 L .19484 .03823 L .19946 .02666 L .20208 .0218 L .20452 .0184 L .20571 .01714 L .207 .01607 L .20822 .01534 L .20934 .01491 L .21035 .01473 L .21147 .01475 L .21263 .01502 L .21372 .0155 L .21499 .01634 L .21619 .01741 L .21845 .02015 L Mistroke .22088 .02415 L .22354 .02972 L .22887 .04466 L .23388 .06307 L .24325 .10769 L .26423 .2435 L .28265 .37886 L .2931 .45085 L .30284 .50926 L .31249 .55529 L .31789 .5749 L .32281 .58847 L .32551 .59409 L .32801 .59812 L .32931 .59977 L .33074 .60123 L .33146 .60182 L .33224 .60234 L .33297 .60273 L .33365 .60301 L .33488 .60329 L .33603 .60329 L .33729 .60301 L .338 .60272 L .33864 .60238 L .33994 .60146 L .34134 .60011 L .34389 .59672 L .34626 .59252 L .3488 .58689 L .35338 .57386 L .35883 .55379 L .36381 .53144 L .38486 .40333 L .40554 .25207 L .41463 .18796 L .42468 .12463 L .43361 .0781 L .4383 .05819 L .44324 .04101 L .44577 .0338 L .44854 .02719 L .45109 .02233 L .45341 .01893 L .45464 .01753 L .45581 .01647 L .45703 .01561 L .45773 .01526 L .45836 .01501 L .45943 .01476 L Mistroke .4606 .01473 L .46183 .01498 L .46297 .01546 L .46422 .01627 L .46555 .01744 L .46794 .02038 L .47079 .02524 L .47336 .0309 L .47845 .04548 L .48324 .06316 L .49214 .10532 L .50177 .1623 L .52133 .30051 L .54279 .45318 L .55266 .51188 L .55809 .53907 L .56323 .56086 L .56801 .57733 L .57053 .58447 L .5732 .59082 L .57545 .59517 L .57793 .59891 L .57901 .60019 L .58018 .60132 L .58129 .60216 L .5823 .60273 L .58358 .60318 L .58478 .60332 L .58587 .60321 L .58704 .60285 L .58832 .60216 L .58897 .6017 L .58968 .6011 L .59211 .59835 L .59438 .59479 L .59683 .58993 L .60123 .57846 L .60679 .55932 L .61206 .53662 L .62194 .4836 L .66021 .21387 L .67037 .1464 L .67993 .09257 L .68523 .06795 L .69095 .0462 L .69348 .03829 L .69615 .03115 L .69844 .02602 L .70092 .02152 L .70225 .01957 L Mistroke .70348 .01806 L .70463 .0169 L .7059 .0159 L .70704 .01527 L .7081 .01489 L .70923 .01472 L .71044 .0148 L .71174 .01519 L .71248 .01555 L .71316 .01598 L .71441 .01699 L .71575 .01839 L .7183 .02196 L .72062 .02623 L .72515 .03739 L .73006 .05344 L .73897 .09232 L .7589 .21494 L .77996 .36904 L .79015 .44027 L .79981 .49989 L .80921 .54714 L .81335 .56384 L .81792 .57906 L .82245 .59063 L .82493 .59542 L .82726 .5989 L .8285 .60035 L .82981 .60157 L .83092 .60235 L .83215 .60295 L .83347 .60328 L .8342 .60332 L .83488 .60327 L .83618 .60293 L .83742 .60232 L .83862 .60144 L .83995 .60017 L .84264 .5966 L .84512 .59212 L .84745 .58692 L .85269 .57173 L .85833 .55032 L .86845 .49998 L .87949 .43114 L .89959 .2859 L .91059 .20651 L .92094 .13883 L .93102 .08397 L .93544 .0643 L Mistroke .94028 .04621 L .94462 .03331 L .94868 .02425 L .95092 .02051 L .95296 .01791 L .95408 .01679 L .95531 .01585 L .95647 .01522 L .95754 .01486 L .95861 .01472 L .95976 .0148 L .96085 .0151 L .96184 .01557 L .96295 .01631 L .96415 .01738 L .96659 .02035 L .96899 .02436 L .97156 .02979 L .97619 .0425 L Mfstroke gsave .71429 .42674 -88.1563 -11.5938 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.1875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (Sin) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 84.563 14.938 moveto (H) show 91.750 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 98.938 14.938 moveto (x) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 106.125 14.938 moveto (L) show 113.313 14.938 moveto %%IncludeResource: font Courier-Italic %%IncludeFont: Courier-Italic /Courier-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ StyleBox["valik\t\t\tvaikv\[ADoubleDot]\[ADoubleDot]rtus\n", FontSlant->"Italic"], "Axes\t\t\tAutomatic \tkas teljed lisada, ntx Axes->No (Yes)\nAxesLabel\t\t\ None\t\tmillised t\[ADoubleDot]hised telgede juurde panna, nt\n\t\t\t\t\t\ AxesLabel->{\"a\",\"b/s\"}\nAxesOrigin\t\tAutomatic\tmillises punktis asub \ telgede ristumiskoht (nullpunkt)\n\t\t\t\t\tnt AxesOrigin->{2,0}\nFrame\t\t\t\ False\t\tkas t\[OTilde]mmata kast \[UDoubleDot]mber joonise True v\[OTilde]i \ False \n\t\t\t\t\tnt Frame->True\nGridLines\t\tNone\t\tabijooned. Automatic \ lisab iga olulisema v\[ADoubleDot]\[ADoubleDot]rtuse kohale joone\nPlotRange\t\ \tAutomatic\tmilline vahemik joonisele pannakse. Tihti joonistab programm\n\t\ \t\t\t\t\"k\[OTilde]ige huvitavama\" piirkonna, mitte k\[OTilde]ike, \ vastupidine oleks\n\t\t\t\t\tPlotRange->All" }], "Text", Background->GrayLevel[0.900008]], Cell["K\[OTilde]ikv\[OTilde]imalikke valikuid saab leida nn 'help-k\ \[ADoubleDot]su abil:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(?? Plot\)], "Input"], Cell[BoxData[ RowBox[{"\<\"Plot[f, {x, xmin, xmax}] generates a plot of f as a function \ of x from xmin to xmax. Plot[{f1, f2, ... }, {x, xmin, xmax}] plots several \ functions fi.\"\>", " ", ButtonBox[ StyleBox["More\[Ellipsis]", "SR"], ButtonData:>"Plot", Active->True, ButtonStyle->"RefGuideLink"]}]], "Print", CellTags->"Info3284449932-5100889"], Cell[BoxData[ InterpretationBox[GridBox[{ {\(Attributes[Plot] = {HoldAll, Protected}\)}, {" "}, {GridBox[{ {\(Options[Plot] = {AspectRatio \[Rule] 1\/GoldenRatio, Axes \[Rule] Automatic, AxesLabel \[Rule] None, AxesOrigin \[Rule] Automatic, AxesStyle \[Rule] Automatic, Background \[Rule] Automatic, ColorOutput \[Rule] Automatic, Compiled \[Rule] True, DefaultColor \[Rule] Automatic, Epilog \[Rule] {}, Frame \[Rule] False, FrameLabel \[Rule] None, FrameStyle \[Rule] Automatic, FrameTicks \[Rule] Automatic, GridLines \[Rule] None, ImageSize \[Rule] Automatic, MaxBend \[Rule] 10.`, PlotDivision \[Rule] 30.`, PlotLabel \[Rule] None, PlotPoints \[Rule] 25, PlotRange \[Rule] Automatic, PlotRegion \[Rule] Automatic, PlotStyle \[Rule] Automatic, Prolog \[Rule] {}, RotateLabel \[Rule] True, Ticks \[Rule] Automatic, DefaultFont \[RuleDelayed] $DefaultFont, DisplayFunction \[RuleDelayed] $DisplayFunction, FormatType \[RuleDelayed] $FormatType, TextStyle \[RuleDelayed] $TextStyle}\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "Plot"], Editable->False]], "Print", CellTags->"Info3284449932-5100889"] }, Open ]], Cell["\<\ Jooniste kujundamisel on abiks veel lisapaketid (vt Help-men\[UDoubleDot]\ \[UDoubleDot]st Add-ons, Standard Packages, Graphics).\ \>", "Text"], Cell[CellGroupData[{ Cell["4.2. Joonised ruumis.", "Subsubtitle"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`Plot3D[ f, {x, x\_min, x\_max}, {y, y\_min, y\_max}]\)]], "\tteeb kolmem\[OTilde]\[OTilde]tmelise joonise kui funktsiooni kahest \n\t\ \t\t\t\t\tmuutujast x ja y" }], "Text", Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot3D[x\^2 + 2 y\^2, {x, \(-2\), 2}, {y, \(-2\), 2}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .81114 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% SurfaceGraphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -7.378e-017 1.04977 -0.0679587 1.04977 [ [.02757 .24618 -12 -8.70276 ] [.02757 .24618 0 .29724 ] [.17646 .18758 -11.7989 -9 ] [.17646 .18758 .20112 0 ] [.3345 .12542 -5.5867 -9 ] [.3345 .12542 .4133 0 ] [.50253 .05935 -5.27396 -9 ] [.50253 .05935 .72604 0 ] [.68156 -0.01098 -4.96123 -9 ] [.68156 -0.01098 1.03877 0 ] [.70096 -0.00478 0 -6.26206 ] [.70096 -0.00478 12 2.73794 ] [.78313 .12104 0 -6.13858 ] [.78313 .12104 12 2.86142 ] [.8565 .23339 0 -6.03127 ] [.8565 .23339 6 2.96873 ] [.9224 .33431 0 -5.93715 ] [.9224 .33431 6 3.06285 ] [.98191 .42546 0 -5.85393 ] [.98191 .42546 6 3.14607 ] [.02411 .26511 -6 -2.74232 ] [.02411 .26511 0 6.25768 ] [.0099 .3542 -6 -2.81773 ] [.0099 .3542 0 6.18227 ] [-0.00516 .4486 -12 -2.89811 ] [-0.00516 .4486 0 6.10189 ] [ 0 0 0 0 ] [ 1 .81114 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .03716 .25514 m .68874 0 L s .03716 .25514 m .04196 .25962 L s [(-2)] .02757 .24618 1 .93395 Mshowa .18558 .19702 m .19014 .20174 L s [(-1)] .17646 .18758 .96648 1 Mshowa .34306 .13535 m .34735 .14032 L s [(0)] .3345 .12542 .86223 1 Mshowa .51046 .06981 m .51442 .07504 L s [(1)] .50253 .05935 .75799 1 Mshowa .68874 0 m .69233 .00549 L s [(2)] .68156 -0.01098 .65374 1 Mshowa .125 Mabswid .06616 .24378 m .06901 .2465 L s .09549 .2323 m .09832 .23504 L s .12517 .22067 m .12797 .22345 L s .1552 .20892 m .15797 .21172 L s .21633 .18498 m .21903 .18784 L s .24744 .1728 m .25012 .17569 L s .27893 .16047 m .28157 .16339 L s .3108 .14799 m .31341 .15094 L s .37572 .12257 m .37826 .12558 L s .40878 .10962 m .41128 .11266 L s .44225 .09652 m .44471 .09959 L s .47614 .08324 m .47856 .08635 L s .54521 .0562 m .54755 .05937 L s .58041 .04242 m .5827 .04562 L s .61605 .02846 m .6183 .03169 L s .65216 .01432 m .65436 .01759 L s .25 Mabswid .68874 0 m .96935 .42924 L s .68874 0 m .68263 .00239 L s [(-2)] .70096 -0.00478 -1 .39157 Mshowa .7708 .12553 m .76464 .12778 L s [(-1)] .78313 .12104 -1 .36413 Mshowa .84407 .23761 m .83786 .23973 L s [(0)] .8565 .23339 -1 .34028 Mshowa .9099 .3383 m .90365 .34029 L s [(1)] .9224 .33431 -1 .31937 Mshowa .96935 .42924 m .96306 .43113 L s [(2)] .98191 .42546 -1 .30087 Mshowa .125 Mabswid .70593 .0263 m .70226 .02771 L s .72272 .05198 m .71904 .05338 L s .73912 .07706 m .73543 .07845 L s .75514 .10158 m .75145 .10294 L s .78611 .14895 m .78241 .15028 L s .80108 .17185 m .79737 .17317 L s .81573 .19425 m .81201 .19555 L s .83006 .21617 m .82633 .21745 L s .8578 .2586 m .85407 .25986 L s .87123 .27915 m .8675 .28039 L s .88439 .29928 m .88065 .3005 L s .89727 .31899 m .89353 .3202 L s .92227 .35722 m .91851 .3584 L s .93439 .37576 m .93063 .37693 L s .94627 .39394 m .94251 .3951 L s .95792 .41176 m .95416 .41291 L s .25 Mabswid .03716 .25514 m 0 .48963 L s .03634 .26033 m .04245 .25795 L s [(0)] .02411 .26511 1 -0.3906 Mshowa .02219 .3496 m .02834 .34731 L s [(5)] .0099 .3542 1 -0.37384 Mshowa .0072 .4442 m .01338 .44199 L s [(10)] -0.00516 .4486 1 -0.35598 Mshowa .125 Mabswid .03357 .27778 m .03724 .27636 L s .03077 .29543 m .03445 .29402 L s .02795 .31328 m .03162 .31188 L s .02508 .33134 m .02877 .32995 L s .01926 .36808 m .02295 .36671 L s .0163 .38677 m .02 .38542 L s .0133 .40569 m .017 .40435 L s .01027 .42483 m .01397 .4235 L s .00409 .46379 m .00781 .46249 L s .00095 .48363 m .00467 .48234 L s .25 Mabswid .03716 .25514 m 0 .48963 L s 0 .48963 m .39787 .81114 L s .39787 .81114 m .40529 .59895 L s .40529 .59895 m .03716 .25514 L s .68874 0 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .03716 .25514 m 0 .48963 L s 0 .48963 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .68874 0 m .03716 .25514 L s .40529 .59895 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .39787 .81114 L s .39787 .81114 m .40529 .59895 L s 0 0 m 1 0 L 1 .81114 L 0 .81114 L closepath clip newpath .5 Mabswid .702 .593 .731 r .37622 .74903 .39806 .80578 .43742 .77665 .41565 .71971 Metetra .693 .588 .734 r .41565 .71971 .43742 .77665 .47689 .75028 .45518 .69311 Metetra .684 .583 .737 r .45518 .69311 .47689 .75028 .51658 .72664 .4949 .66919 Metetra .674 .578 .74 r .4949 .66919 .51658 .72664 .55658 .70569 .53493 .64792 Metetra .663 .573 .743 r .53493 .64792 .55658 .70569 .597 .68741 .57535 .62929 Metetra .652 .567 .746 r .57535 .62929 .597 .68741 .63794 .67182 .61627 .61329 Metetra .641 .56 .748 r .61627 .61329 .63794 .67182 .67951 .65891 .65781 .59993 Metetra .629 .554 .751 r .65781 .59993 .67951 .65891 .72184 .64871 .70009 .58924 Metetra .616 .547 .754 r .70009 .58924 .72184 .64871 .76504 .64126 .74323 .58125 Metetra .603 .539 .756 r .74323 .58125 .76504 .64126 .80924 .63662 .78735 .576 Metetra .589 .531 .758 r .78735 .576 .80924 .63662 .8546 .63486 .83261 .57358 Metetra .575 .523 .76 r .83261 .57358 .8546 .63486 .90127 .63606 .87917 .57406 Metetra .561 .515 .761 r .87917 .57406 .90127 .63606 .94941 .64033 .92718 .57756 Metetra .546 .506 .763 r .92718 .57756 .94941 .64033 .99922 .6478 .97684 .58419 Metetra .711 .611 .743 r .35399 .69765 .37622 .74903 .41565 .71971 .39355 .66809 Metetra .702 .606 .747 r .39355 .66809 .41565 .71971 .45518 .69311 .43319 .64122 Metetra .692 .601 .75 r .43319 .64122 .45518 .69311 .4949 .66919 .47302 .61701 Metetra .681 .596 .754 r .47302 .61701 .4949 .66919 .53493 .64792 .51312 .59541 Metetra .67 .59 .757 r .51312 .59541 .53493 .64792 .57535 .62929 .55361 .57642 Metetra .658 .584 .761 r .55361 .57642 .57535 .62929 .61627 .61329 .59459 .56002 Metetra .645 .578 .764 r .59459 .56002 .61627 .61329 .65781 .59993 .63617 .54622 Metetra .632 .571 .767 r .63617 .54622 .65781 .59993 .70009 .58924 .67847 .53505 Metetra .618 .563 .77 r .67847 .53505 .70009 .58924 .74323 .58125 .72162 .52654 Metetra .604 .555 .773 r .72162 .52654 .74323 .58125 .78735 .576 .76574 .52073 Metetra .589 .547 .776 r .76574 .52073 .78735 .576 .83261 .57358 .81099 .5177 Metetra .573 .538 .778 r .81099 .5177 .83261 .57358 .87917 .57406 .85751 .51753 Metetra .557 .529 .78 r .85751 .51753 .87917 .57406 .92718 .57756 .90548 .52032 Metetra .54 .519 .781 r .90548 .52032 .92718 .57756 .97684 .58419 .95509 .52618 Metetra .721 .631 .756 r .33124 .65144 .35399 .69765 .39355 .66809 .371 .62161 Metetra .711 .626 .761 r .371 .62161 .39355 .66809 .43319 .64122 .41082 .59444 Metetra .701 .622 .765 r .41082 .59444 .43319 .64122 .47302 .61701 .45081 .56991 Metetra .689 .617 .77 r .45081 .56991 .47302 .61701 .51312 .59541 .49106 .54796 Metetra .677 .611 .774 r .49106 .54796 .51312 .59541 .55361 .57642 .53169 .5286 Metetra .664 .605 .778 r .53169 .5286 .55361 .57642 .59459 .56002 .57279 .5118 Metetra .651 .598 .782 r .57279 .5118 .59459 .56002 .63617 .54622 .61448 .49757 Metetra .636 .591 .786 r .61448 .49757 .63617 .54622 .67847 .53505 .65687 .48594 Metetra .621 .583 .79 r .65687 .48594 .67847 .53505 .72162 .52654 .70011 .47694 Metetra .605 .574 .793 r .70011 .47694 .72162 .52654 .76574 .52073 .7443 .47061 Metetra .588 .565 .796 r .7443 .47061 .76574 .52073 .81099 .5177 .78961 .46701 Metetra .57 .556 .799 r .78961 .46701 .81099 .5177 .85751 .51753 .83619 .46624 Metetra .552 .546 .801 r .83619 .46624 .85751 .51753 .90548 .52032 .88421 .46838 Metetra .534 .535 .803 r .88421 .46838 .90548 .52032 .95509 .52618 .93386 .47356 Metetra .732 .654 .772 r .30785 .61028 .33124 .65144 .371 .62161 .34788 .58013 Metetra .722 .65 .777 r .34788 .58013 .371 .62161 .41082 .59444 .38795 .55264 Metetra .711 .646 .783 r .38795 .55264 .41082 .59444 .45081 .56991 .42817 .52775 Metetra .698 .641 .788 r .42817 .52775 .45081 .56991 .49106 .54796 .46864 .50544 Metetra .685 .635 .793 r .46864 .50544 .49106 .54796 .53169 .5286 .50946 .48569 Metetra .671 .629 .799 r .50946 .48569 .53169 .5286 .57279 .5118 .55075 .46849 Metetra .656 .622 .804 r .55075 .46849 .57279 .5118 .61448 .49757 .59262 .45384 Metetra .64 .615 .808 r .59262 .45384 .61448 .49757 .65687 .48594 .63519 .44176 Metetra .623 .606 .813 r .63519 .44176 .65687 .48594 .70011 .47694 .67858 .43229 Metetra .605 .597 .817 r .67858 .43229 .70011 .47694 .7443 .47061 .72293 .42546 Metetra .586 .587 .82 r .72293 .42546 .7443 .47061 .78961 .46701 .76839 .42134 Metetra .567 .577 .823 r .76839 .42134 .78961 .46701 .83619 .46624 .81511 .42001 Metetra .546 .566 .826 r .81511 .42001 .83619 .46624 .88421 .46838 .86326 .42157 Metetra .525 .554 .827 r .86326 .42157 .88421 .46838 .93386 .47356 .91304 .42613 Metetra .744 .681 .789 r .2837 .57408 .30785 .61028 .34788 .58013 .32406 .54357 Metetra .734 .677 .796 r .32406 .54357 .34788 .58013 .38795 .55264 .36444 .51571 Metetra .722 .673 .802 r .36444 .51571 .38795 .55264 .42817 .52775 .40496 .49045 Metetra .709 .669 .809 r .40496 .49045 .42817 .52775 .46864 .50544 .44572 .46775 Metetra .694 .663 .815 r .44572 .46775 .46864 .50544 .50946 .48569 .48682 .44761 Metetra .679 .657 .822 r .48682 .44761 .50946 .48569 .55075 .46849 .52837 .42999 Metetra .662 .651 .828 r .52837 .42999 .55075 .46849 .59262 .45384 .57049 .41492 Metetra .645 .643 .834 r .57049 .41492 .59262 .45384 .63519 .44176 .6133 .4024 Metetra .625 .634 .839 r .6133 .4024 .63519 .44176 .67858 .43229 .65692 .39248 Metetra .605 .624 .844 r .65692 .39248 .67858 .43229 .72293 .42546 .70151 .38518 Metetra .584 .614 .848 r .70151 .38518 .72293 .42546 .76839 .42134 .74719 .38057 Metetra .561 .602 .851 r .74719 .38057 .76839 .42134 .81511 .42001 .79414 .37874 Metetra .537 .589 .854 r .79414 .37874 .81511 .42001 .86326 .42157 .84253 .37977 Metetra .513 .576 .856 r .84253 .37977 .86326 .42157 .91304 .42613 .89254 .38378 Metetra .758 .711 .808 r .25864 .54281 .2837 .57408 .32406 .54357 .2994 .51189 Metetra .746 .709 .816 r .2994 .51189 .32406 .54357 .36444 .51571 .34018 .48362 Metetra .734 .706 .824 r .34018 .48362 .36444 .51571 .40496 .49045 .38107 .45795 Metetra .72 .702 .832 r .38107 .45795 .40496 .49045 .44572 .46775 .42218 .43484 Metetra .704 .697 .84 r .42218 .43484 .44572 .46775 .48682 .44761 .46362 .41428 Metetra .687 .691 .848 r .46362 .41428 .48682 .44761 .52837 .42999 .50551 .39625 Metetra .669 .684 .856 r .50551 .39625 .52837 .42999 .57049 .41492 .54795 .38075 Metetra .648 .676 .863 r .54795 .38075 .57049 .41492 .6133 .4024 .59108 .36781 Metetra .627 .667 .869 r .59108 .36781 .6133 .4024 .65692 .39248 .63502 .35744 Metetra .603 .656 .875 r .63502 .35744 .65692 .39248 .70151 .38518 .67992 .3497 Metetra .579 .645 .88 r .67992 .3497 .70151 .38518 .74719 .38057 .72592 .34464 Metetra .552 .632 .884 r .72592 .34464 .74719 .38057 .79414 .37874 .77318 .34234 Metetra .525 .617 .887 r .77318 .34234 .79414 .37874 .84253 .37977 .8219 .3429 Metetra .496 .602 .888 r .8219 .3429 .84253 .37977 .89254 .38378 .87225 .34644 Metetra .772 .746 .829 r .23251 .51647 .25864 .54281 .2994 .51189 .27375 .48509 Metetra .76 .745 .839 r .27375 .48509 .2994 .51189 .34018 .48362 .31499 .45636 Metetra .746 .743 .849 r .31499 .45636 .34018 .48362 .38107 .45795 .35633 .43025 Metetra .731 .74 .858 r .35633 .43025 .38107 .45795 .42218 .43484 .39788 .4067 Metetra .714 .735 .868 r .39788 .4067 .42218 .43484 .46362 .41428 .43974 .38571 Metetra .695 .73 .878 r .43974 .38571 .46362 .41428 .50551 .39625 .48204 .36725 Metetra .674 .723 .887 r .48204 .36725 .50551 .39625 .54795 .38075 .52489 .35133 Metetra .651 .715 .895 r .52489 .35133 .54795 .38075 .59108 .36781 .56841 .33796 Metetra .626 .706 .903 r .56841 .33796 .59108 .36781 .63502 .35744 .61275 .32717 Metetra .599 .694 .91 r .61275 .32717 .63502 .35744 .67992 .3497 .65805 .31901 Metetra .569 .681 .915 r .65805 .31901 .67992 .3497 .72592 .34464 .70445 .31353 Metetra .538 .666 .92 r .70445 .31353 .72592 .34464 .77318 .34234 .75213 .31081 Metetra .506 .649 .922 r .75213 .31081 .77318 .34234 .8219 .3429 .80126 .31096 Metetra .472 .631 .923 r .80126 .31096 .8219 .3429 .87225 .34644 .85205 .31407 Metetra .787 .786 .852 r .20513 .49514 .23251 .51647 .27375 .48509 .24694 .46323 Metetra .774 .786 .863 r .24694 .46323 .27375 .48509 .31499 .45636 .28872 .434 Metetra .759 .785 .875 r .28872 .434 .31499 .45636 .35633 .43025 .33059 .4074 Metetra .741 .783 .886 r .33059 .4074 .35633 .43025 .39788 .4067 .37265 .38339 Metetra .722 .78 .898 r .37265 .38339 .39788 .4067 .43974 .38571 .41502 .36194 Metetra .701 .775 .909 r .41502 .36194 .43974 .38571 .48204 .36725 .4578 .34304 Metetra .676 .769 .92 r .4578 .34304 .48204 .36725 .52489 .35133 .50114 .32669 Metetra .65 .76 .93 r .50114 .32669 .52489 .35133 .56841 .33796 .54515 .3129 Metetra .62 .75 .939 r .54515 .3129 .56841 .33796 .61275 .32717 .58997 .3017 Metetra .588 .737 .946 r .58997 .3017 .61275 .32717 .65805 .31901 .63576 .29314 Metetra .553 .722 .952 r .63576 .29314 .65805 .31901 .70445 .31353 .68265 .28727 Metetra .515 .704 .956 r .68265 .28727 .70445 .31353 .75213 .31081 .73084 .28418 Metetra .476 .684 .957 r .73084 .28418 .75213 .31081 .80126 .31096 .7805 .28396 Metetra .435 .662 .957 r .7805 .28396 .80126 .31096 .85205 .31407 .83184 .28673 Metetra .8 .83 .874 r .1763 .47891 .20513 .49514 .24694 .46323 .21877 .44643 Metetra .786 .831 .887 r .21877 .44643 .24694 .46323 .28872 .434 .26118 .41664 Metetra .769 .832 .901 r .26118 .41664 .28872 .434 .33059 .4074 .30367 .38952 Metetra .749 .831 .914 r .30367 .38952 .33059 .4074 .37265 .38339 .34632 .365 Metetra .727 .829 .928 r .34632 .365 .37265 .38339 .41502 .36194 .38928 .34307 Metetra .702 .825 .941 r .38928 .34307 .41502 .36194 .4578 .34304 .43264 .32371 Metetra .673 .818 .953 r .43264 .32371 .4578 .34304 .50114 .32669 .47655 .30692 Metetra .641 .809 .964 r .47655 .30692 .50114 .32669 .54515 .3129 .52114 .29272 Metetra .605 .797 .973 r .52114 .29272 .54515 .3129 .58997 .3017 .56654 .28112 Metetra .566 .782 .98 r .56654 .28112 .58997 .3017 .63576 .29314 .6129 .27219 Metetra .523 .763 .984 r .6129 .27219 .63576 .29314 .68265 .28727 .6604 .26597 Metetra .478 .741 .986 r .6604 .26597 .68265 .28727 .73084 .28418 .70919 .26254 Metetra .429 .716 .984 r .70919 .26254 .73084 .28418 .7805 .28396 .75949 .26201 Metetra .38 .688 .98 r .75949 .26201 .7805 .28396 .83184 .28673 .8115 .2645 Metetra .811 .876 .894 r .1458 .46799 .1763 .47891 .21877 .44643 .18901 .43485 Metetra .794 .88 .909 r .18901 .43485 .21877 .44643 .26118 .41664 .23216 .40446 Metetra .774 .882 .924 r .23216 .40446 .26118 .41664 .30367 .38952 .27535 .37675 Metetra .751 .882 .939 r .27535 .37675 .30367 .38952 .34632 .365 .31869 .3517 Metetra .724 .88 .953 r .31869 .3517 .34632 .365 .38928 .34307 .36233 .32926 Metetra .693 .875 .966 r .36233 .32926 .38928 .34307 .43264 .32371 .40637 .30942 Metetra .658 .867 .978 r .40637 .30942 .43264 .32371 .47655 .30692 .45094 .29219 Metetra .618 .856 .988 r .45094 .29219 .47655 .30692 .52114 .29272 .4962 .27757 Metetra .574 .841 .995 r .4962 .27757 .52114 .29272 .56654 .28112 .54227 .26559 Metetra .525 .821 .999 r .54227 .26559 .56654 .28112 .6129 .27219 .58932 .2563 Metetra .472 .797 .999 r .58932 .2563 .6129 .27219 .6604 .26597 .63752 .24976 Metetra .416 .768 .996 r .63752 .24976 .6604 .26597 .70919 .26254 .68704 .24605 Metetra .358 .735 .988 r .68704 .24605 .70919 .26254 .75949 .26201 .73809 .24528 Metetra .299 .699 .976 r .73809 .24528 .75949 .26201 .8115 .2645 .79089 .24756 Metetra .814 .923 .909 r .11335 .46261 .1458 .46799 .18901 .43485 .15742 .42875 Metetra .793 .927 .924 r .15742 .42875 .18901 .43485 .23216 .40446 .20139 .39768 Metetra .769 .929 .938 r .20139 .39768 .23216 .40446 .27535 .37675 .24539 .36935 Metetra .74 .929 .952 r .24539 .36935 .27535 .37675 .31869 .3517 .28953 .34371 Metetra .706 .925 .965 r .28953 .34371 .31869 .3517 .36233 .32926 .33395 .32073 Metetra .667 .918 .976 r .33395 .32073 .36233 .32926 .40637 .30942 .37876 .3004 Metetra .623 .906 .984 r .37876 .3004 .40637 .30942 .45094 .29219 .42411 .28271 Metetra .572 .889 .989 r .42411 .28271 .45094 .29219 .4962 .27757 .47013 .26768 Metetra .517 .867 .99 r .47013 .26768 .4962 .27757 .54227 .26559 .51699 .25533 Metetra .456 .839 .986 r .51699 .25533 .54227 .26559 .58932 .2563 .56483 .24571 Metetra .392 .806 .977 r .56483 .24571 .58932 .2563 .63752 .24976 .61384 .23889 Metetra .325 .767 .964 r .61384 .23889 .63752 .24976 .68704 .24605 .66421 .23495 Metetra .258 .725 .946 r .66421 .23495 .68704 .24605 .73809 .24528 .71615 .23399 Metetra .19 .679 .924 r .71615 .23399 .73809 .24528 .79089 .24756 .76988 .23615 Metetra .805 .963 .911 r .07865 .46311 .11335 .46261 .15742 .42875 .12369 .42844 Metetra .778 .966 .923 r .12369 .42844 .15742 .42875 .20139 .39768 .16861 .39663 Metetra .746 .965 .935 r .16861 .39663 .20139 .39768 .24539 .36935 .21353 .36761 Metetra .708 .961 .944 r .21353 .36761 .24539 .36935 .28953 .34371 .25857 .34135 Metetra .664 .953 .951 r .25857 .34135 .28953 .34371 .33395 .32073 .30387 .3178 Metetra .614 .938 .954 r .30387 .3178 .33395 .32073 .37876 .3004 .34957 .29694 Metetra .558 .918 .953 r .34957 .29694 .37876 .3004 .42411 .28271 .3958 .27879 Metetra .495 .891 .948 r .3958 .27879 .42411 .28271 .47013 .26768 .44271 .26334 Metetra .427 .858 .937 r .44271 .26334 .47013 .26768 .51699 .25533 .49046 .25064 Metetra .356 .818 .921 r .49046 .25064 .51699 .25533 .56483 .24571 .53922 .24072 Metetra .282 .774 .899 r .53922 .24072 .56483 .24571 .61384 .23889 .58918 .23366 Metetra .208 .724 .874 r .58918 .23366 .61384 .23889 .66421 .23495 .64053 .22955 Metetra .135 .673 .846 r .64053 .22955 .66421 .23495 .71615 .23399 .69348 .22848 Metetra .065 .62 .815 r .69348 .22848 .71615 .23399 .76988 .23615 .74829 .23061 Metetra .776 .988 .894 r .04132 .46993 .07865 .46311 .12369 .42844 .08747 .43437 Metetra .74 .986 .9 r .08747 .43437 .12369 .42844 .16861 .39663 .13346 .40173 Metetra .698 .979 .903 r .13346 .40173 .16861 .39663 .21353 .36761 .17942 .37196 Metetra .649 .966 .903 r .17942 .37196 .21353 .36761 .25857 .34135 .22549 .34502 Metetra .592 .947 .898 r .22549 .34502 .25857 .34135 .30387 .3178 .27181 .32085 Metetra .529 .921 .889 r .27181 .32085 .30387 .3178 .34957 .29694 .31851 .29946 Metetra .461 .888 .874 r .31851 .29946 .34957 .29694 .3958 .27879 .36574 .28083 Metetra .387 .848 .855 r .36574 .28083 .3958 .27879 .44271 .26334 .41366 .26497 Metetra .311 .802 .83 r .41366 .26497 .44271 .26334 .49046 .25064 .46244 .25193 Metetra .233 .752 .801 r .46244 .25193 .49046 .25064 .53922 .24072 .51225 .24175 Metetra .156 .697 .769 r .51225 .24175 .53922 .24072 .58918 .23366 .56329 .2345 Metetra .081 .641 .736 r .56329 .2345 .58918 .23366 .64053 .22955 .61576 .23028 Metetra .61576 .23028 .64053 .22955 .69348 .22848 .66989 .22919 Metetra .057 0 0 r .66989 .22919 .69348 .22848 .74829 .23061 .72595 .2314 Metetra .724 .989 .85 r .00095 .48363 .04132 .46993 .08747 .43437 .04835 .44706 Metetra .677 .977 .846 r .04835 .44706 .08747 .43437 .13346 .40173 .09555 .41351 Metetra .622 .959 .837 r .09555 .41351 .13346 .40173 .17942 .37196 .14269 .38292 Metetra .56 .934 .823 r .14269 .38292 .17942 .37196 .22549 .34502 .18993 .35523 Metetra .493 .901 .805 r .18993 .35523 .22549 .34502 .27181 .32085 .23739 .33042 Metetra .42 .861 .782 r .23739 .33042 .27181 .32085 .31851 .29946 .28523 .30845 Metetra .343 .816 .754 r .28523 .30845 .31851 .29946 .36574 .28083 .3336 .28934 Metetra .264 .765 .722 r .3336 .28934 .36574 .28083 .41366 .26497 .38267 .27308 Metetra .186 .71 .687 r .38267 .27308 .41366 .26497 .46244 .25193 .43262 .25973 Metetra .43262 .25973 .46244 .25193 .51225 .24175 .48362 .24933 Metetra .48362 .24933 .51225 .24175 .56329 .2345 .53589 .24195 Metetra .033 0 0 r .53589 .24195 .56329 .2345 .61576 .23028 .58965 .2377 Metetra .097 0 0 r .58965 .2377 .61576 .23028 .66989 .22919 .64513 .2367 Metetra .156 0 0 r .64513 .2367 .66989 .22919 .72595 .2314 .70262 .2391 Metetra 0 g .25 Mabswid .68874 0 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .03716 .25514 m 0 .48963 L s 0 .48963 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .68874 0 m .03716 .25514 L s .03716 .25514 m .68874 0 L s .03716 .25514 m .04196 .25962 L s [(-2)] .02757 .24618 1 .93395 Mshowa .18558 .19702 m .19014 .20174 L s [(-1)] .17646 .18758 .96648 1 Mshowa .34306 .13535 m .34735 .14032 L s [(0)] .3345 .12542 .86223 1 Mshowa .51046 .06981 m .51442 .07504 L s [(1)] .50253 .05935 .75799 1 Mshowa .68874 0 m .69233 .00549 L s [(2)] .68156 -0.01098 .65374 1 Mshowa .125 Mabswid .06616 .24378 m .06901 .2465 L s .09549 .2323 m .09832 .23504 L s .12517 .22067 m .12797 .22345 L s .1552 .20892 m .15797 .21172 L s .21633 .18498 m .21903 .18784 L s .24744 .1728 m .25012 .17569 L s .27893 .16047 m .28157 .16339 L s .3108 .14799 m .31341 .15094 L s .37572 .12257 m .37826 .12558 L s .40878 .10962 m .41128 .11266 L s .44225 .09652 m .44471 .09959 L s .47614 .08324 m .47856 .08635 L s .54521 .0562 m .54755 .05937 L s .58041 .04242 m .5827 .04562 L s .61605 .02846 m .6183 .03169 L s .65216 .01432 m .65436 .01759 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 233.563}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] SurfaceGraphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot3D[2 y\ Sin[x\ y], {x, \(-1\), \[Pi]}, {y, \(-1\), 2}, AxesLabel \[Rule] {x, y, z}, \[IndentingNewLine]ViewPoint \[Rule] {1.6, \(-1.5\), 2}, Mesh -> False, PlotPoints \[Rule] 25, PlotLabel \[Rule] "\"]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .85741 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% SurfaceGraphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.0059453 1.00595 -0.0183071 1.00595 [ [.5 .86991 -62 0 ] [.5 .86991 62 12.5625 ] [.03202 .39335 -12 -7.07145 ] [.03202 .39335 0 1.92855 ] [.12317 .30973 -6 -7.25834 ] [.12317 .30973 0 1.74166 ] [.22264 .2185 -6 -7.47453 ] [.22264 .2185 0 1.52547 ] [.33161 .11857 -6 -7.72749 ] [.33161 .11857 0 1.27251 ] [.45152 .00864 -6 -8.02746 ] [.45152 .00864 0 .97254 ] [.17767 .17692 -10 -10.4564 ] [.17767 .17692 0 2.10614 ] [.48859 -0.00849 0 -8.62057 ] [.48859 -0.00849 12 .37943 ] [.66752 .13383 0 -8.11289 ] [.66752 .13383 6 .88711 ] [.82574 .25973 0 -7.71658 ] [.82574 .25973 6 1.28342 ] [.96664 .37189 0 -7.39863 ] [.96664 .37189 6 1.60137 ] [.79913 .16073 0 -11.0316 ] [.79913 .16073 10 1.5309 ] [.96754 .37595 0 -7.3917 ] [.96754 .37595 12 1.6083 ] [.97746 .42093 0 -7.31528 ] [.97746 .42093 12 1.68472 ] [.98782 .46787 0 -7.23605 ] [.98782 .46787 6 1.76395 ] [.99863 .51692 0 -7.15384 ] [.99863 .51692 6 1.84616 ] [1.00994 .56821 0 -7.0685 ] [1.00994 .56821 6 1.9315 ] [1.0415 .43503 0 -10.1007 ] [1.0415 .43503 10 2.46178 ] [ 0 0 0 0 ] [ 1 .85741 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g gsave .5 .86991 -123 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (z) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 69.000 12.813 moveto (H) show 75.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 81.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (,) show 87.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (y) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 93.000 12.813 moveto (L) show 105.000 12.813 moveto %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (=) show 117.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 123.000 12.813 moveto (y) show 135.000 12.813 moveto (sin) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 153.000 12.813 moveto (H) show 159.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 165.000 12.813 moveto %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (*) show 171.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (y) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 177.000 12.813 moveto (L) show 183.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .25 Mabswid [ ] 0 setdash .04294 .39959 m .47932 0 L s .04294 .39959 m .0484 .4027 L s [(-1)] .03202 .39335 1 .57143 Mshowa .13389 .3163 m .13925 .31959 L s [(0)] .12317 .30973 1 .61297 Mshowa .23313 .22543 m .23837 .2289 L s [(1)] .22264 .2185 1 .66101 Mshowa .34183 .1259 m .34694 .12956 L s [(2)] .33161 .11857 1 .71722 Mshowa .46141 .0164 m .46636 .02028 L s [(3)] .45152 .00864 1 .78388 Mshowa .125 Mabswid .06052 .38349 m .06378 .38538 L s .0784 .36712 m .08165 .36903 L s .09658 .35047 m .09982 .3524 L s .11507 .33353 m .1183 .33548 L s .15304 .29877 m .15625 .30076 L s .17253 .28092 m .17572 .28293 L s .19237 .26276 m .19555 .26479 L s .21257 .24426 m .21573 .24632 L s .25407 .20626 m .2572 .20836 L s .2754 .18673 m .27851 .18885 L s .29713 .16683 m .30023 .16898 L s .31927 .14656 m .32235 .14873 L s .36482 .10484 m .36787 .10707 L s .38827 .08338 m .39129 .08563 L s .41217 .06149 m .41518 .06376 L s .43655 .03917 m .43954 .04147 L s gsave .17767 .17692 -71 -14.4564 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 1.000 setlinewidth grestore .25 Mabswid .47932 0 m .95607 .3787 L s .47932 0 m .47468 .00425 L s [(-1)] .48859 -0.00849 -1 .91568 Mshowa .65771 .1417 m .65281 .14564 L s [(0)] .66752 .13383 -1 .80286 Mshowa .81551 .26704 m .81039 .2707 L s [(1)] .82574 .25973 -1 .7148 Mshowa .95607 .3787 m .95079 .38211 L s [(2)] .96664 .37189 -1 .64414 Mshowa .125 Mabswid .51684 .0298 m .51402 .03231 L s .5534 .05884 m .55055 .06132 L s .58904 .08716 m .58616 .08959 L s .6238 .11477 m .62089 .11717 L s .6908 .16799 m .68783 .17031 L s .72309 .19364 m .7201 .19593 L s .75463 .21869 m .75161 .22094 L s .78542 .24315 m .78238 .24537 L s .8449 .2904 m .84181 .29256 L s .87364 .31322 m .87052 .31535 L s .90173 .33553 m .8986 .33763 L s .9292 .35736 m .92605 .35943 L s gsave .79913 .16073 -61 -15.0316 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (y) show 1.000 setlinewidth grestore .25 Mabswid .95607 .3787 m 1 .5789 L s .95696 .38275 m .95167 .38615 L s [(-4)] .96754 .37595 -1 .6426 Mshowa .9668 .4276 m .96147 .43093 L s [(-2)] .97746 .42093 -1 .62562 Mshowa .97707 .4744 m .9717 .47767 L s [(0)] .98782 .46787 -1 .60801 Mshowa .9878 .5233 m .98238 .5265 L s [(2)] .99863 .51692 -1 .58974 Mshowa .99902 .57444 m .99356 .57756 L s [(4)] 1.00994 .56821 -1 .57078 Mshowa .125 Mabswid .95938 .39378 m .9562 .39581 L s .96183 .40494 m .95864 .40696 L s .9643 .41621 m .96111 .41822 L s .96933 .43911 m .96612 .4411 L s .97188 .45075 m .96867 .45273 L s .97446 .46251 m .97124 .46448 L s .97971 .48643 m .97648 .48838 L s .98238 .49858 m .97914 .50052 L s .98507 .51088 m .98183 .5128 L s .99056 .53587 m .9873 .53778 L s .99335 .54858 m .99008 .55048 L s .99617 .56144 m .9929 .56332 L s gsave 1.0415 .43503 -61 -14.1007 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (z) show 1.000 setlinewidth grestore .25 Mabswid .04294 .39959 m 0 .5994 L s 0 .5994 m .51065 .85741 L s .51065 .85741 m .50963 .66627 L s .50963 .66627 m .04294 .39959 L s .47932 0 m .95607 .3787 L s .95607 .3787 m 1 .5789 L s 1 .5789 m .47725 .19982 L s .47725 .19982 m .47932 0 L s .04294 .39959 m 0 .5994 L s 0 .5994 m .47725 .19982 L s .47725 .19982 m .47932 0 L s .47932 0 m .04294 .39959 L s .50963 .66627 m .95607 .3787 L s .95607 .3787 m 1 .5789 L s 1 .5789 m .51065 .85741 L s .51065 .85741 m .50963 .66627 L s 0 0 m 1 0 L 1 .85741 L 0 .85741 L closepath clip newpath .731 .75 .867 r .49278 .6696 .5097 .67792 .52562 .66023 .50877 .65556 Mtetra .546 .825 .998 r .50877 .65556 .52562 .66023 .54183 .65244 .52501 .64974 Mtetra 0 .518 .736 r .52501 .64974 .54183 .65244 .55854 .65436 .54168 .65179 Mtetra .463 0 0 r .54168 .65179 .55854 .65436 .57593 .66485 .55892 .66068 Mtetra .596 .028 0 r .55892 .66068 .57593 .66485 .59411 .68185 .57684 .67467 Mtetra .628 .063 0 r .57684 .67467 .59411 .68185 .61311 .70246 .59549 .69147 Mtetra .566 .002 0 r .59549 .69147 .61311 .70246 .63284 .72311 .6148 .70827 Mtetra 0 .174 .648 r .6148 .70827 .63284 .72311 .65307 .7399 .63463 .72208 Mtetra .056 .398 .855 r .63463 .72208 .65307 .7399 .67348 .74915 .65476 .73002 Mtetra .39 .546 .89 r .65476 .73002 .67348 .74915 .69366 .74798 .67488 .72972 Mtetra .595 .627 .854 r .67488 .72972 .69366 .74798 .71326 .73485 .69469 .71974 Mtetra .725 .685 .811 r .69469 .71974 .71326 .73485 .73198 .70994 .71394 .69982 Mtetra .819 .738 .775 r .71394 .69982 .73198 .70994 .74972 .6751 .73246 .67094 Mtetra .89 .79 .744 r .73246 .67094 .74972 .6751 .76658 .63348 .75025 .63514 Mtetra .941 .839 .715 r .75025 .63514 .76658 .63348 .78284 .58891 .76742 .59516 Mtetra .97 .884 .69 r .76742 .59516 .78284 .58891 .79893 .54533 .78425 .55408 Mtetra .973 .92 .678 r .78425 .55408 .79893 .54533 .81538 .50623 .8011 .51485 Mtetra .955 .95 .695 r .8011 .51485 .81538 .50623 .83272 .4744 .81838 .48004 Mtetra .919 .975 .766 r .81838 .48004 .83272 .4744 .85149 .45169 .83655 .45164 Mtetra .84 .959 .887 r .83655 .45164 .85149 .45169 .87212 .43903 .85601 .43095 Mtetra .67 .819 .955 r .85601 .43095 .87212 .43903 .89495 .4364 .87714 .41861 Mtetra .472 .601 .899 r .87714 .41861 .89495 .4364 .92014 .44283 .9002 .41453 Mtetra .345 .437 .812 r .9002 .41453 .92014 .44283 .94762 .45643 .92534 .41794 Mtetra .287 .346 .75 r .92534 .41794 .94762 .45643 .97707 .4744 .95253 .42737 Mtetra .699 .788 .92 r .47563 .66277 .49278 .6696 .50877 .65556 .49164 .65165 Mtetra .461 .817 .997 r .49164 .65165 .50877 .65556 .52501 .64974 .50789 .64721 Mtetra 0 .528 .739 r .50789 .64721 .52501 .64974 .54168 .65179 .5245 .64901 Mtetra .382 0 0 r .5245 .64901 .54168 .65179 .55892 .66068 .54161 .65614 Mtetra .507 0 0 r .54161 .65614 .55892 .66068 .57684 .67467 .55932 .66721 Mtetra .527 0 0 r .55932 .66721 .57684 .67467 .59549 .69147 .57765 .68039 Mtetra .439 0 0 r .57765 .68039 .59549 .69147 .6148 .70827 .59661 .69356 Mtetra 0 .275 .744 r .59661 .69356 .6148 .70827 .63463 .72208 .61609 .70444 Mtetra .112 .434 .874 r .61609 .70444 .63463 .72208 .65476 .73002 .63593 .71081 Mtetra .374 .54 .891 r .63593 .71081 .65476 .73002 .67488 .72972 .65593 .7108 Mtetra .552 .61 .864 r .65593 .7108 .67488 .72972 .69469 .71974 .67584 .70313 Mtetra .676 .666 .832 r .67584 .70313 .69469 .71974 .71394 .69982 .69545 .68731 Mtetra .772 .72 .805 r .69545 .68731 .71394 .69982 .73246 .67094 .71459 .66372 Mtetra .849 .776 .78 r .71459 .66372 .73246 .67094 .75025 .63514 .73317 .63355 Mtetra .91 .831 .755 r .73317 .63355 .75025 .63514 .76742 .59516 .75122 .59865 Mtetra .951 .881 .729 r .75122 .59865 .76742 .59516 .78425 .55408 .76887 .56124 Mtetra .966 .92 .706 r .76887 .56124 .78425 .55408 .8011 .51485 .78634 .52365 Mtetra .957 .948 .695 r .78634 .52365 .8011 .51485 .81838 .48004 .80392 .48808 Mtetra .932 .97 .718 r .80392 .48808 .81838 .48004 .83655 .45164 .82196 .45639 Mtetra .896 .985 .793 r .82196 .45639 .83655 .45164 .85601 .43095 .8408 .43006 Mtetra .824 .954 .901 r .8408 .43006 .85601 .43095 .87714 .41861 .86078 .41004 Mtetra .68 .816 .948 r .86078 .41004 .87714 .41861 .9002 .41453 .8822 .39682 Mtetra .515 .622 .896 r .8822 .39682 .9002 .41453 .92534 .41794 .90531 .39034 Mtetra .401 .472 .818 r .90531 .39034 .92534 .41794 .95253 .42737 .93024 .39006 Mtetra .653 .821 .964 r .45821 .65725 .47563 .66277 .49164 .65165 .47422 .64834 Mtetra .392 .801 .98 r .47422 .64834 .49164 .65165 .50789 .64721 .49045 .64472 Mtetra 0 .562 .767 r .49045 .64472 .50789 .64721 .5245 .64901 .50701 .64594 Mtetra .275 0 0 r .50701 .64594 .5245 .64901 .54161 .65614 .52401 .65122 Mtetra .384 0 0 r .52401 .65122 .54161 .65614 .55932 .66721 .54152 .65944 Mtetra .385 0 0 r .54152 .65944 .55932 .66721 .57765 .68039 .55961 .66923 Mtetra 0 .267 .685 r .55961 .66923 .57765 .68039 .59661 .69356 .57825 .67898 Mtetra 0 .374 .825 r .57825 .67898 .59661 .69356 .61609 .70444 .59742 .687 Mtetra .175 .472 .892 r .59742 .687 .61609 .70444 .63593 .71081 .61699 .69163 Mtetra .373 .542 .893 r .61699 .69163 .63593 .71081 .65593 .7108 .63682 .69141 Mtetra .518 .595 .871 r .63682 .69141 .65593 .7108 .67584 .70313 .65675 .68527 Mtetra .629 .645 .847 r .65675 .68527 .67584 .70313 .69545 .68731 .67658 .67264 Mtetra .721 .698 .827 r .67658 .67264 .69545 .68731 .71459 .66372 .69617 .65352 Mtetra .8 .754 .811 r .69617 .65352 .71459 .66372 .73317 .63355 .7154 .62852 Mtetra .868 .813 .794 r .7154 .62852 .73317 .63355 .75122 .59865 .73423 .59877 Mtetra .92 .87 .773 r .73423 .59877 .75122 .59865 .76887 .56124 .75269 .56574 Mtetra .949 .917 .747 r .75269 .56574 .76887 .56124 .78634 .52365 .7709 .53114 Mtetra .952 .95 .722 r .7709 .53114 .78634 .52365 .80392 .48808 .78903 .49669 Mtetra .934 .969 .711 r .78903 .49669 .80392 .48808 .82196 .45639 .80731 .464 Mtetra .907 .983 .735 r .80731 .464 .82196 .45639 .8408 .43006 .82601 .43447 Mtetra .877 .991 .806 r .82601 .43447 .8408 .43006 .86078 .41004 .84541 .40917 Mtetra .821 .959 .902 r .84541 .40917 .86078 .41004 .8822 .39682 .86578 .38888 Mtetra .708 .838 .944 r .86578 .38888 .8822 .39682 .90531 .39034 .88738 .37397 Mtetra .569 .665 .903 r .88738 .37397 .90531 .39034 .93024 .39006 .91041 .3645 Mtetra .599 .842 .99 r .44049 .65281 .45821 .65725 .47422 .64834 .45648 .64547 Mtetra .354 .79 .965 r .45648 .64547 .47422 .64834 .49045 .64472 .47268 .64217 Mtetra .057 .613 .814 r .47268 .64217 .49045 .64472 .50701 .64594 .48919 .64252 Mtetra .141 0 0 r .48919 .64252 .50701 .64594 .52401 .65122 .5061 .64587 Mtetra .223 0 0 r .5061 .64587 .52401 .65122 .54152 .65944 .52346 .65137 Mtetra 0 .362 .716 r .52346 .65137 .54152 .65944 .55961 .66923 .54134 .65798 Mtetra 0 .403 .812 r .54134 .65798 .55961 .66923 .57825 .67898 .55973 .66454 Mtetra .07 .461 .885 r .55973 .66454 .57825 .67898 .59742 .687 .57862 .6698 Mtetra .242 .51 .907 r .57862 .6698 .59742 .687 .61699 .69163 .59793 .67255 Mtetra .384 .549 .895 r .59793 .67255 .61699 .69163 .63682 .69141 .61759 .67171 Mtetra .496 .586 .874 r .61759 .67171 .63682 .69141 .65675 .68527 .63745 .6664 Mtetra .589 .626 .856 r .63745 .6664 .65675 .68527 .67658 .67264 .65739 .65607 Mtetra .67 .672 .843 r .65739 .65607 .67658 .67264 .69617 .65352 .67727 .64054 Mtetra .745 .726 .834 r .67727 .64054 .69617 .65352 .7154 .62852 .69698 .62003 Mtetra .815 .785 .825 r .69698 .62003 .7154 .62852 .73423 .59877 .71646 .59512 Mtetra .874 .847 .814 r .71646 .59512 .73423 .59877 .75269 .56574 .73566 .56673 Mtetra .918 .904 .795 r .73566 .56673 .75269 .56574 .7709 .53114 .75463 .53597 Mtetra .937 .946 .768 r .75463 .53597 .7709 .53114 .78903 .49669 .77345 .50409 Mtetra .93 .971 .739 r .77345 .50409 .78903 .49669 .80731 .464 .79225 .47234 Mtetra .907 .982 .725 r .79225 .47234 .80731 .464 .82601 .43447 .8112 .4419 Mtetra .881 .99 .744 r .8112 .4419 .82601 .43447 .84541 .40917 .83052 .4138 Mtetra .859 .996 .805 r .83052 .4138 .84541 .40917 .86578 .38888 .85041 .38887 Mtetra .825 .974 .891 r .85041 .38887 .86578 .38888 .88738 .37397 .8711 .36772 Mtetra .747 .88 .941 r .8711 .36772 .88738 .37397 .91041 .3645 .8928 .35072 Mtetra .549 .85 .998 r .42244 .64923 .44049 .65281 .45648 .64547 .4384 .64284 Mtetra .349 .792 .959 r .4384 .64284 .45648 .64547 .47268 .64217 .45458 .63944 Mtetra .146 .674 .87 r .45458 .63944 .47268 .64217 .48919 .64252 .47105 .6387 Mtetra .013 .572 .81 r .47105 .6387 .48919 .64252 .5061 .64587 .48788 .64009 Mtetra 0 .518 .809 r .48788 .64009 .5061 .64587 .52346 .65137 .50513 .643 Mtetra 0 .506 .853 r .50513 .643 .52346 .65137 .54134 .65798 .52284 .64665 Mtetra .079 .518 .902 r .52284 .64665 .54134 .65798 .55973 .66454 .54102 .65023 Mtetra .195 .533 .924 r .54102 .65023 .55973 .66454 .57862 .6698 .55968 .65285 Mtetra .308 .547 .917 r .55968 .65285 .57862 .6698 .59793 .67255 .57877 .65366 Mtetra .404 .562 .897 r .57877 .65366 .59793 .67255 .61759 .67171 .59823 .65186 Mtetra .486 .582 .876 r .59823 .65186 .61759 .67171 .63745 .6664 .61798 .64678 Mtetra .559 .61 .861 r .61798 .64678 .63745 .6664 .65739 .65607 .63793 .63795 Mtetra .626 .647 .852 r .63793 .63795 .65739 .65607 .67727 .64054 .65797 .6251 Mtetra .691 .693 .847 r .65797 .6251 .67727 .64054 .69698 .62003 .67801 .60823 Mtetra .755 .748 .846 r .67801 .60823 .69698 .62003 .71646 .59512 .69797 .58758 Mtetra .816 .81 .844 r .69797 .58758 .71646 .59512 .73566 .56673 .71779 .56364 Mtetra .869 .873 .837 r .71779 .56364 .73566 .56673 .75463 .53597 .73746 .53706 Mtetra .905 .928 .82 r .73746 .53706 .75463 .53597 .77345 .50409 .757 .50866 Mtetra .917 .966 .791 r .757 .50866 .77345 .50409 .79225 .47234 .77646 .47931 Mtetra .904 .985 .759 r .77646 .47931 .79225 .47234 .8112 .4419 .79593 .4499 Mtetra .878 .99 .738 r .79593 .4499 .8112 .4419 .83052 .4138 .81555 .42127 Mtetra .854 .993 .745 r .81555 .42127 .83052 .4138 .85041 .38887 .83546 .39418 Mtetra .839 .999 .792 r .83546 .39418 .85041 .38887 .8711 .36772 .85583 .36928 Mtetra .825 .991 .867 r .85583 .36928 .8711 .36772 .8928 .35072 .87684 .34706 Mtetra .517 .853 .996 r .40405 .64625 .42244 .64923 .4384 .64284 .41998 .64027 Mtetra .374 .805 .966 r .41998 .64027 .4384 .64284 .45458 .63944 .43615 .63642 Mtetra .248 .735 .925 r .43615 .63642 .45458 .63944 .47105 .6387 .45259 .6344 Mtetra .17 .674 .907 r .45259 .6344 .47105 .6387 .48788 .64009 .46937 .63385 Mtetra .147 .637 .917 r .46937 .63385 .48788 .64009 .50513 .643 .48653 .6343 Mtetra .174 .616 .939 r .48653 .6343 .50513 .643 .52284 .64665 .50411 .63523 Mtetra .232 .601 .951 r .50411 .63523 .52284 .64665 .54102 .65023 .52213 .63605 Mtetra .302 .588 .943 r .52213 .63605 .54102 .65023 .55968 .65285 .54059 .63618 Mtetra .37 .579 .922 r .54059 .63618 .55968 .65285 .57877 .65366 .55947 .63502 Mtetra .432 .578 .898 r .55947 .63502 .57877 .65366 .59823 .65186 .57875 .63202 Mtetra .487 .584 .878 r .57875 .63202 .59823 .65186 .61798 .64678 .59836 .62667 Mtetra .54 .601 .863 r .59836 .62667 .61798 .64678 .63793 .63795 .61825 .61861 Mtetra .591 .627 .855 r .61825 .61861 .63793 .63795 .65797 .6251 .63835 .60757 Mtetra .643 .662 .854 r .63835 .60757 .65797 .6251 .67801 .60823 .65857 .59344 Mtetra .697 .708 .856 r .65857 .59344 .67801 .60823 .69797 .58758 .67886 .57627 Mtetra .752 .763 .862 r .67886 .57627 .69797 .58758 .71779 .56364 .69914 .55625 Mtetra .806 .825 .865 r .69914 .55625 .71779 .56364 .73746 .53706 .71939 .53372 Mtetra .853 .887 .862 r .71939 .53372 .73746 .53706 .757 .50866 .73959 .50914 Mtetra .883 .942 .847 r .73959 .50914 .757 .50866 .77646 .47931 .75973 .48305 Mtetra .891 .978 .819 r .75973 .48305 .77646 .47931 .79593 .4499 .77986 .45603 Mtetra .877 .994 .783 r .77986 .45603 .79593 .4499 .81555 .42127 .80003 .4287 Mtetra .85 .995 .753 r .80003 .4287 .81555 .42127 .83546 .39418 .82033 .40165 Mtetra .825 .993 .746 r .82033 .40165 .83546 .39418 .85583 .36928 .84087 .37543 Mtetra .812 .996 .771 r .84087 .37543 .85583 .36928 .87684 .34706 .86176 .35052 Mtetra .51 .857 .993 r .38529 .6436 .40405 .64625 .41998 .64027 .40122 .63758 Mtetra .421 .825 .979 r .40122 .63758 .41998 .64027 .43615 .63642 .41737 .63298 Mtetra .351 .784 .967 r .41737 .63298 .43615 .63642 .45259 .6344 .4338 .62958 Mtetra .311 .748 .968 r .4338 .62958 .45259 .6344 .46937 .63385 .45055 .62713 Mtetra .304 .716 .976 r .45055 .62713 .46937 .63385 .48653 .6343 .46766 .62529 Mtetra .322 .686 .979 r .46766 .62529 .48653 .6343 .50411 .63523 .48515 .62371 Mtetra .353 .657 .97 r .48515 .62371 .50411 .63523 .52213 .63605 .50304 .62202 Mtetra .39 .629 .949 r .50304 .62202 .52213 .63605 .54059 .63618 .52134 .61982 Mtetra .427 .608 .924 r .52134 .61982 .54059 .63618 .55947 .63502 .54005 .61671 Mtetra .463 .595 .899 r .54005 .61671 .55947 .63502 .57875 .63202 .55915 .61233 Mtetra .497 .591 .879 r .55915 .61233 .57875 .63202 .59836 .62667 .57861 .60633 Mtetra .532 .597 .864 r .57861 .60633 .59836 .62667 .61825 .61861 .5984 .59843 Mtetra .568 .612 .857 r .5984 .59843 .61825 .61861 .63835 .60757 .61846 .58841 Mtetra .607 .637 .855 r .61846 .58841 .63835 .60757 .65857 .59344 .63875 .57613 Mtetra .648 .671 .858 r .63875 .57613 .65857 .59344 .67886 .57627 .65922 .56154 Mtetra .692 .714 .866 r .65922 .56154 .67886 .57627 .69914 .55625 .67981 .54467 Mtetra .739 .767 .876 r .67981 .54467 .69914 .55625 .71939 .53372 .70049 .52566 Mtetra .785 .826 .884 r .70049 .52566 .71939 .53372 .73959 .50914 .72121 .50473 Mtetra .826 .887 .887 r .72121 .50473 .73959 .50914 .75973 .48305 .74196 .48214 Mtetra .854 .942 .877 r .74196 .48214 .75973 .48305 .77986 .45603 .76275 .45824 Mtetra .863 .98 .852 r .76275 .45824 .77986 .45603 .80003 .4287 .78357 .43341 Mtetra .851 .997 .816 r .78357 .43341 .80003 .4287 .82033 .40165 .80447 .40804 Mtetra .825 .998 .778 r .80447 .40804 .82033 .40165 .84087 .37543 .8255 .38252 Mtetra .798 .992 .754 r .8255 .38252 .84087 .37543 .86176 .35052 .84672 .35725 Mtetra .527 .863 .994 r .36618 .64101 .38529 .6436 .40122 .63758 .3821 .63457 Mtetra .478 .843 .991 r .3821 .63457 .40122 .63758 .41737 .63298 .39826 .62901 Mtetra .443 .818 .992 r .39826 .62901 .41737 .63298 .4338 .62958 .4147 .62418 Mtetra .426 .79 .995 r .4147 .62418 .4338 .62958 .45055 .62713 .43144 .61989 Mtetra .424 .759 .996 r .43144 .61989 .45055 .62713 .46766 .62529 .44851 .61594 Mtetra .431 .726 .988 r .44851 .61594 .46766 .62529 .48515 .62371 .46594 .6121 Mtetra .445 .691 .97 r .46594 .6121 .48515 .62371 .50304 .62202 .48373 .60812 Mtetra .46 .659 .947 r .48373 .60812 .50304 .62202 .52134 .61982 .50191 .60377 Mtetra .477 .632 .922 r .50191 .60377 .52134 .61982 .54005 .61671 .52048 .59879 Mtetra .495 .613 .898 r .52048 .59879 .54005 .61671 .55915 .61233 .53942 .59294 Mtetra .514 .602 .879 r .53942 .59294 .55915 .61233 .57861 .60633 .55873 .586 Mtetra .535 .6 .865 r .55873 .586 .57861 .60633 .5984 .59843 .57839 .57778 Mtetra .557 .605 .857 r .57839 .57778 .5984 .59843 .61846 .58841 .59837 .5681 Mtetra .583 .619 .853 r .59837 .5681 .61846 .58841 .63875 .57613 .61864 .55685 Mtetra .611 .641 .855 r .61864 .55685 .63875 .57613 .65922 .56154 .63917 .54394 Mtetra .643 .671 .862 r .63917 .54394 .65922 .56154 .67981 .54467 .65992 .52934 Mtetra .678 .71 .872 r .65992 .52934 .67981 .54467 .70049 .52566 .68086 .51306 Mtetra .716 .757 .885 r .68086 .51306 .70049 .52566 .72121 .50473 .70195 .49518 Mtetra .755 .812 .898 r .70195 .49518 .72121 .50473 .74196 .48214 .72317 .47581 Mtetra .791 .869 .906 r .72317 .47581 .74196 .48214 .76275 .45824 .74451 .45511 Mtetra .819 .924 .905 r .74451 .45511 .76275 .45824 .78357 .43341 .76594 .43326 Mtetra .832 .968 .89 r .76594 .43326 .78357 .43341 .80447 .40804 .78749 .41049 Mtetra .827 .993 .86 r .78749 .41049 .80447 .40804 .8255 .38252 .80915 .38703 Mtetra .807 1 .82 r .80915 .38703 .8255 .38252 .84672 .35725 .83096 .36312 Mtetra .558 .869 .995 r .3467 .6382 .36618 .64101 .3821 .63457 .36264 .63107 Mtetra .535 .854 .997 r .36264 .63107 .3821 .63457 .39826 .62901 .37883 .62442 Mtetra .519 .834 1 r .37883 .62442 .39826 .62901 .4147 .62418 .39528 .61815 Mtetra .511 .808 .999 r .39528 .61815 .4147 .62418 .43144 .61989 .41203 .61214 Mtetra .509 .779 .993 r .41203 .61214 .43144 .61989 .44851 .61594 .42909 .60626 Mtetra .509 .745 .98 r .42909 .60626 .44851 .61594 .46594 .6121 .44648 .60039 Mtetra .512 .712 .962 r .44648 .60039 .46594 .6121 .48373 .60812 .46421 .59437 Mtetra .516 .68 .94 r .46421 .59437 .48373 .60812 .50191 .60377 .4823 .58805 Mtetra .52 .653 .918 r .4823 .58805 .50191 .60377 .52048 .59879 .50075 .5813 Mtetra .527 .631 .897 r .50075 .5813 .52048 .59879 .53942 .59294 .51956 .57396 Mtetra .535 .616 .88 r .51956 .57396 .53942 .59294 .55873 .586 .53873 .56591 Mtetra .545 .607 .866 r .53873 .56591 .55873 .586 .57839 .57778 .55825 .557 Mtetra .557 .605 .857 r .55825 .557 .57839 .57778 .59837 .5681 .57812 .54714 Mtetra .572 .61 .852 r .57812 .54714 .59837 .5681 .61864 .55685 .59831 .53622 Mtetra .589 .621 .851 r .59831 .53622 .61864 .55685 .63917 .54394 .61881 .52417 Mtetra .609 .639 .855 r .61881 .52417 .63917 .54394 .65992 .52934 .6396 .51094 Mtetra .632 .663 .862 r .6396 .51094 .65992 .52934 .68086 .51306 .66065 .4965 Mtetra .658 .696 .873 r .66065 .4965 .68086 .51306 .70195 .49518 .68195 .48085 Mtetra .687 .735 .887 r .68195 .48085 .70195 .49518 .72317 .47581 .70347 .46402 Mtetra .718 .781 .902 r .70347 .46402 .72317 .47581 .74451 .45511 .72519 .44605 Mtetra .749 .832 .915 r .72519 .44605 .74451 .45511 .76594 .43326 .74711 .42701 Mtetra .776 .885 .924 r .74711 .42701 .76594 .43326 .78749 .41049 .7692 .407 Mtetra .795 .933 .923 r .7692 .407 .78749 .41049 .80915 .38703 .79147 .38613 Mtetra .802 .971 .908 r .79147 .38613 .80915 .38703 .83096 .36312 .81392 .36451 Mtetra .594 .87 .994 r .32688 .6349 .3467 .6382 .36264 .63107 .34286 .6269 Mtetra .584 .855 .995 r .34286 .6269 .36264 .63107 .37883 .62442 .35908 .61909 Mtetra .577 .836 .994 r .35908 .61909 .37883 .62442 .39528 .61815 .37556 .61143 Mtetra .572 .812 .989 r .37556 .61143 .39528 .61815 .41203 .61214 .39233 .60384 Mtetra .568 .784 .98 r .39233 .60384 .41203 .61214 .42909 .60626 .40939 .59625 Mtetra .564 .754 .967 r .40939 .59625 .42909 .60626 .44648 .60039 .42676 .58858 Mtetra .561 .724 .95 r .42676 .58858 .44648 .60039 .46421 .59437 .44446 .58075 Mtetra .559 .695 .932 r .44446 .58075 .46421 .59437 .4823 .58805 .46248 .57269 Mtetra .557 .67 .913 r .46248 .57269 .4823 .58805 .50075 .5813 .48084 .5643 Mtetra .556 .648 .896 r .48084 .5643 .50075 .5813 .51956 .57396 .49954 .55552 Mtetra .557 .631 .88 r .49954 .55552 .51956 .57396 .53873 .56591 .51859 .54625 Mtetra .56 .619 .868 r .51859 .54625 .53873 .56591 .55825 .557 .53799 .53643 Mtetra .565 .612 .858 r .53799 .53643 .55825 .557 .57812 .54714 .55773 .52599 Mtetra .571 .609 .852 r .55773 .52599 .57812 .54714 .59831 .53622 .57781 .51486 Mtetra .58 .612 .849 r .57781 .51486 .59831 .53622 .61881 .52417 .59822 .503 Mtetra .591 .619 .849 r .59822 .503 .61881 .52417 .6396 .51094 .61896 .49035 Mtetra .604 .632 .852 r .61896 .49035 .6396 .51094 .66065 .4965 .64002 .47687 Mtetra .619 .65 .859 r .64002 .47687 .66065 .4965 .68195 .48085 .66138 .46256 Mtetra .637 .674 .868 r .66138 .46256 .68195 .48085 .70347 .46402 .68303 .44739 Mtetra .658 .703 .881 r .68303 .44739 .70347 .46402 .72519 .44605 .70497 .43136 Mtetra .68 .739 .895 r .70497 .43136 .72519 .44605 .74711 .42701 .72718 .41448 Mtetra .704 .779 .91 r .72718 .41448 .74711 .42701 .7692 .407 .74965 .39678 Mtetra .728 .824 .924 r .74965 .39678 .7692 .407 .79147 .38613 .77237 .37829 Mtetra .75 .871 .935 r .77237 .37829 .79147 .38613 .81392 .36451 .79535 .35904 Mtetra .627 .862 .987 r .30674 .63086 .32688 .6349 .34286 .6269 .32276 .62189 Mtetra .622 .847 .985 r .32276 .62189 .34286 .6269 .35908 .61909 .33902 .61294 Mtetra .618 .828 .981 r .33902 .61294 .35908 .61909 .37556 .61143 .35555 .60399 Mtetra .613 .806 .974 r .35555 .60399 .37556 .61143 .39233 .60384 .37234 .59498 Mtetra .608 .782 .964 r .37234 .59498 .39233 .60384 .40939 .59625 .38942 .58588 Mtetra .602 .756 .952 r .38942 .58588 .40939 .59625 .42676 .58858 .40679 .57666 Mtetra .597 .731 .938 r .40679 .57666 .42676 .58858 .44446 .58075 .42446 .56728 Mtetra .592 .707 .923 r .42446 .56728 .44446 .58075 .46248 .57269 .44244 .55768 Mtetra .587 .684 .908 r .44244 .55768 .46248 .57269 .48084 .5643 .46073 .54783 Mtetra .583 .664 .894 r .46073 .54783 .48084 .5643 .49954 .55552 .47935 .53769 Mtetra .58 .647 .881 r .47935 .53769 .49954 .55552 .51859 .54625 .4983 .52722 Mtetra .578 .634 .87 r .4983 .52722 .51859 .54625 .53799 .53643 .51758 .51638 Mtetra .578 .623 .861 r .51758 .51638 .53799 .53643 .55773 .52599 .53721 .50512 Mtetra .579 .616 .854 r .53721 .50512 .55773 .52599 .57781 .51486 .55717 .49341 Mtetra .581 .613 .849 r .55717 .49341 .57781 .51486 .59822 .503 .57747 .48123 Mtetra .585 .613 .846 r .57747 .48123 .59822 .503 .61896 .49035 .59811 .46853 Mtetra .591 .616 .846 r .59811 .46853 .61896 .49035 .64002 .47687 .61909 .45529 Mtetra .599 .624 .848 r .61909 .45529 .64002 .47687 .66138 .46256 .64042 .44149 Mtetra .608 .635 .852 r .64042 .44149 .66138 .46256 .68303 .44739 .66207 .4271 Mtetra .619 .65 .859 r .66207 .4271 .68303 .44739 .70497 .43136 .68407 .41212 Mtetra .631 .669 .868 r .68407 .41212 .70497 .43136 .72718 .41448 .70639 .39653 Mtetra .646 .692 .879 r .70639 .39653 .72718 .41448 .74965 .39678 .72904 .38032 Mtetra .662 .72 .892 r .72904 .38032 .74965 .39678 .77237 .37829 .75201 .36349 Mtetra .679 .752 .906 r .75201 .36349 .77237 .37829 .79535 .35904 .77531 .34605 Mtetra .653 .848 .975 r .2863 .62583 .30674 .63086 .32276 .62189 .30237 .6159 Mtetra .649 .832 .971 r .30237 .6159 .32276 .62189 .33902 .61294 .31868 .60589 Mtetra .645 .815 .965 r .31868 .60589 .33902 .61294 .35555 .60399 .33525 .59578 Mtetra .64 .796 .958 r .33525 .59578 .35555 .60399 .37234 .59498 .35207 .58554 Mtetra .634 .776 .949 r .35207 .58554 .37234 .59498 .38942 .58588 .36917 .57517 Mtetra .629 .755 .938 r .36917 .57517 .38942 .58588 .40679 .57666 .38654 .56464 Mtetra .623 .735 .927 r .38654 .56464 .40679 .57666 .42446 .56728 .4042 .55394 Mtetra .617 .715 .916 r .4042 .55394 .42446 .56728 .44244 .55768 .42215 .54304 Mtetra .611 .697 .904 r .42215 .54304 .44244 .55768 .46073 .54783 .4404 .53193 Mtetra .606 .679 .893 r .4404 .53193 .46073 .54783 .47935 .53769 .45896 .52058 Mtetra .602 .664 .883 r .45896 .52058 .47935 .53769 .4983 .52722 .47784 .50897 Mtetra .598 .65 .873 r .47784 .50897 .4983 .52722 .51758 .51638 .49703 .4971 Mtetra .595 .639 .865 r .49703 .4971 .51758 .51638 .53721 .50512 .51655 .48492 Mtetra .592 .63 .858 r .51655 .48492 .53721 .50512 .55717 .49341 .53639 .47244 Mtetra .591 .623 .852 r .53639 .47244 .55717 .49341 .57747 .48123 .55658 .45962 Mtetra .591 .618 .847 r .55658 .45962 .57747 .48123 .59811 .46853 .57711 .44645 Mtetra .591 .615 .844 r .57711 .44645 .59811 .46853 .61909 .45529 .59798 .43291 Mtetra .593 .615 .843 r .59798 .43291 .61909 .45529 .64042 .44149 .61921 .419 Mtetra .596 .617 .843 r .61921 .419 .64042 .44149 .66207 .4271 .64079 .40468 Mtetra .6 .622 .845 r .64079 .40468 .66207 .4271 .68407 .41212 .66273 .38995 Mtetra .606 .629 .848 r .66273 .38995 .68407 .41212 .70639 .39653 .68503 .37479 Mtetra .612 .639 .853 r .68503 .37479 .70639 .39653 .72904 .38032 .70769 .3592 Mtetra .62 .651 .859 r .70769 .3592 .72904 .38032 .75201 .36349 .73073 .34316 Mtetra .629 .666 .867 r .73073 .34316 .75201 .36349 .77531 .34605 .75413 .32666 Mtetra .669 .827 .96 r .2656 .61961 .2863 .62583 .30237 .6159 .28172 .6088 Mtetra .665 .814 .955 r .28172 .6088 .30237 .6159 .31868 .60589 .29807 .59786 Mtetra .661 .799 .949 r .29807 .59786 .31868 .60589 .33525 .59578 .31467 .58677 Mtetra .656 .784 .942 r .31467 .58677 .33525 .59578 .35207 .58554 .33153 .57552 Mtetra .652 .769 .935 r .33153 .57552 .35207 .58554 .36917 .57517 .34864 .5641 Mtetra .646 .753 .927 r .34864 .5641 .36917 .57517 .38654 .56464 .36602 .55251 Mtetra .641 .738 .919 r .36602 .55251 .38654 .56464 .4042 .55394 .38368 .54074 Mtetra .636 .722 .91 r .38368 .54074 .4042 .55394 .42215 .54304 .40161 .52878 Mtetra .631 .708 .902 r .40161 .52878 .42215 .54304 .4404 .53193 .41983 .51661 Mtetra .626 .694 .893 r .41983 .51661 .4404 .53193 .45896 .52058 .43835 .50424 Mtetra .621 .681 .885 r .43835 .50424 .45896 .52058 .47784 .50897 .45716 .49164 Mtetra .616 .669 .878 r .45716 .49164 .47784 .50897 .49703 .4971 .47628 .47881 Mtetra .612 .658 .871 r .47628 .47881 .49703 .4971 .51655 .48492 .49572 .46574 Mtetra .609 .648 .864 r .49572 .46574 .51655 .48492 .53639 .47244 .51548 .45243 Mtetra .606 .64 .858 r .51548 .45243 .53639 .47244 .55658 .45962 .53556 .43885 Mtetra .603 .633 .853 r .53556 .43885 .55658 .45962 .57711 .44645 .55598 .425 Mtetra .601 .627 .849 r .55598 .425 .57711 .44645 .59798 .43291 .57674 .41087 Mtetra .6 .622 .846 r .57674 .41087 .59798 .43291 .61921 .419 .59786 .39645 Mtetra .599 .619 .843 r .59786 .39645 .61921 .419 .64079 .40468 .61932 .38173 Mtetra .599 .617 .841 r .61932 .38173 .64079 .40468 .66273 .38995 .64115 .36671 Mtetra .6 .617 .841 r .64115 .36671 .66273 .38995 .68503 .37479 .66336 .35136 Mtetra .601 .618 .841 r .66336 .35136 .68503 .37479 .70769 .3592 .68594 .33568 Mtetra .603 .621 .842 r .68594 .33568 .70769 .3592 .73073 .34316 .7089 .31966 Mtetra .605 .624 .844 r .7089 .31966 .73073 .34316 .75413 .32666 .73226 .3033 Mtetra .676 .804 .943 r .24468 .61202 .2656 .61961 .28172 .6088 .26083 .60049 Mtetra .672 .793 .939 r .26083 .60049 .28172 .6088 .29807 .59786 .27721 .58879 Mtetra .669 .783 .934 r .27721 .58879 .29807 .59786 .31467 .58677 .29384 .57693 Mtetra .665 .772 .929 r .29384 .57693 .31467 .58677 .33153 .57552 .31071 .56489 Mtetra .661 .761 .924 r .31071 .56489 .33153 .57552 .34864 .5641 .32783 .55267 Mtetra .657 .75 .918 r .32783 .55267 .34864 .5641 .36602 .55251 .34522 .54027 Mtetra .653 .739 .913 r .34522 .54027 .36602 .55251 .38368 .54074 .36287 .52768 Mtetra .649 .728 .907 r .36287 .52768 .38368 .54074 .40161 .52878 .38079 .5149 Mtetra .645 .718 .901 r .38079 .5149 .40161 .52878 .41983 .51661 .39899 .50191 Mtetra .641 .708 .895 r .39899 .50191 .41983 .51661 .43835 .50424 .41747 .48872 Mtetra .637 .698 .89 r .41747 .48872 .43835 .50424 .45716 .49164 .43624 .47532 Mtetra .633 .689 .884 r .43624 .47532 .45716 .49164 .47628 .47881 .45532 .4617 Mtetra .63 .68 .879 r .45532 .4617 .47628 .47881 .49572 .46574 .47469 .44786 Mtetra .626 .671 .874 r .47469 .44786 .49572 .46574 .51548 .45243 .49438 .43379 Mtetra .623 .664 .869 r .49438 .43379 .51548 .45243 .53556 .43885 .51438 .41948 Mtetra .62 .656 .864 r .51438 .41948 .53556 .43885 .55598 .425 .53472 .40493 Mtetra .617 .65 .86 r .53472 .40493 .55598 .425 .57674 .41087 .55538 .39013 Mtetra .614 .644 .856 r .55538 .39013 .57674 .41087 .59786 .39645 .57639 .37507 Mtetra .612 .638 .852 r .57639 .37507 .59786 .39645 .61932 .38173 .59776 .35975 Mtetra .61 .633 .849 r .59776 .35975 .61932 .38173 .64115 .36671 .61947 .34416 Mtetra .608 .629 .847 r .61947 .34416 .64115 .36671 .66336 .35136 .64156 .3283 Mtetra .607 .626 .844 r .64156 .3283 .66336 .35136 .68594 .33568 .66403 .31215 Mtetra .606 .623 .842 r .66403 .31215 .68594 .33568 .7089 .31966 .68688 .2957 Mtetra .605 .621 .841 r .68688 .2957 .7089 .31966 .73226 .3033 .71012 .27896 Mtetra .675 .779 .928 r .22358 .60292 .24468 .61202 .26083 .60049 .23974 .59087 Mtetra .673 .773 .925 r .23974 .59087 .26083 .60049 .27721 .58879 .25613 .57864 Mtetra .67 .766 .922 r .25613 .57864 .27721 .58879 .29384 .57693 .27276 .56624 Mtetra .668 .76 .919 r .27276 .56624 .29384 .57693 .31071 .56489 .28963 .55365 Mtetra .666 .753 .916 r .28963 .55365 .31071 .56489 .32783 .55267 .30675 .54088 Mtetra .663 .747 .912 r .30675 .54088 .32783 .55267 .34522 .54027 .32413 .52791 Mtetra .661 .74 .909 r .32413 .52791 .34522 .54027 .36287 .52768 .34176 .51476 Mtetra .658 .734 .906 r .34176 .51476 .36287 .52768 .38079 .5149 .35967 .5014 Mtetra .655 .728 .902 r .35967 .5014 .38079 .5149 .39899 .50191 .37784 .48784 Mtetra .653 .721 .899 r .37784 .48784 .39899 .50191 .41747 .48872 .3963 .47407 Mtetra .65 .715 .896 r .3963 .47407 .41747 .48872 .43624 .47532 .41504 .46009 Mtetra .648 .709 .892 r .41504 .46009 .43624 .47532 .45532 .4617 .43408 .44589 Mtetra .645 .704 .889 r .43408 .44589 .45532 .4617 .47469 .44786 .45341 .43146 Mtetra .643 .698 .886 r .45341 .43146 .47469 .44786 .49438 .43379 .47305 .41681 Mtetra .64 .692 .882 r .47305 .41681 .49438 .43379 .51438 .41948 .493 .40193 Mtetra .638 .687 .879 r .493 .40193 .51438 .41948 .53472 .40493 .51327 .3868 Mtetra .636 .682 .876 r .51327 .3868 .53472 .40493 .55538 .39013 .53387 .37143 Mtetra .634 .677 .873 r .53387 .37143 .55538 .39013 .57639 .37507 .55481 .3558 Mtetra .631 .672 .87 r .55481 .3558 .57639 .37507 .59776 .35975 .5761 .33992 Mtetra .629 .667 .868 r .5761 .33992 .59776 .35975 .61947 .34416 .59773 .32377 Mtetra .627 .663 .865 r .59773 .32377 .61947 .34416 .64156 .3283 .61974 .30735 Mtetra .625 .658 .862 r .61974 .30735 .64156 .3283 .66403 .31215 .64211 .29065 Mtetra .624 .654 .86 r .64211 .29065 .66403 .31215 .68688 .2957 .66486 .27367 Mtetra .622 .651 .858 r .66486 .27367 .68688 .2957 .71012 .27896 .68801 .25639 Mtetra .668 .754 .915 r .20235 .59225 .22358 .60292 .23974 .59087 .21848 .5799 Mtetra .667 .752 .914 r .21848 .5799 .23974 .59087 .25613 .57864 .23484 .56738 Mtetra .667 .75 .912 r .23484 .56738 .25613 .57864 .27276 .56624 .25144 .55468 Mtetra .666 .748 .911 r .25144 .55468 .27276 .56624 .28963 .55365 .26829 .54179 Mtetra .665 .745 .91 r .26829 .54179 .28963 .55365 .30675 .54088 .28539 .52871 Mtetra .664 .743 .909 r .28539 .52871 .30675 .54088 .32413 .52791 .30274 .51544 Mtetra .663 .741 .908 r .30274 .51544 .32413 .52791 .34176 .51476 .32035 .50197 Mtetra .662 .739 .907 r .32035 .50197 .34176 .51476 .35967 .5014 .33822 .48829 Mtetra .661 .737 .906 r .33822 .48829 .35967 .5014 .37784 .48784 .35637 .4744 Mtetra .661 .735 .905 r .35637 .4744 .37784 .48784 .3963 .47407 .3748 .46031 Mtetra .66 .733 .904 r .3748 .46031 .3963 .47407 .41504 .46009 .39351 .44599 Mtetra .659 .731 .903 r .39351 .44599 .41504 .46009 .43408 .44589 .41251 .43145 Mtetra .658 .729 .902 r .41251 .43145 .43408 .44589 .45341 .43146 .43181 .41669 Mtetra .657 .727 .9 r .43181 .41669 .45341 .43146 .47305 .41681 .45142 .40168 Mtetra .656 .725 .899 r .45142 .40168 .47305 .41681 .493 .40193 .47134 .38644 Mtetra .655 .723 .898 r .47134 .38644 .493 .40193 .51327 .3868 .49158 .37096 Mtetra .654 .721 .897 r .49158 .37096 .51327 .3868 .53387 .37143 .51214 .35522 Mtetra .654 .719 .896 r .51214 .35522 .53387 .37143 .55481 .3558 .53305 .33923 Mtetra .653 .717 .895 r .53305 .33923 .55481 .3558 .5761 .33992 .55429 .32297 Mtetra .652 .715 .894 r .55429 .32297 .5761 .33992 .59773 .32377 .57589 .30645 Mtetra .651 .713 .893 r .57589 .30645 .59773 .32377 .61974 .30735 .59786 .28964 Mtetra .65 .711 .892 r .59786 .28964 .61974 .30735 .64211 .29065 .62019 .27256 Mtetra .649 .709 .891 r .62019 .27256 .64211 .29065 .66486 .27367 .64291 .25518 Mtetra .649 .707 .89 r .64291 .25518 .66486 .27367 .68801 .25639 .66601 .2375 Mtetra .656 .73 .903 r .18101 .57994 .20235 .59225 .21848 .5799 .19708 .56756 Mtetra .657 .732 .905 r .19708 .56756 .21848 .5799 .23484 .56738 .21338 .555 Mtetra .658 .734 .906 r .21338 .555 .23484 .56738 .25144 .55468 .22992 .54225 Mtetra .659 .736 .907 r .22992 .54225 .25144 .55468 .26829 .54179 .24671 .52931 Mtetra .66 .738 .908 r .24671 .52931 .26829 .54179 .28539 .52871 .26374 .51617 Mtetra .66 .74 .909 r .26374 .51617 .28539 .52871 .30274 .51544 .28104 .50284 Mtetra .661 .742 .91 r .28104 .50284 .30274 .51544 .32035 .50197 .2986 .4893 Mtetra .662 .744 .911 r .2986 .4893 .32035 .50197 .33822 .48829 .31643 .47556 Mtetra .663 .746 .912 r .31643 .47556 .33822 .48829 .35637 .4744 .33453 .46161 Mtetra .664 .748 .913 r .33453 .46161 .35637 .4744 .3748 .46031 .35292 .44743 Mtetra .665 .75 .914 r .35292 .44743 .3748 .46031 .39351 .44599 .37159 .43304 Mtetra .666 .753 .915 r .37159 .43304 .39351 .44599 .41251 .43145 .39056 .41842 Mtetra .666 .755 .916 r .39056 .41842 .41251 .43145 .43181 .41669 .40984 .40356 Mtetra .667 .757 .917 r .40984 .40356 .43181 .41669 .45142 .40168 .42942 .38846 Mtetra .668 .759 .918 r .42942 .38846 .45142 .40168 .47134 .38644 .44932 .37312 Mtetra .669 .761 .919 r .44932 .37312 .47134 .38644 .49158 .37096 .46954 .35753 Mtetra .67 .763 .92 r .46954 .35753 .49158 .37096 .51214 .35522 .4901 .34168 Mtetra .671 .765 .921 r .4901 .34168 .51214 .35522 .53305 .33923 .511 .32557 Mtetra .671 .767 .922 r .511 .32557 .53305 .33923 .55429 .32297 .53225 .30918 Mtetra .672 .769 .923 r .53225 .30918 .55429 .32297 .57589 .30645 .55385 .29252 Mtetra .673 .771 .924 r .55385 .29252 .57589 .30645 .59786 .28964 .57583 .27558 Mtetra .674 .773 .925 r .57583 .27558 .59786 .28964 .62019 .27256 .59818 .25834 Mtetra .675 .776 .926 r .59818 .25834 .62019 .27256 .64291 .25518 .62092 .2408 Mtetra .675 .778 .927 r .62092 .2408 .64291 .25518 .66601 .2375 .64406 .22296 Mtetra .639 .706 .895 r .15962 .56603 .18101 .57994 .19708 .56756 .17557 .55385 Mtetra .642 .712 .898 r .17557 .55385 .19708 .56756 .21338 .555 .19176 .54148 Mtetra .644 .718 .901 r .19176 .54148 .21338 .555 .22992 .54225 .20819 .52893 Mtetra .647 .724 .905 r .20819 .52893 .22992 .54225 .24671 .52931 .22488 .51619 Mtetra .65 .73 .908 r .22488 .51619 .24671 .52931 .26374 .51617 .24182 .50325 Mtetra .652 .736 .911 r .24182 .50325 .26374 .51617 .28104 .50284 .25903 .49012 Mtetra .655 .743 .914 r .25903 .49012 .28104 .50284 .2986 .4893 .27651 .47677 Mtetra .657 .749 .918 r .27651 .47677 .2986 .4893 .31643 .47556 .29426 .46322 Mtetra .66 .755 .921 r .29426 .46322 .31643 .47556 .33453 .46161 .3123 .44945 Mtetra .663 .762 .924 r .3123 .44945 .33453 .46161 .35292 .44743 .33063 .43545 Mtetra .665 .768 .927 r .33063 .43545 .35292 .44743 .37159 .43304 .34925 .42122 Mtetra .668 .774 .93 r .34925 .42122 .37159 .43304 .39056 .41842 .36818 .40676 Mtetra .67 .781 .932 r .36818 .40676 .39056 .41842 .40984 .40356 .38742 .39205 Mtetra .672 .787 .935 r .38742 .39205 .40984 .40356 .42942 .38846 .40698 .37709 Mtetra .675 .793 .938 r .40698 .37709 .42942 .38846 .44932 .37312 .42686 .36187 Mtetra .677 .799 .94 r .42686 .36187 .44932 .37312 .46954 .35753 .44708 .34639 Mtetra .679 .805 .942 r .44708 .34639 .46954 .35753 .4901 .34168 .46765 .33064 Mtetra .681 .81 .944 r .46765 .33064 .4901 .34168 .511 .32557 .48856 .3146 Mtetra .683 .816 .946 r .48856 .3146 .511 .32557 .53225 .30918 .50984 .29828 Mtetra .685 .821 .948 r .50984 .29828 .53225 .30918 .55385 .29252 .53148 .28166 Mtetra .687 .826 .95 r .53148 .28166 .55385 .29252 .57583 .27558 .55351 .26474 Mtetra .689 .831 .951 r .55351 .26474 .57583 .27558 .59818 .25834 .57592 .24751 Mtetra .69 .836 .953 r .57592 .24751 .59818 .25834 .62092 .2408 .59873 .22995 Mtetra .692 .84 .954 r .59873 .22995 .62092 .2408 .64406 .22296 .62195 .21206 Mtetra .619 .683 .888 r .13819 .55058 .15962 .56603 .17557 .55385 .15398 .5388 Mtetra .623 .692 .894 r .15398 .5388 .17557 .55385 .19176 .54148 .17001 .52685 Mtetra .627 .702 .899 r .17001 .52685 .19176 .54148 .20819 .52893 .18629 .51473 Mtetra .631 .712 .905 r .18629 .51473 .20819 .52893 .22488 .51619 .20282 .50244 Mtetra .635 .722 .911 r .20282 .50244 .22488 .51619 .24182 .50325 .21963 .48995 Mtetra .639 .732 .916 r .21963 .48995 .24182 .50325 .25903 .49012 .2367 .47726 Mtetra .643 .743 .921 r .2367 .47726 .25903 .49012 .27651 .47677 .25406 .46437 Mtetra .647 .754 .927 r .25406 .46437 .27651 .47677 .29426 .46322 .2717 .45125 Mtetra .652 .764 .932 r .2717 .45125 .29426 .46322 .3123 .44945 .28964 .43791 Mtetra .656 .775 .936 r .28964 .43791 .3123 .44945 .33063 .43545 .30788 .42432 Mtetra .66 .785 .941 r .30788 .42432 .33063 .43545 .34925 .42122 .32643 .41049 Mtetra .664 .795 .945 r .32643 .41049 .34925 .42122 .36818 .40676 .3453 .39639 Mtetra .668 .805 .949 r .3453 .39639 .36818 .40676 .38742 .39205 .36449 .38203 Mtetra .672 .815 .952 r .36449 .38203 .38742 .39205 .40698 .37709 .38402 .36738 Mtetra .675 .823 .955 r .38402 .36738 .40698 .37709 .42686 .36187 .40389 .35244 Mtetra .678 .832 .957 r .40389 .35244 .42686 .36187 .44708 .34639 .42411 .33719 Mtetra .682 .84 .959 r .42411 .33719 .44708 .34639 .46765 .33064 .44469 .32163 Mtetra .684 .847 .961 r .44469 .32163 .46765 .33064 .48856 .3146 .46563 .30574 Mtetra .687 .853 .962 r .46563 .30574 .48856 .3146 .50984 .29828 .48695 .28951 Mtetra .69 .859 .963 r .48695 .28951 .50984 .29828 .53148 .28166 .50865 .27293 Mtetra .692 .864 .963 r .50865 .27293 .53148 .28166 .55351 .26474 .53074 .25599 Mtetra .694 .868 .964 r .53074 .25599 .55351 .26474 .57592 .24751 .55323 .23868 Mtetra .696 .871 .964 r .55323 .23868 .57592 .24751 .59873 .22995 .57612 .22099 Mtetra .698 .874 .964 r .57612 .22099 .59873 .22995 .62195 .21206 .59944 .20291 Mtetra .596 .661 .884 r .11676 .53371 .13819 .55058 .15398 .5388 .13233 .52248 Mtetra .6 .673 .891 r .13233 .52248 .15398 .5388 .17001 .52685 .14814 .51114 Mtetra .604 .685 .899 r .14814 .51114 .17001 .52685 .18629 .51473 .16421 .49967 Mtetra .609 .699 .907 r .16421 .49967 .18629 .51473 .20282 .50244 .18054 .48805 Mtetra .614 .713 .915 r .18054 .48805 .20282 .50244 .21963 .48995 .19715 .47626 Mtetra .62 .727 .923 r .19715 .47626 .21963 .48995 .2367 .47726 .21404 .46427 Mtetra .625 .742 .931 r .21404 .46427 .2367 .47726 .25406 .46437 .23123 .45208 Mtetra .631 .757 .938 r .23123 .45208 .25406 .46437 .2717 .45125 .24871 .43965 Mtetra .637 .772 .945 r .24871 .43965 .2717 .45125 .28964 .43791 .26651 .42697 Mtetra .643 .787 .951 r .26651 .42697 .28964 .43791 .30788 .42432 .28464 .41402 Mtetra .649 .801 .956 r .28464 .41402 .30788 .42432 .32643 .41049 .30309 .40077 Mtetra .655 .815 .96 r .30309 .40077 .32643 .41049 .3453 .39639 .32188 .3872 Mtetra .66 .827 .963 r .32188 .3872 .3453 .39639 .36449 .38203 .34101 .3733 Mtetra .666 .838 .966 r .34101 .3733 .36449 .38203 .38402 .36738 .3605 .35904 Mtetra .671 .848 .968 r .3605 .35904 .38402 .36738 .40389 .35244 .38035 .3444 Mtetra .676 .857 .968 r .38035 .3444 .40389 .35244 .42411 .33719 .40057 .32936 Mtetra .68 .864 .969 r .40057 .32936 .42411 .33719 .44469 .32163 .42117 .3139 Mtetra .684 .869 .969 r .42117 .3139 .44469 .32163 .46563 .30574 .44214 .29802 Mtetra .689 .873 .968 r .44214 .29802 .46563 .30574 .48695 .28951 .46351 .28168 Mtetra .693 .876 .967 r .46351 .28168 .48695 .28951 .50865 .27293 .48526 .26487 Mtetra .696 .877 .966 r .48526 .26487 .50865 .27293 .53074 .25599 .50742 .24759 Mtetra .7 .876 .964 r .50742 .24759 .53074 .25599 .55323 .23868 .52997 .22981 Mtetra .702 .874 .962 r .52997 .22981 .55323 .23868 .57612 .22099 .55294 .21152 Mtetra .705 .87 .96 r .55294 .21152 .57612 .22099 .59944 .20291 .57631 .19272 Mtetra .571 .641 .881 r .09532 .51557 .11676 .53371 .13233 .52248 .11063 .50499 Mtetra .573 .653 .891 r .11063 .50499 .13233 .52248 .14814 .51114 .12618 .4944 Mtetra .576 .668 .901 r .12618 .4944 .14814 .51114 .16421 .49967 .14198 .48376 Mtetra .581 .684 .912 r .14198 .48376 .16421 .49967 .18054 .48805 .15805 .47303 Mtetra .586 .702 .922 r .15805 .47303 .18054 .48805 .19715 .47626 .1744 .46218 Mtetra .593 .721 .933 r .1744 .46218 .19715 .47626 .21404 .46427 .19104 .45115 Mtetra .6 .74 .943 r .19104 .45115 .21404 .46427 .23123 .45208 .208 .43991 Mtetra .607 .76 .952 r .208 .43991 .23123 .45208 .24871 .43965 .22528 .42842 Mtetra .615 .779 .96 r .22528 .42842 .24871 .43965 .26651 .42697 .24289 .41662 Mtetra .624 .798 .966 r .24289 .41662 .26651 .42697 .28464 .41402 .26085 .40449 Mtetra .632 .815 .971 r .26085 .40449 .28464 .41402 .30309 .40077 .27917 .39196 Mtetra .64 .831 .974 r .27917 .39196 .30309 .40077 .32188 .3872 .29786 .37901 Mtetra .649 .844 .975 r .29786 .37901 .32188 .3872 .34101 .3733 .31693 .36559 Mtetra .657 .856 .976 r .31693 .36559 .34101 .3733 .3605 .35904 .33637 .35166 Mtetra .665 .865 .975 r .33637 .35166 .3605 .35904 .38035 .3444 .35621 .33719 Mtetra .673 .871 .974 r .35621 .33719 .38035 .3444 .40057 .32936 .37643 .32214 Mtetra .681 .875 .971 r .37643 .32214 .40057 .32936 .42117 .3139 .39706 .30649 Mtetra .689 .877 .969 r .39706 .30649 .42117 .3139 .44214 .29802 .41807 .29022 Mtetra .695 .876 .966 r .41807 .29022 .44214 .29802 .46351 .28168 .43949 .27329 Mtetra .701 .871 .962 r .43949 .27329 .46351 .28168 .48526 .26487 .4613 .2557 Mtetra .706 .864 .957 r .4613 .2557 .48526 .26487 .50742 .24759 .48351 .23743 Mtetra .71 .854 .951 r .48351 .23743 .50742 .24759 .52997 .22981 .50612 .21848 Mtetra .711 .841 .944 r .50612 .21848 .52997 .22981 .55294 .21152 .52911 .19884 Mtetra .711 .826 .936 r .52911 .19884 .55294 .21152 .57631 .19272 .55249 .17851 Mtetra .546 .622 .879 r .07388 .49636 .09532 .51557 .11063 .50499 .0889 .48644 Mtetra .543 .634 .891 r .0889 .48644 .11063 .50499 .12618 .4944 .10414 .47668 Mtetra .543 .649 .903 r .10414 .47668 .12618 .4944 .14198 .48376 .11961 .46702 Mtetra .545 .667 .917 r .11961 .46702 .14198 .48376 .15805 .47303 .13535 .45738 Mtetra .549 .688 .93 r .13535 .45738 .15805 .47303 .1744 .46218 .15137 .4477 Mtetra .555 .711 .944 r .15137 .4477 .1744 .46218 .19104 .45115 .16769 .43789 Mtetra .564 .735 .956 r .16769 .43789 .19104 .45115 .208 .43991 .18435 .42786 Mtetra .573 .76 .966 r .18435 .42786 .208 .43991 .22528 .42842 .20136 .41753 Mtetra .584 .784 .975 r .20136 .41753 .22528 .42842 .24289 .41662 .21873 .40683 Mtetra .596 .806 .98 r .21873 .40683 .24289 .41662 .26085 .40449 .2365 .39565 Mtetra .609 .826 .983 r .2365 .39565 .26085 .40449 .27917 .39196 .25466 .38393 Mtetra .622 .843 .984 r .25466 .38393 .27917 .39196 .29786 .37901 .27323 .37159 Mtetra .636 .857 .983 r .27323 .37159 .29786 .37901 .31693 .36559 .29221 .35854 Mtetra .651 .867 .981 r .29221 .35854 .31693 .36559 .33637 .35166 .31162 .34474 Mtetra .665 .874 .977 r .31162 .34474 .33637 .35166 .35621 .33719 .33146 .33012 Mtetra .678 .876 .973 r .33146 .33012 .35621 .33719 .37643 .32214 .35171 .31464 Mtetra .691 .874 .967 r .35171 .31464 .37643 .32214 .39706 .30649 .37239 .29826 Mtetra .702 .868 .961 r .37239 .29826 .39706 .30649 .41807 .29022 .39347 .28096 Mtetra .71 .858 .952 r .39347 .28096 .41807 .29022 .43949 .27329 .41496 .26272 Mtetra .715 .843 .943 r .41496 .26272 .43949 .27329 .4613 .2557 .43684 .24355 Mtetra .717 .823 .931 r .43684 .24355 .4613 .2557 .48351 .23743 .45911 .22345 Mtetra .716 .8 .917 r .45911 .22345 .48351 .23743 .50612 .21848 .48174 .20244 Mtetra .711 .774 .901 r .48174 .20244 .50612 .21848 .52911 .19884 .50473 .18056 Mtetra .704 .746 .884 r .50473 .18056 .52911 .19884 .55249 .17851 .52807 .15786 Mtetra .522 .607 .879 r .05241 .47632 .07388 .49636 .0889 .48644 .06714 .46697 Mtetra .511 .614 .891 r .06714 .46697 .0889 .48644 .10414 .47668 .08203 .45806 Mtetra .504 .628 .906 r .08203 .45806 .10414 .47668 .11961 .46702 .09712 .44948 Mtetra .5 .646 .922 r .09712 .44948 .11961 .46702 .13535 .45738 .11245 .44111 Mtetra .501 .669 .939 r .11245 .44111 .13535 .45738 .15137 .4477 .12806 .43283 Mtetra .505 .696 .955 r .12806 .43283 .15137 .4477 .16769 .43789 .14399 .42448 Mtetra .513 .725 .969 r .14399 .42448 .16769 .43789 .18435 .42786 .16027 .41591 Mtetra .525 .754 .98 r .16027 .41591 .18435 .42786 .20136 .41753 .17693 .40699 Mtetra .541 .783 .988 r .17693 .40699 .20136 .41753 .21873 .40683 .19401 .39754 Mtetra .56 .81 .992 r .19401 .39754 .21873 .40683 .2365 .39565 .21152 .38743 Mtetra .581 .833 .993 r .21152 .38743 .2365 .39565 .25466 .38393 .2295 .37652 Mtetra .604 .852 .991 r .2295 .37652 .25466 .38393 .27323 .37159 .24794 .36466 Mtetra .628 .865 .987 r .24794 .36466 .27323 .37159 .29221 .35854 .26686 .35176 Mtetra .652 .873 .981 r .26686 .35176 .29221 .35854 .31162 .34474 .28626 .33771 Mtetra .674 .875 .974 r .28626 .33771 .31162 .34474 .33146 .33012 .30614 .32243 Mtetra .694 .871 .965 r .30614 .32243 .33146 .33012 .35171 .31464 .32647 .30587 Mtetra .71 .859 .953 r .32647 .30587 .35171 .31464 .37239 .29826 .34725 .28802 Mtetra .72 .842 .939 r .34725 .28802 .37239 .29826 .39347 .28096 .36845 .26886 Mtetra .725 .818 .922 r .36845 .26886 .39347 .28096 .41496 .26272 .39006 .24842 Mtetra .725 .79 .903 r .39006 .24842 .41496 .26272 .43684 .24355 .41204 .22676 Mtetra .72 .758 .883 r .41204 .22676 .43684 .24355 .45911 .22345 .43437 .20395 Mtetra .71 .724 .861 r .43437 .20395 .45911 .22345 .48174 .20244 .45703 .18008 Mtetra .697 .69 .839 r .45703 .18008 .48174 .20244 .50473 .18056 .48 .15527 Mtetra .682 .657 .818 r .48 .15527 .50473 .18056 .52807 .15786 .50326 .12965 Mtetra .503 .595 .879 r .03088 .4557 .05241 .47632 .06714 .46697 .04533 .44674 Mtetra .479 .596 .892 r .04533 .44674 .06714 .46697 .08203 .45806 .05985 .43862 Mtetra .459 .604 .908 r .05985 .43862 .08203 .45806 .09712 .44948 .07451 .43118 Mtetra .444 .62 .926 r .07451 .43118 .09712 .44948 .11245 .44111 .08937 .42423 Mtetra .436 .643 .944 r .08937 .42423 .11245 .44111 .12806 .43283 .10448 .41755 Mtetra .436 .672 .962 r .10448 .41755 .12806 .43283 .14399 .42448 .11992 .41092 Mtetra .444 .705 .977 r .11992 .41092 .14399 .42448 .16027 .41591 .13572 .40407 Mtetra .46 .741 .989 r .13572 .40407 .16027 .41591 .17693 .40699 .15196 .39676 Mtetra .485 .776 .996 r .15196 .39676 .17693 .40699 .19401 .39754 .16868 .38873 Mtetra .516 .808 .999 r .16868 .38873 .19401 .39754 .21152 .38743 .18591 .37973 Mtetra .552 .836 .998 r .18591 .37973 .21152 .38743 .2295 .37652 .20368 .36953 Mtetra .591 .857 .994 r .20368 .36953 .2295 .37652 .24794 .36466 .22201 .35794 Mtetra .63 .87 .987 r .22201 .35794 .24794 .36466 .26686 .35176 .2409 .34477 Mtetra .666 .874 .977 r .2409 .34477 .26686 .35176 .28626 .33771 .26035 .32991 Mtetra .696 .868 .963 r .26035 .32991 .28626 .33771 .30614 .32243 .28033 .31328 Mtetra .718 .853 .946 r .28033 .31328 .30614 .32243 .32647 .30587 .30082 .29484 Mtetra .732 .828 .925 r .30082 .29484 .32647 .30587 .34725 .28802 .32179 .27462 Mtetra .737 .797 .901 r .32179 .27462 .34725 .28802 .36845 .26886 .34319 .25269 Mtetra .734 .761 .875 r .34319 .25269 .36845 .26886 .39006 .24842 .36498 .22917 Mtetra .725 .723 .849 r .36498 .22917 .39006 .24842 .41204 .22676 .38711 .20424 Mtetra .711 .685 .823 r .38711 .20424 .41204 .22676 .43437 .20395 .40954 .17808 Mtetra .694 .648 .8 r .40954 .17808 .43437 .20395 .45703 .18008 .43224 .15092 Mtetra .676 .614 .778 r .43224 .15092 .45703 .18008 .48 .15527 .45518 .123 Mtetra .657 .583 .76 r .45518 .123 .48 .15527 .50326 .12965 .47834 .09458 Mtetra 0 g .47932 0 m .95607 .3787 L s .95607 .3787 m 1 .5789 L s 1 .5789 m .47725 .19982 L s .47725 .19982 m .47932 0 L s .04294 .39959 m 0 .5994 L s 0 .5994 m .47725 .19982 L s .47725 .19982 m .47932 0 L s .47932 0 m .04294 .39959 L s .04294 .39959 m .47932 0 L s .04294 .39959 m .0484 .4027 L s [(-1)] .03202 .39335 1 .57143 Mshowa .13389 .3163 m .13925 .31959 L s [(0)] .12317 .30973 1 .61297 Mshowa .23313 .22543 m .23837 .2289 L s [(1)] .22264 .2185 1 .66101 Mshowa .34183 .1259 m .34694 .12956 L s [(2)] .33161 .11857 1 .71722 Mshowa .46141 .0164 m .46636 .02028 L s [(3)] .45152 .00864 1 .78388 Mshowa .125 Mabswid .06052 .38349 m .06378 .38538 L s .0784 .36712 m .08165 .36903 L s .09658 .35047 m .09982 .3524 L s .11507 .33353 m .1183 .33548 L s .15304 .29877 m .15625 .30076 L s .17253 .28092 m .17572 .28293 L s .19237 .26276 m .19555 .26479 L s .21257 .24426 m .21573 .24632 L s .25407 .20626 m .2572 .20836 L s .2754 .18673 m .27851 .18885 L s .29713 .16683 m .30023 .16898 L s .31927 .14656 m .32235 .14873 L s .36482 .10484 m .36787 .10707 L s .38827 .08338 m .39129 .08563 L s .41217 .06149 m .41518 .06376 L s .43655 .03917 m .43954 .04147 L s gsave .17767 .17692 -71 -14.4564 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 1.000 setlinewidth grestore .25 Mabswid .95607 .3787 m 1 .5789 L s .95696 .38275 m .95167 .38615 L s [(-4)] .96754 .37595 -1 .6426 Mshowa .9668 .4276 m .96147 .43093 L s [(-2)] .97746 .42093 -1 .62562 Mshowa .97707 .4744 m .9717 .47767 L s [(0)] .98782 .46787 -1 .60801 Mshowa .9878 .5233 m .98238 .5265 L s [(2)] .99863 .51692 -1 .58974 Mshowa .99902 .57444 m .99356 .57756 L s [(4)] 1.00994 .56821 -1 .57078 Mshowa .125 Mabswid .95938 .39378 m .9562 .39581 L s .96183 .40494 m .95864 .40696 L s .9643 .41621 m .96111 .41822 L s .96933 .43911 m .96612 .4411 L s .97188 .45075 m .96867 .45273 L s .97446 .46251 m .97124 .46448 L s .97971 .48643 m .97648 .48838 L s .98238 .49858 m .97914 .50052 L s .98507 .51088 m .98183 .5128 L s .99056 .53587 m .9873 .53778 L s .99335 .54858 m .99008 .55048 L s .99617 .56144 m .9929 .56332 L s gsave 1.0415 .43503 -61 -14.1007 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20.5625 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (z) show 1.000 setlinewidth grestore % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 246.875}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] SurfaceGraphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ Ka antud leiab kogu v\[OTilde]imalike valikute hulga k\[ADoubleDot]su \ ??Plot3D abil, soovi korral koos n\[ADoubleDot]idetega.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["4.3. Parameetrilised joonised.", "Subsubtitle"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`ParametricPlot[{x(t), \ y(t)}, {t, t\_1, t\_2}]\)]], "\tparameetrilise joonise tegemine\n", Cell[BoxData[ \(TraditionalForm\`\(\(ParametricPlot[{{\(x\_1\)(t), \ \(y\_1\)( t)}, {\(x\_2\)(t), \(y\_2\)(t)}, ... }, {t, t\_1, t\_2}]\)\(\ \)\)\)]], "\t\n\t\t\t\t\t\tmitme parameetrilise joonise tegemine\n", Cell[BoxData[ \(TraditionalForm\`ParametricPlot[{x(t), \ y(t)}, {t, t\_1, t\_2}, AspectRatio \[Rule] Automatic\ ]\)]], "\t\n\t\t\t\t\t\tparameetriline joonis, selline, et ka joonise \[OTilde]ige \ kuju s\[ADoubleDot]iliks\n", Cell[BoxData[ \(TraditionalForm\`ParametricPlot3D[{x(t), y(t), z(t)}, {t, t\_1, t\_2}]\)]], "\t\t\n\t\t\t\t\t\tparameetriline joon 3-m\[OTilde]\[OTilde]tmelises ruumis\ \t\t" }], "Text", Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[ \(ParametricPlot[{Sin[t], \ Cos[t]}, {t, 0, 2 \[Pi]}, AspectRatio \[Rule] Automatic]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.476191 0.499997 0.476191 [ [.02381 .4875 -6 -9 ] [.02381 .4875 6 0 ] [.2619 .4875 -12 -9 ] [.2619 .4875 12 0 ] [.7381 .4875 -9 -9 ] [.7381 .4875 9 0 ] [.97619 .4875 -3 -9 ] [.97619 .4875 3 0 ] [.4875 .02381 -12 -4.5 ] [.4875 .02381 0 4.5 ] [.4875 .2619 -24 -4.5 ] [.4875 .2619 0 4.5 ] [.4875 .73809 -18 -4.5 ] [.4875 .73809 0 4.5 ] [.4875 .97619 -6 -4.5 ] [.4875 .97619 0 4.5 ] [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 .5 m .02381 .50625 L s [(-1)] .02381 .4875 0 1 Mshowa .2619 .5 m .2619 .50625 L s [(-0.5)] .2619 .4875 0 1 Mshowa .7381 .5 m .7381 .50625 L s [(0.5)] .7381 .4875 0 1 Mshowa .97619 .5 m .97619 .50625 L s [(1)] .97619 .4875 0 1 Mshowa .125 Mabswid .07143 .5 m .07143 .50375 L s .11905 .5 m .11905 .50375 L s .16667 .5 m .16667 .50375 L s .21429 .5 m .21429 .50375 L s .30952 .5 m .30952 .50375 L s .35714 .5 m .35714 .50375 L s .40476 .5 m .40476 .50375 L s .45238 .5 m .45238 .50375 L s .54762 .5 m .54762 .50375 L s .59524 .5 m .59524 .50375 L s .64286 .5 m .64286 .50375 L s .69048 .5 m .69048 .50375 L s .78571 .5 m .78571 .50375 L s .83333 .5 m .83333 .50375 L s .88095 .5 m .88095 .50375 L s .92857 .5 m .92857 .50375 L s .25 Mabswid 0 .5 m 1 .5 L s .5 .02381 m .50625 .02381 L s [(-1)] .4875 .02381 1 0 Mshowa .5 .2619 m .50625 .2619 L s [(-0.5)] .4875 .2619 1 0 Mshowa .5 .73809 m .50625 .73809 L s [(0.5)] .4875 .73809 1 0 Mshowa .5 .97619 m .50625 .97619 L s [(1)] .4875 .97619 1 0 Mshowa .125 Mabswid .5 .07143 m .50375 .07143 L s .5 .11904 m .50375 .11904 L s .5 .16666 m .50375 .16666 L s .5 .21428 m .50375 .21428 L s .5 .30952 m .50375 .30952 L s .5 .35714 m .50375 .35714 L s .5 .40476 m .50375 .40476 L s .5 .45238 m .50375 .45238 L s .5 .54762 m .50375 .54762 L s .5 .59524 m .50375 .59524 L s .5 .64285 m .50375 .64285 L s .5 .69047 m .50375 .69047 L s .5 .78571 m .50375 .78571 L s .5 .83333 m .50375 .83333 L s .5 .88095 m .50375 .88095 L s .5 .92857 m .50375 .92857 L s .25 Mabswid .5 0 m .5 1 L s 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 Mabswid .5 .97619 m .50369 .97617 L .50705 .97614 L .51093 .97606 L .5146 .97596 L .52111 .97572 L .52818 .97535 L .53596 .97483 L .5442 .97413 L .55893 .97253 L .57409 .97039 L .58822 .96795 L .62007 .9608 L .65197 .95129 L .68052 .94065 L .74191 .91017 L .79125 .87673 L .83988 .83352 L .88019 .78673 L .9161 .73155 L .93084 .7028 L .94456 .67066 L .95448 .64213 L .96327 .61017 L .96664 .5949 L .96969 .57842 L .97186 .5641 L .97372 .54845 L .97457 .53926 L .9752 .53074 L .97565 .52259 L .97583 .51847 L .97599 .51392 L .97609 .50983 L .97615 .50609 L .97619 .50197 L .97619 .4999 L .97618 .49764 L .97615 .49381 L .97608 .48972 L .97598 .48587 L .97586 .48236 L .97554 .47512 L .97506 .46715 L .97367 .45109 L .9719 .43625 L .96983 .42243 L .96368 .39155 L .95481 .3589 L .94437 .32884 L Mistroke .93073 .29695 L .9001 .24177 L .86323 .19207 L .81726 .14489 L .764 .10369 L .70905 .07215 L .681 .05955 L .65059 .04825 L .62147 .03956 L .59452 .03328 L .56509 .02828 L .54878 .02631 L .54128 .0256 L .5333 .02497 L .52649 .02454 L .52287 .02436 L .51897 .02418 L .5154 .02406 L .51212 .02396 L .509 .02389 L .50571 .02384 L .50211 .02381 L .49827 .02381 L .49465 .02384 L .49136 .02388 L .48749 .02397 L .4833 .0241 L .4757 .02443 L .46828 .02486 L .46033 .02546 L .446 .02688 L .42902 .02913 L .41361 .03171 L .38047 .03905 L .3496 .04818 L .29179 .07174 L .24143 .10012 L .19433 .13486 L .14769 .17963 L .10982 .22702 L .07608 .28309 L .05121 .3408 L .04163 .37094 L .03713 .38817 L .03347 .40458 L .03062 .41978 L .02808 .43635 L .02629 .45149 L .02506 .4655 L .02456 .47333 L Mistroke .0242 .48068 L .02405 .48489 L .02394 .48874 L .0239 .49087 L .02386 .49319 L .02383 .49538 L .02382 .49741 L .02381 .49954 L .02381 .50184 L .02383 .50401 L .02385 .50601 L .02391 .5098 L .02401 .5138 L .02415 .5181 L .02432 .52212 L .02484 .53124 L .02544 .5394 L .02613 .54693 L .02812 .56393 L .03038 .57885 L .0333 .59461 L .0396 .62161 L .04836 .65091 L .07126 .70721 L .10374 .76408 L .14205 .81404 L .18909 .86068 L .23861 .89803 L .28865 .92672 L .31879 .94036 L .34804 .95129 L .37519 .95954 L .4044 .96649 L .42788 .97069 L .44131 .97256 L .45391 .97395 L .4655 .97494 L .47611 .97559 L .48197 .97585 L .48507 .97595 L .48836 .97605 L .49153 .97611 L .4944 .97615 L .49729 .97618 L .5 .97619 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{216.75, 216.75}, ImageMargins->{{35, 0}, {0, 71.1875}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ J\[ADoubleDot]rgnevalt veel m\[OTilde]ned n\[ADoubleDot]ited nn Lissajoux' \ kujunditest (eelmine on k\[OTilde]ige lihtsam).\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(ParametricPlot[{{Sin[2 t], Sin[5 t]}, {Sin[2 t], Cos[3 t]}}, {t, 0, 2\ \[Pi]}, \[IndentingNewLine]PlotStyle \[Rule] {RGBColor[1, 0.5, 0.8], Hue[0.6]}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.476191 0.309017 0.294302 [ [.02381 .29652 -6 -9 ] [.02381 .29652 6 0 ] [.2619 .29652 -12 -9 ] [.2619 .29652 12 0 ] [.7381 .29652 -9 -9 ] [.7381 .29652 9 0 ] [.97619 .29652 -3 -9 ] [.97619 .29652 3 0 ] [.4875 .01471 -12 -4.5 ] [.4875 .01471 0 4.5 ] [.4875 .16187 -24 -4.5 ] [.4875 .16187 0 4.5 ] [.4875 .45617 -18 -4.5 ] [.4875 .45617 0 4.5 ] [.4875 .60332 -6 -4.5 ] [.4875 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 .30902 m .02381 .31527 L s [(-1)] .02381 .29652 0 1 Mshowa .2619 .30902 m .2619 .31527 L s [(-0.5)] .2619 .29652 0 1 Mshowa .7381 .30902 m .7381 .31527 L s [(0.5)] .7381 .29652 0 1 Mshowa .97619 .30902 m .97619 .31527 L s [(1)] .97619 .29652 0 1 Mshowa .125 Mabswid .07143 .30902 m .07143 .31277 L s .11905 .30902 m .11905 .31277 L s .16667 .30902 m .16667 .31277 L s .21429 .30902 m .21429 .31277 L s .30952 .30902 m .30952 .31277 L s .35714 .30902 m .35714 .31277 L s .40476 .30902 m .40476 .31277 L s .45238 .30902 m .45238 .31277 L s .54762 .30902 m .54762 .31277 L s .59524 .30902 m .59524 .31277 L s .64286 .30902 m .64286 .31277 L s .69048 .30902 m .69048 .31277 L s .78571 .30902 m .78571 .31277 L s .83333 .30902 m .83333 .31277 L s .88095 .30902 m .88095 .31277 L s .92857 .30902 m .92857 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .5 .01471 m .50625 .01471 L s [(-1)] .4875 .01471 1 0 Mshowa .5 .16187 m .50625 .16187 L s [(-0.5)] .4875 .16187 1 0 Mshowa .5 .45617 m .50625 .45617 L s [(0.5)] .4875 .45617 1 0 Mshowa .5 .60332 m .50625 .60332 L s [(1)] .4875 .60332 1 0 Mshowa .125 Mabswid .5 .04414 m .50375 .04414 L s .5 .07358 m .50375 .07358 L s .5 .10301 m .50375 .10301 L s .5 .13244 m .50375 .13244 L s .5 .1913 m .50375 .1913 L s .5 .22073 m .50375 .22073 L s .5 .25016 m .50375 .25016 L s .5 .27959 m .50375 .27959 L s .5 .33845 m .50375 .33845 L s .5 .36788 m .50375 .36788 L s .5 .39731 m .50375 .39731 L s .5 .42674 m .50375 .42674 L s .5 .4856 m .50375 .4856 L s .5 .51503 m .50375 .51503 L s .5 .54446 m .50375 .54446 L s .5 .57389 m .50375 .57389 L s .25 Mabswid .5 0 m .5 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 1 .5 .8 r .5 Mabswid .5 .30902 m .55627 .39489 L .61696 .48011 L .6469 .51683 L .67822 .54994 L .70679 .5743 L .73237 .59049 L .74671 .5969 L .75383 .59931 L .76158 .60131 L .76559 .60208 L .76923 .60263 L .77342 .60306 L .77736 .60328 L .78096 .60331 L .78429 .6032 L .78791 .60291 L .79174 .60243 L .79533 .6018 L .7986 .60107 L .80591 .59891 L .81224 .59642 L .81884 .59318 L .83001 .58613 L .84189 .57635 L .86304 .55246 L .88395 .51951 L .90192 .48234 L .91674 .4442 L .9305 .40123 L .94323 .35307 L .961 .26437 L .96797 .21638 L .97259 .17368 L .97439 .15069 L .97503 .14021 L .9755 .13074 L .97587 .12076 L .97601 .11562 L .97612 .11024 L .97618 .10472 L .97619 .09962 L .97616 .09516 L .97609 .09043 L .97587 .08261 L .97555 .07579 L .97506 .06831 L .97446 .06162 L .97309 .05077 L .97215 .04522 L Mistroke .97115 .04047 L .96984 .03533 L .96846 .03099 L .96552 .02424 L .96367 .02123 L .96184 .01896 L .95969 .01702 L .95855 .01627 L .95726 .01561 L .95605 .01517 L .9547 .01486 L .95338 .01473 L .95213 .01474 L .94967 .01513 L .94694 .01605 L .94548 .01674 L .94387 .01764 L .94085 .01967 L .93351 .02627 L .91868 .04479 L .9033 .06883 L .82068 .22874 L .77148 .32496 L .72271 .41106 L .67207 .48631 L .64443 .52022 L .61461 .55063 L .59921 .56373 L .58217 .57609 L .5664 .5855 L .55194 .5924 L .53703 .59776 L .5288 .59996 L .52099 .60153 L .51378 .60255 L .5071 .60311 L .49977 .60332 L .49198 .60306 L .48486 .60239 L .47707 .60119 L .46894 .59941 L .46137 .59728 L .44784 .59231 L .43343 .58541 L .40073 .56368 L .37141 .53719 L .31571 .46964 L .26566 .39162 L .17336 .21673 L .12903 .1281 L Mistroke .09382 .06406 L .0786 .04098 L .06577 .02553 L .05939 .01985 L .05601 .01756 L .05445 .0167 L .05301 .01603 L .05037 .01514 L .04808 .01475 L .04573 .0148 L .04332 .01538 L .04104 .01652 L .03905 .01807 L .037 .02033 L .03497 .02337 L .03301 .02726 L .03134 .03159 L .02996 .03606 L .02864 .04136 L .02764 .04638 L .02666 .05239 L .02589 .05835 L .02529 .06416 L .02472 .0714 L .02447 .07538 L .02425 .0797 L .02399 .08727 L .02389 .09171 L .02383 .09595 L .02382 .10469 L .02387 .10924 L .02396 .11434 L .02422 .12363 L .02458 .1326 L .02516 .14351 L .02582 .15377 L .02779 .17781 L .03298 .22377 L .03987 .26963 L .0574 .35569 L .07003 .40306 L .08343 .44468 L .09989 .48649 L .11968 .52597 L .14022 .55672 L .15058 .56884 L .16057 .57858 L .1707 .58664 L .18017 .59264 L .19097 .59776 L Mistroke .19704 .59987 L .20284 .60141 L .20856 .60247 L .21469 .60314 L .21998 .60332 L .22588 .60311 L .23227 .60242 L .23589 .60182 L .23923 .60113 L .24575 .59943 L .25201 .59737 L .26603 .5913 L .27949 .58371 L .30524 .56479 L .36541 .50227 L .47907 .34131 L .59386 .16895 L .65701 .08986 L .68685 .0601 L .71333 .03904 L .72651 .03074 L .7406 .02362 L .74696 .02104 L .75365 .01878 L .75931 .01724 L .7655 .01597 L .76888 .01545 L .77242 .01506 L .77869 .01472 L .78536 .0149 L .7891 .01525 L .79256 .01573 L .79879 .01701 L .80438 .01861 L .81074 .02097 L .81667 .02371 L .82846 .0308 L .84055 .04045 L .86113 .06305 L .88162 .09435 L .90208 .13608 L .91865 .17934 L .93256 .22398 L .95365 .31287 L .96248 .36289 L .96874 .40792 L .97145 .43234 L .97344 .45443 L .97432 .46623 L .97507 .47859 L Mistroke .97559 .48945 L .97593 .4991 L .97613 .50831 L .97619 .51672 L .97615 .52399 L .97599 .53158 L .97569 .53946 L .97549 .54328 L .97523 .54738 L .97467 .55429 L .97402 .5604 L .97331 .56585 L .97244 .57122 L .97061 .57982 L .96944 .58406 L .96824 .58763 L .96671 .59139 L .96518 .59441 L .96337 .59722 L .96126 .59967 L .95927 .60131 L .95703 .60252 L .95491 .60314 L .95283 .60332 L .95043 .60308 L .94774 .6023 L .9462 .60165 L .94473 .6009 L .94129 .59869 L .9346 .59287 L .92055 .57588 L .88894 .52394 L .85354 .45549 L .75497 .26264 L .70093 .17264 L .66996 .12895 L .64035 .09326 L .61235 .06536 L .58651 .04488 L .57264 .03602 L .55751 .02809 L .54917 .0245 L .54146 .02168 L .53419 .01945 L .52625 .01751 L .51841 .01609 L .51097 .0152 L .50371 .01477 L .49698 .01475 L .48898 .01521 L Mistroke .48174 .01607 L .47772 .01673 L .47338 .01759 L .46552 .01953 L .45116 .02437 L .43603 .03125 L .40913 .04797 L .37798 .07434 L .34941 .10491 L .28681 .19161 L .18955 .36881 L .10515 .5346 L .08735 .56429 L .07846 .57724 L .0707 .58712 L .06406 .59418 L .05839 .59891 L .0555 .60076 L .05259 .60217 L .05113 .60269 L .0498 .60303 L .04839 .60325 L .04692 .60332 L .04566 .60323 L .04437 .60298 L .04215 .60215 L .04097 .60147 L .0399 .6007 L .0376 .59844 L .03573 .59591 L .03414 .59314 L .03242 .58937 L .03097 .58535 L .02865 .57668 L .0276 .57144 L .02663 .56539 L .02583 .55915 L .0252 .55289 L .02474 .54696 L .02434 .54021 L .02404 .53252 L .02387 .52519 L .02381 .51636 L .02389 .50764 L .02407 .49929 L .02433 .49134 L .02473 .48235 L .02528 .47254 L .02681 .45127 L .02875 .4304 L Mistroke .03491 .38024 L .0432 .32948 L .05274 .28243 L .06522 .23197 L .08086 .18076 L .09719 .13778 L .11362 .10303 L .13163 .07303 L .14989 .04993 L .16081 .03924 L .17275 .02996 L .18327 .02375 L .18933 .02094 L .19515 .01876 L .19841 .01775 L .20198 .01682 L .20831 .0156 L .21192 .01514 L .21579 .01483 L .21912 .01472 L .22282 .01476 L .22946 .01525 L .23322 .01576 L .2367 .01637 L .24315 .01787 L .25003 .01997 L .2639 .02568 L .27725 .03295 L .30285 .05126 L .33119 .0774 L .36273 .11253 L .47613 .27222 L .5 .30902 L Mfstroke 0 .4 1 r .5 .60332 m .50739 .60324 L .51411 .60303 L .52186 .60262 L .52918 .60208 L .54219 .60072 L .55627 .59869 L .57172 .59578 L .58801 .59195 L .61696 .58316 L .64637 .57159 L .67338 .55852 L .73237 .52139 L .78805 .4743 L .83409 .42481 L .88088 .36178 L .91674 .30083 L .94155 .24776 L .96085 .19344 L .96844 .16423 L .97123 .15053 L .97325 .13833 L .97464 .12759 L .97517 .12232 L .97563 .11665 L .97595 .11108 L .97607 .10801 L .97615 .10525 L .97619 .09997 L .97611 .0951 L .97592 .0906 L .97559 .08587 L .97517 .08153 L .97469 .07765 L .97321 .06905 L .97227 .06494 L .97111 .06061 L .96848 .05291 L .96509 .04542 L .96132 .03906 L .95744 .03389 L .95339 .02959 L .94868 .02562 L .94303 .02196 L .93737 .01923 L .93469 .01822 L .93171 .01727 L .92907 .01657 L .9261 .01594 L .92251 .01536 L Mistroke .91901 .01498 L .91549 .01477 L .91215 .01472 L .90802 .01482 L .9059 .01495 L .90354 .01515 L .89928 .01563 L .8952 .01625 L .88565 .01824 L .87489 .02126 L .85381 .02915 L .83315 .03893 L .74039 .09918 L .5013 .30781 L .27016 .51082 L .21615 .54976 L .17018 .57737 L .14732 .5884 L .12786 .59589 L .11793 .59888 L .10798 .6012 L .103 .60207 L .0985 .60268 L .09596 .60293 L .09369 .60311 L .09112 .60325 L .08873 .60331 L .08511 .60328 L .08133 .60308 L .07787 .60272 L .0748 .60226 L .07131 .60155 L .06765 .60057 L .06134 .59825 L .05526 .59508 L .04936 .59088 L .0448 .58663 L .04027 .58124 L .03682 .57604 L .03361 .57 L .03062 .56272 L .02834 .55547 L .02663 .54819 L .0254 .54101 L .02485 .53671 L .02445 .53268 L .02411 .52791 L .02391 .52329 L .02382 .51864 L .02384 .51353 L Mistroke .02398 .50858 L .02421 .50397 L .02459 .49847 L .02516 .49234 L .02658 .48083 L .02861 .4684 L .03137 .4547 L .03788 .42899 L .05627 .37564 L .07919 .32514 L .14874 .21465 L .1982 .15742 L .24915 .11088 L .30313 .07284 L .35644 .04522 L .38803 .03317 L .41729 .02475 L .43361 .02117 L .44226 .01959 L .45146 .01816 L .45949 .01711 L .46837 .01618 L .47645 .01552 L .48404 .01509 L .49144 .01482 L .49935 .01472 L .5068 .01478 L .51358 .01498 L .52155 .01539 L .52604 .01571 L .53018 .01605 L .5458 .01778 L .56077 .02012 L .57715 .02344 L .60994 .0325 L .63792 .04284 L .66739 .05641 L .71872 .08695 L .77319 .12991 L .82696 .18484 L .87185 .24287 L .90629 .29794 L .93412 .35302 L .95652 .4107 L .96533 .44083 L .96838 .45354 L .97115 .46707 L .97309 .47864 L .97466 .4906 L .97529 .49701 L Mistroke .97572 .50272 L .97601 .50833 L .97616 .51352 L .97619 .51827 L .9761 .52326 L .97589 .52785 L .97561 .53195 L .97516 .53662 L .97452 .54155 L .97297 .55011 L .97191 .55454 L .97081 .55841 L .96791 .56654 L .96468 .57339 L .96115 .57923 L .95744 .58414 L .95308 .58873 L .94895 .59221 L .94417 .59542 L .9386 .59828 L .93302 .60037 L .92943 .60137 L .92591 .60213 L .92264 .60266 L .91897 .60305 L .91529 .60327 L .91182 .60332 L .9079 .6032 L .90366 .6029 L .89987 .60248 L .89626 .60195 L .88778 .6003 L .87797 .59772 L .86866 .5947 L .84645 .58561 L .79653 .55797 L .74384 .52144 L .51438 .32234 L .39293 .21082 L .26772 .10534 L .21602 .06819 L .16577 .03838 L .14371 .0281 L .13342 .02408 L .12425 .02099 L .11561 .01855 L .10809 .01686 L .10419 .01615 L .10007 .01555 L .09583 .01509 L Mistroke .09193 .01482 L .08796 .01472 L .08443 .01478 L .08048 .01503 L .07685 .01545 L .0736 .016 L .07068 .01663 L .06439 .01855 L .06129 .01981 L .05849 .02114 L .05251 .02475 L .04721 .02903 L .04209 .03446 L .03794 .04018 L .034 .04723 L .03057 .05544 L .02801 .06383 L .02698 .06815 L .02615 .07237 L .0255 .07633 L .02493 .08064 L .02444 .0855 L .02411 .09009 L .02389 .09518 L .02383 .09813 L .02381 .10093 L .02388 .10617 L .02396 .10886 L .02409 .11187 L .02442 .11728 L .02484 .12247 L .02621 .1345 L .02831 .148 L .03385 .17393 L .04083 .19898 L .05908 .24926 L .08507 .30427 L .11762 .35949 L .1591 .41652 L .20356 .46606 L .24879 .50686 L .30546 .5466 L .3368 .56373 L .37092 .57872 L .40111 .58895 L .42977 .59609 L .44631 .5991 L .46151 .60115 L .46991 .602 L .47436 .60236 L Mistroke .4791 .60268 L .48365 .60293 L .48778 .6031 L .49584 .60329 L .5 .60332 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ParametricPlot3D[{Sin[t], Cos[t], 0.1 t}, {t, 0, 25}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.21873 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics3D %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.113816 1.26975 -3.25261e-019 1.26975 [ [.40398 1.23148 -6.15686 0 ] [.40398 1.23148 5.84314 9 ] [.54027 1.19955 -11.9482 0 ] [.54027 1.19955 12.0518 9 ] [.68248 1.16622 -2.89027 0 ] [.68248 1.16622 3.10973 9 ] [.83101 1.13139 -8.36287 0 ] [.83101 1.13139 9.63713 9 ] [.98628 1.09496 -2.67856 0 ] [.98628 1.09496 3.32144 9 ] [.00902 .95482 -6.73119 0 ] [.00902 .95482 5.26881 9 ] [.11468 1.03227 -13.1396 0 ] [.11468 1.03227 10.8604 9 ] [.21153 1.10326 -3.21346 0 ] [.21153 1.10326 2.78654 9 ] [.30062 1.16856 -9.44933 0 ] [.30062 1.16856 8.55067 9 ] [.38284 1.22882 -3.09265 0 ] [.38284 1.22882 2.90735 9 ] [.07034 .25512 -6 -2.6701 ] [.07034 .25512 0 6.3299 ] [.04049 .49246 -6 -2.83818 ] [.04049 .49246 0 6.16182 ] [.0063 .76441 -6 -3.03283 ] [.0063 .76441 0 5.96717 ] [ 0 0 0 0 ] [ 1 1.21873 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .39118 1.21873 m 1 1.07556 L s .4044 1.21562 m .4046 1.20769 L s [(-1)] .40398 1.23148 .02614 -1 Mshowa .5402 1.18368 m .54017 1.17575 L s [(-0.5)] .54027 1.19955 -0.00432 -1 Mshowa .6819 1.15036 m .68161 1.14243 L s [(0)] .68248 1.16622 -0.03658 -1 Mshowa .82988 1.11556 m .82932 1.10764 L s [(0.5)] .83101 1.13139 -0.07079 -1 Mshowa .98458 1.07918 m .98374 1.07129 L s [(1)] .98628 1.09496 -0.10715 -1 Mshowa .125 Mabswid .4311 1.20934 m .4312 1.20458 L s .45803 1.203 m .4581 1.19824 L s .48519 1.19662 m .48523 1.19186 L s .51258 1.19018 m .51259 1.18542 L s .56806 1.17713 m .56801 1.17237 L s .59615 1.17053 m .59607 1.16576 L s .62449 1.16386 m .62438 1.1591 L s .65307 1.15714 m .65293 1.15238 L s .71098 1.14352 m .71077 1.13877 L s .74032 1.13662 m .74008 1.13187 L s .76991 1.12966 m .76964 1.12491 L s .79976 1.12264 m .79946 1.11789 L s .86027 1.10841 m .8599 1.10367 L s .89093 1.1012 m .89053 1.09646 L s .92187 1.09393 m .92143 1.08919 L s .95309 1.08659 m .95261 1.08185 L s .25 Mabswid 0 .93102 m .39118 1.21873 L s .01094 .93907 m .0119 .93119 L s [(-1)] .00902 .95482 .12187 -1 Mshowa .11618 1.01647 m .11693 1.00857 L s [(-0.5)] .11468 1.03227 .09497 -1 Mshowa .21265 1.08743 m .21322 1.07951 L s [(0)] .21153 1.10326 .07115 -1 Mshowa .30141 1.1527 m .3018 1.14478 L s [(0.5)] .30062 1.16856 .04993 -1 Mshowa .38333 1.21296 m .38358 1.20503 L s [(1)] .38284 1.22882 .03088 -1 Mshowa .125 Mabswid .03275 .95511 m .0333 .95038 L s .05416 .97086 m .05469 .96613 L s .0752 .98633 m .0757 .9816 L s .09587 1.00154 m .09635 .9968 L s .13614 1.03115 m .13657 1.02641 L s .15576 1.04558 m .15616 1.04084 L s .17505 1.05977 m .17543 1.05502 L s .19401 1.07371 m .19437 1.06897 L s .23099 1.10091 m .23131 1.09616 L s .24903 1.11418 m .24932 1.10943 L s .26677 1.12723 m .26705 1.12248 L s .28423 1.14007 m .28449 1.13531 L s .31831 1.16514 m .31853 1.16038 L s .33495 1.17737 m .33515 1.17262 L s .35133 1.18942 m .35151 1.18466 L s .36745 1.20128 m .36762 1.19652 L s .25 Mabswid .08677 .23528 m 0 .93102 L s .08504 .24914 m .09239 .24615 L s [(0)] .07034 .25512 1 -0.40664 Mshowa .05538 .48696 m .06283 .48421 L s [(1)] .04049 .49246 1 -0.36929 Mshowa .02139 .75949 m .02894 .75703 L s [(2)] .0063 .76441 1 -0.32604 Mshowa .125 Mabswid .07942 .29425 m .08384 .29248 L s .07364 .34054 m .07808 .3388 L s .06772 .38805 m .07216 .38634 L s .06163 .43684 m .06609 .43516 L s .04896 .53846 m .05344 .53684 L s .04236 .5914 m .04685 .58981 L s .03557 .64584 m .04007 .64429 L s .02858 .70185 m .0331 .70033 L s .01399 .81884 m .01853 .81741 L s .00637 .87998 m .01092 .87858 L s .25 Mabswid .08677 .23528 m 0 .93102 L s 0 .93102 m .39118 1.21873 L s .39118 1.21873 m .40982 .57755 L s .40982 .57755 m .08677 .23528 L s .66229 0 m .92569 .4049 L s .92569 .4049 m 1 1.07556 L s 1 1.07556 m .69378 .72389 L s .69378 .72389 m .66229 0 L s .08677 .23528 m 0 .93102 L s 0 .93102 m .69378 .72389 L s .69378 .72389 m .66229 0 L s .66229 0 m .08677 .23528 L s .40982 .57755 m .92569 .4049 L s .92569 .4049 m 1 1.07556 L s 1 1.07556 m .39118 1.21873 L s .39118 1.21873 m .40982 .57755 L s 0 0 m 1 0 L 1 1.21873 L 0 1.21873 L closepath clip newpath .5 Mabswid .65231 .50027 m .72892 .47102 L s .72892 .47102 m .78611 .42656 L s .50891 .64761 m .60341 .64836 L s .41584 .62809 m .50891 .64761 L s .33244 .59043 m .41584 .62809 L s .60341 .64836 m .69108 .63085 L s .26679 .53656 m .33244 .59043 L s .78611 .42656 m .81661 .37119 L s .69108 .63085 m .76362 .59683 L s .22648 .46998 m .26679 .53656 L s .54817 .79929 m .64451 .79371 L s .44991 .78685 m .54817 .79929 L s .35821 .75652 m .44991 .78685 L s .76362 .59683 m .81302 .54944 L s .64451 .79371 m .73042 .77107 L s .28147 .70957 m .35821 .75652 L s .81661 .37119 m .81473 .31102 L s .21775 .39603 m .22648 .46998 L s .22785 .64865 m .28147 .70957 L s .73042 .77107 m .7974 .73354 L s .81302 .54944 m .83215 .49353 L s .4878 .95462 m .59024 .9606 L s .38863 .93142 m .4878 .95462 L s .81473 .31102 m .77776 .2538 L s .59024 .9606 m .68722 .94968 L s .30141 .89167 m .38863 .93142 L s .24425 .32186 m .21775 .39603 L s .20458 .5781 m .22785 .64865 L s .7974 .73354 m .83732 .68474 L s .68722 .94968 m .76996 .92319 L s .23471 .83726 m .30141 .89167 L s .83215 .49353 m .816 .4357 L s .77776 .2538 m .70758 .20816 L s .30541 .25595 m .24425 .32186 L s .76996 .92319 m .82972 .88369 L s .21689 .50413 m .20458 .5781 L s .52938 1.13324 m .63491 1.13372 L s .42365 1.11662 m .52938 1.13324 L s .19662 .77156 m .23471 .83726 L s .32663 1.08404 m .42365 1.11662 L s .83732 .68474 m .84337 .62998 L s .24726 1.0367 m .32663 1.08404 L s .70758 .20816 m .61158 .18211 L s .816 .4357 m .76331 .38403 L s .39523 .20683 m .30541 .25595 L s .26629 .43462 m .21689 .50413 L s .82972 .88369 m .85836 .83522 L s .19371 .69975 m .19662 .77156 L s .61158 .18211 m .5023 .18119 L s .5023 .18119 m .39523 .20683 L s .19424 .97707 m .24726 1.0367 L s .84337 .62998 m .81147 .5763 L s .76331 .38403 m .67815 .34699 L s .34901 .37813 m .26629 .43462 L s .22951 .62881 m .19371 .69975 L s .17533 .90924 m .19424 .97707 L s .85836 .83522 m .84952 .78351 L s .67815 .34699 m .57055 .33174 L s .4553 .34226 m .34901 .37813 L s .81147 .5763 m .74222 .53187 L s .57055 .33174 m .4553 .34226 L s .30263 .56694 m .22951 .62881 L s .19591 .83913 m .17533 .90924 L s .84952 .78351 m .80047 .73583 L s .74222 .53187 m .64226 .50468 L s .40545 .52224 m .30263 .56694 L s .64226 .50468 m .52438 .50073 L s .25702 .77421 m .19591 .83913 L s .52438 .50073 m .40545 .52224 L s .80047 .73583 m .71404 .7002 L s .35352 .72257 m .25702 .77421 L s .71404 .7002 m .59984 .6838 L s .47349 .69113 m .35352 .72257 L s .59984 .6838 m .47349 .69113 L s .25 Mabswid .66229 0 m .92569 .4049 L s .92569 .4049 m 1 1.07556 L s 1 1.07556 m .69378 .72389 L s .69378 .72389 m .66229 0 L s .08677 .23528 m 0 .93102 L s 0 .93102 m .69378 .72389 L s .69378 .72389 m .66229 0 L s .66229 0 m .08677 .23528 L s 0 .93102 m .39118 1.21873 L s .01094 .93907 m .0119 .93119 L s [(-1)] .00902 .95482 .12187 -1 Mshowa .11618 1.01647 m .11693 1.00857 L s [(-0.5)] .11468 1.03227 .09497 -1 Mshowa .21265 1.08743 m .21322 1.07951 L s [(0)] .21153 1.10326 .07115 -1 Mshowa .30141 1.1527 m .3018 1.14478 L s [(0.5)] .30062 1.16856 .04993 -1 Mshowa .38333 1.21296 m .38358 1.20503 L s [(1)] .38284 1.22882 .03088 -1 Mshowa .125 Mabswid .03275 .95511 m .0333 .95038 L s .05416 .97086 m .05469 .96613 L s .0752 .98633 m .0757 .9816 L s .09587 1.00154 m .09635 .9968 L s .13614 1.03115 m .13657 1.02641 L s .15576 1.04558 m .15616 1.04084 L s .17505 1.05977 m .17543 1.05502 L s .19401 1.07371 m .19437 1.06897 L s .23099 1.10091 m .23131 1.09616 L s .24903 1.11418 m .24932 1.10943 L s .26677 1.12723 m .26705 1.12248 L s .28423 1.14007 m .28449 1.13531 L s .31831 1.16514 m .31853 1.16038 L s .33495 1.17737 m .33515 1.17262 L s .35133 1.18942 m .35151 1.18466 L s .36745 1.20128 m .36762 1.19652 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{259.5, 316.25}, ImageMargins->{{51, 0}, {0, 176}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics3D \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ 5. Diferentsiaalv\[OTilde]rrandite lahendamine. Integraalide ja diferentsiaalv\[OTilde]rrandite numbriline lahendamine.\ \>", "Subtitle"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\(\(DSolve[{vor1\_vas \[Equal] vor1\_par, \ vor2\_vas \[Equal] vor2\_par, ... }, \ {f\_1[x], f\_2[x], ... }, x]\)\(\ \)\)\)]], "\n\t\t\t\tdiferentsiaalv\[OTilde]rrandite s\[UDoubleDot]steemi lahendamine\ \nN", Cell[BoxData[ \(TraditionalForm\`\(\(DSolve[{vor1\_vas \[Equal] vor1\_par, \ vor2\_vas \[Equal] vor2\_par, ... }, \ {f\_1, f\_2, ... }, {x, x\_1, x\_2}]\)\(\ \)\)\)]], "\n\t\t\t\tdiferentsiaalv\[OTilde]rrandite s\[UDoubleDot]steemi numbriline \ lahendamine l\[OTilde]igus ", Cell[BoxData[ \(TraditionalForm\`\([x\_1, x\_2]\)\)]], "\n", Cell[BoxData[ \(TraditionalForm\`NIntegrate[f[x], {x, x\_1, x\_2}]\)]], " \t\tnumbriline integreerimine\t\t" }], "Text", Background->GrayLevel[0.900008]], Cell[TextData[{ "Vaatame n\[ADoubleDot]itena j\[ADoubleDot]rgmist \ diferentsiaalv\[OTilde]rrandit: ", Cell[BoxData[ \(TraditionalForm\`\(\(d\^2\) \(y(x)\)\)\/dx\^2 = a\ \(y(x)\) + 1\)]], ", mis on teist j\[ADoubleDot]rku diferentsiaalv\[OTilde]rrand. Selle \ lahendamine:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(DSolve[\[PartialD]\_x y[x] \[Equal] a*y[x] + 1, y[x], x]\)], "Input"], Cell[BoxData[ \({{y[ x] \[Rule] \(-\(1\/a\)\) + \[ExponentialE]\^\(a\ x\)\ C[ 1]}}\)], "Output"] }, Open ]], Cell["Selle t\[ADoubleDot]histusviisiga analoogiline on \ j\[ADoubleDot]rgmine:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(DSolve[\(y'\)[x] \[Equal] a*y[x] + 1, y[x], x]\)], "Input"], Cell[BoxData[ \({{y[ x] \[Rule] \(-\(1\/a\)\) + \[ExponentialE]\^\(a\ x\)\ C[ 1]}}\)], "Output"] }, Open ]], Cell["\<\ Nagu n\[ADoubleDot]ha, on siin sees ka kaks konstanti, mis m\[ADoubleDot]\ \[ADoubleDot]ratakse lisatingimustest. Anname ette ka lisatingimused ning vaatame, milline n\[ADoubleDot]eb v\ \[ADoubleDot]lja lahendi graafik.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(lahend = DSolve[{\[PartialD]\_x y[x] \[Equal] a*y[x] + 1, y[1] == 2\/a}, y[x], x]\)], "Input"], Cell[BoxData[ \({{y[ x] \[Rule] \(\[ExponentialE]\^\(-a\)\ \((\(-\[ExponentialE]\^a\) \ + 3\ \[ExponentialE]\^\(a\ x\))\)\)\/a}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(lahend[\([1]\)]\)[\([1]\)]\)[\([2]\)]\)], "Input"], Cell[BoxData[ \(\(\[ExponentialE]\^\(-a\)\ \((\(-\[ExponentialE]\^a\) + 3\ \ \[ExponentialE]\^\(a\ x\))\)\)\/a\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[\(\(lahend[\([1]\)]\)[\([1]\)]\)[\([2]\)]\ /. a \[Rule] 3, {x, \(-1\), 2}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.31746 0.031941 0.0520649 [ [.02381 .01944 -6 -9 ] [.02381 .01944 6 0 ] [.18254 .01944 -12 -9 ] [.18254 .01944 12 0 ] [.5 .01944 -9 -9 ] [.5 .01944 9 0 ] [.65873 .01944 -3 -9 ] [.65873 .01944 3 0 ] [.81746 .01944 -9 -9 ] [.81746 .01944 9 0 ] [.97619 .01944 -3 -9 ] [.97619 .01944 3 0 ] [.32877 .13607 -6 -4.5 ] [.32877 .13607 0 4.5 ] [.32877 .2402 -6 -4.5 ] [.32877 .2402 0 4.5 ] [.32877 .34433 -6 -4.5 ] [.32877 .34433 0 4.5 ] [.32877 .44846 -6 -4.5 ] [.32877 .44846 0 4.5 ] [.32877 .55259 -12 -4.5 ] [.32877 .55259 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 .03194 m .02381 .03819 L s [(-1)] .02381 .01944 0 1 Mshowa .18254 .03194 m .18254 .03819 L s [(-0.5)] .18254 .01944 0 1 Mshowa .5 .03194 m .5 .03819 L s [(0.5)] .5 .01944 0 1 Mshowa .65873 .03194 m .65873 .03819 L s [(1)] .65873 .01944 0 1 Mshowa .81746 .03194 m .81746 .03819 L s [(1.5)] .81746 .01944 0 1 Mshowa .97619 .03194 m .97619 .03819 L s [(2)] .97619 .01944 0 1 Mshowa .125 Mabswid .05556 .03194 m .05556 .03569 L s .0873 .03194 m .0873 .03569 L s .11905 .03194 m .11905 .03569 L s .15079 .03194 m .15079 .03569 L s .21429 .03194 m .21429 .03569 L s .24603 .03194 m .24603 .03569 L s .27778 .03194 m .27778 .03569 L s .30952 .03194 m .30952 .03569 L s .37302 .03194 m .37302 .03569 L s .40476 .03194 m .40476 .03569 L s .43651 .03194 m .43651 .03569 L s .46825 .03194 m .46825 .03569 L s .53175 .03194 m .53175 .03569 L s .56349 .03194 m .56349 .03569 L s .59524 .03194 m .59524 .03569 L s .62698 .03194 m .62698 .03569 L s .69048 .03194 m .69048 .03569 L s .72222 .03194 m .72222 .03569 L s .75397 .03194 m .75397 .03569 L s .78571 .03194 m .78571 .03569 L s .84921 .03194 m .84921 .03569 L s .88095 .03194 m .88095 .03569 L s .9127 .03194 m .9127 .03569 L s .94444 .03194 m .94444 .03569 L s .25 Mabswid 0 .03194 m 1 .03194 L s .34127 .13607 m .34752 .13607 L s [(2)] .32877 .13607 1 0 Mshowa .34127 .2402 m .34752 .2402 L s [(4)] .32877 .2402 1 0 Mshowa .34127 .34433 m .34752 .34433 L s [(6)] .32877 .34433 1 0 Mshowa .34127 .44846 m .34752 .44846 L s [(8)] .32877 .44846 1 0 Mshowa .34127 .55259 m .34752 .55259 L s [(10)] .32877 .55259 1 0 Mshowa .125 Mabswid .34127 .05797 m .34502 .05797 L s .34127 .08401 m .34502 .08401 L s .34127 .11004 m .34502 .11004 L s .34127 .1621 m .34502 .1621 L s .34127 .18814 m .34502 .18814 L s .34127 .21417 m .34502 .21417 L s .34127 .26623 m .34502 .26623 L s .34127 .29227 m .34502 .29227 L s .34127 .3183 m .34502 .3183 L s .34127 .37036 m .34502 .37036 L s .34127 .39639 m .34502 .39639 L s .34127 .42243 m .34502 .42243 L s .34127 .47449 m .34502 .47449 L s .34127 .50052 m .34502 .50052 L s .34127 .52656 m .34502 .52656 L s .34127 .00591 m .34502 .00591 L s .34127 .57862 m .34502 .57862 L s .34127 .60465 m .34502 .60465 L s .25 Mabswid .34127 0 m .34127 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .04262 .01474 L .06244 .01477 L .08426 .01481 L .10458 .01486 L .14264 .01498 L .16305 .01507 L .18163 .01516 L .20239 .01528 L .22156 .01542 L .25997 .01579 L .2787 .01602 L .29932 .01633 L .32036 .01671 L .33961 .01714 L .37838 .01827 L .39737 .01899 L .41809 .01994 L .43941 .02114 L .45874 .02245 L .49787 .02597 L .51711 .02824 L .53793 .03121 L .55748 .03459 L .57894 .03908 L .61842 .05016 L .63793 .05736 L .65885 .06671 L .67866 .07744 L .70021 .09164 L .74005 .12687 L .75983 .14994 L .78084 .17966 L .81859 .25042 L .83793 .29773 L .85879 .35942 L .87844 .42977 L .89993 .52327 L s .89993 .52327 m .91791 .61803 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{36.3125, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ \[CapitalUDoubleDot]laltoodud t\[ADoubleDot]histus lahend[[1]][[1]][[2]] \ annab parasjagu kahekordsetes loogelistes sulgudes oleva avaldise teise \ liikme, st funktsiooni. (Proovige j\[ADoubleDot]rgi, mis on lahend[[1]], \ lahend[[1]][[1]] ja lahend[[1]][[1]][[1]] ). Loomulikult oleksime v\[OTilde]inud lihtsalt defineerida uue funktsiooni \ (cut-paste abil) ning siis selle graafiku \[UDoubleDot]les joonistada juhul, \ kui a=5 n\[ADoubleDot]iteks:\ \>", "Text"], Cell[BoxData[ \(u[x_] := \(\[ExponentialE]\^\(-a\)\ \((\(-\[ExponentialE]\^a\) + 3\ \ \[ExponentialE]\^\(a\ x\))\)\)\/a\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[u[x] /. a \[Rule] 5, {x, \(-2\), 1}, PlotRange \[Rule] All]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.65873 0.31746 0.210916 0.981007 [ [.02381 .19842 -6 -9 ] [.02381 .19842 6 0 ] [.18254 .19842 -12 -9 ] [.18254 .19842 12 0 ] [.34127 .19842 -6 -9 ] [.34127 .19842 6 0 ] [.5 .19842 -12 -9 ] [.5 .19842 12 0 ] [.81746 .19842 -9 -9 ] [.81746 .19842 9 0 ] [.97619 .19842 -3 -9 ] [.97619 .19842 3 0 ] [.64623 .01471 -24 -4.5 ] [.64623 .01471 0 4.5 ] [.64623 .11282 -24 -4.5 ] [.64623 .11282 0 4.5 ] [.64623 .30902 -18 -4.5 ] [.64623 .30902 0 4.5 ] [.64623 .40712 -18 -4.5 ] [.64623 .40712 0 4.5 ] [.64623 .50522 -18 -4.5 ] [.64623 .50522 0 4.5 ] [.64623 .60332 -18 -4.5 ] [.64623 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 .21092 m .02381 .21717 L s [(-2)] .02381 .19842 0 1 Mshowa .18254 .21092 m .18254 .21717 L s [(-1.5)] .18254 .19842 0 1 Mshowa .34127 .21092 m .34127 .21717 L s [(-1)] .34127 .19842 0 1 Mshowa .5 .21092 m .5 .21717 L s [(-0.5)] .5 .19842 0 1 Mshowa .81746 .21092 m .81746 .21717 L s [(0.5)] .81746 .19842 0 1 Mshowa .97619 .21092 m .97619 .21717 L s [(1)] .97619 .19842 0 1 Mshowa .125 Mabswid .05556 .21092 m .05556 .21467 L s .0873 .21092 m .0873 .21467 L s .11905 .21092 m .11905 .21467 L s .15079 .21092 m .15079 .21467 L s .21429 .21092 m .21429 .21467 L s .24603 .21092 m .24603 .21467 L s .27778 .21092 m .27778 .21467 L s .30952 .21092 m .30952 .21467 L s .37302 .21092 m .37302 .21467 L s .40476 .21092 m .40476 .21467 L s .43651 .21092 m .43651 .21467 L s .46825 .21092 m .46825 .21467 L s .53175 .21092 m .53175 .21467 L s .56349 .21092 m .56349 .21467 L s .59524 .21092 m .59524 .21467 L s .62698 .21092 m .62698 .21467 L s .69048 .21092 m .69048 .21467 L s .72222 .21092 m .72222 .21467 L s .75397 .21092 m .75397 .21467 L s .78571 .21092 m .78571 .21467 L s .84921 .21092 m .84921 .21467 L s .88095 .21092 m .88095 .21467 L s .9127 .21092 m .9127 .21467 L s .94444 .21092 m .94444 .21467 L s .25 Mabswid 0 .21092 m 1 .21092 L s .65873 .01471 m .66498 .01471 L s [(-0.2)] .64623 .01471 1 0 Mshowa .65873 .11282 m .66498 .11282 L s [(-0.1)] .64623 .11282 1 0 Mshowa .65873 .30902 m .66498 .30902 L s [(0.1)] .64623 .30902 1 0 Mshowa .65873 .40712 m .66498 .40712 L s [(0.2)] .64623 .40712 1 0 Mshowa .65873 .50522 m .66498 .50522 L s [(0.3)] .64623 .50522 1 0 Mshowa .65873 .60332 m .66498 .60332 L s [(0.4)] .64623 .60332 1 0 Mshowa .125 Mabswid .65873 .03434 m .66248 .03434 L s .65873 .05396 m .66248 .05396 L s .65873 .07358 m .66248 .07358 L s .65873 .0932 m .66248 .0932 L s .65873 .13244 m .66248 .13244 L s .65873 .15206 m .66248 .15206 L s .65873 .17168 m .66248 .17168 L s .65873 .1913 m .66248 .1913 L s .65873 .23054 m .66248 .23054 L s .65873 .25016 m .66248 .25016 L s .65873 .26978 m .66248 .26978 L s .65873 .2894 m .66248 .2894 L s .65873 .32864 m .66248 .32864 L s .65873 .34826 m .66248 .34826 L s .65873 .36788 m .66248 .36788 L s .65873 .3875 m .66248 .3875 L s .65873 .42674 m .66248 .42674 L s .65873 .44636 m .66248 .44636 L s .65873 .46598 m .66248 .46598 L s .65873 .4856 m .66248 .4856 L s .65873 .52484 m .66248 .52484 L s .65873 .54446 m .66248 .54446 L s .65873 .56408 m .66248 .56408 L s .65873 .5837 m .66248 .5837 L s .25 Mabswid .65873 0 m .65873 .61803 L s .5 Mabswid .02381 .01472 m .04262 .01472 L .06244 .01472 L .08255 .01472 L .10458 .01472 L .12415 .01472 L .14509 .01472 L .16639 .01472 L .18653 .01472 L .20651 .01472 L .22495 .01472 L .24367 .01472 L .2643 .01472 L .28371 .01473 L .30459 .01473 L .32572 .01474 L .34581 .01474 L .36562 .01475 L .384 .01477 L .40453 .01479 L .42313 .01481 L .44238 .01485 L .4632 .0149 L .48314 .01496 L .5042 .01506 L .52384 .01519 L .54217 .01535 L .56253 .01559 L .58108 .01588 L .60017 .01629 L .62093 .0169 L .6407 .0177 L .66171 .01887 L .68118 .02036 L .69946 .02225 L .71964 .02507 L .73815 .02857 L .75707 .03338 L .77777 .04057 L .79738 .04993 L .81833 .0637 L .83968 .08328 L .85983 .10889 L .87985 .14378 L .8983 .18731 L .91706 .24665 L .9377 .33575 L .95626 .44472 L .97619 .60332 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg`0oooo00<000000?ooo`3oool07@3oool5000005L0oooo003/0?ooo`8000008`3oool20000 05D0oooo003/0?ooo`030000003oool0oooo02@0oooo0P00001C0?ooo`00k03oool00`000000oooo 0?ooo`0V0?ooo`<00000D03oool00>`0oooo00<000000?ooo`3oool0:@3oool2000004h0oooo003/ 0?ooo`030000003oool0oooo02/0oooo0P00001<0?ooo`00k03oool00`000000oooo0?ooo`0]0?oo o`800000BP3oool00>`0oooo00<000000?ooo`3oool0;`3oool2000004P0oooo003/0?ooo`800000 `0oooo00<000000?ooo`3oool0=03oool2000004<0oooo003/0?ooo`030000003oool0oooo 03H0oooo00<000000?ooo`3oool0@03oool00>`0oooo00<000000?ooo`3oool0=`3oool00`000000 oooo0?ooo`0o0?ooo`00k03oool00`000000oooo0?ooo`0h0?ooo`030000003oool0oooo03h0oooo 003/0?ooo`030000003oool0oooo03T0oooo00<000000?ooo`3oool0?@3oool00>`0oooo0P00000k 0?ooo`030000003oool0oooo03`0oooo003/0?ooo`030000003oool0oooo03/0oooo00<000000?oo o`3oool0>`3oool00>`0oooo00<000000?ooo`3oool0?03oool00`000000oooo0?ooo`0j0?ooo`00 k03oool00`000000oooo0?ooo`0m0?ooo`030000003oool0oooo03T0oooo003/0?ooo`030000003o ool0oooo03h0oooo00<000000?ooo`3oool0>03oool00>`0oooo00<000000?ooo`3oool0?`3oool0 0`000000oooo0?ooo`0g0?ooo`00k03oool00`000000oooo0?ooo`0o0?ooo`030000003oool0oooo 03L0oooo003/0?ooo`800000@@3oool00`000000oooo0?ooo`0f0?ooo`00k03oool00`000000oooo 0?ooo`110?ooo`030000003oool0oooo03D0oooo003/0?ooo`030000003oool0oooo0480oooo00<0 00000?ooo`3oool0=03oool00>`0oooo00<000000?ooo`3oool0@P3oool00`000000oooo0?ooo`0d 0?ooo`00d@3oool4000000D0oooo0P0000050?ooo`D000001P3oool00`000000oooo0?ooo`130?oo o`030000003oool0oooo03<0oooo003@0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3o ool00P3oool2000000L0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`140?ooo`03 0000003oool0oooo0380oooo003@0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0 2`3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo04D0oooo00<000000?ooo`3oool0 <@3oool00`0oooo00<000000?ooo`3oool0B03oool00`000000oooo0?oo o`0^0?ooo`00k03oool00`000000oooo0?ooo`190?ooo`030000003oool0oooo02d0oooo003/0?oo o`800000B`3oool00`000000oooo0?ooo`0/0?ooo`00k03oool00`000000oooo0?ooo`1:0?ooo`03 0000003oool0oooo02`0oooo003/0?ooo`030000003oool0oooo04/0oooo00<000000?ooo`3oool0 :`3oool00>`0oooo00<000000?ooo`3oool0B`3oool00`000000oooo0?ooo`0[0?ooo`00k03oool0 0`000000oooo0?ooo`1<0?ooo`030000003oool0oooo02X0oooo003/0?ooo`030000003oool0oooo 04`0oooo00<000000?ooo`3oool0:P3oool00>`0oooo00<000000?ooo`3oool0C@3oool00`000000 oooo0?ooo`0Y0?ooo`00k03oool2000004h0oooo00<000000?ooo`3oool0:@3oool00>`0oooo00<0 00000?ooo`3oool0CP3oool00`000000oooo0?ooo`0X0?ooo`00k03oool00`000000oooo0?ooo`1> 0?ooo`030000003oool0oooo02P0oooo003/0?ooo`030000003oool0oooo04h0oooo00<000000?oo o`3oool0:03oool00>`0oooo00<000000?ooo`3oool0C`3oool00`000000oooo0?ooo`0W0?ooo`00 2P3oool5000002d0oooo1@0000040?ooo`8000001@3oool4000002`0oooo1@00000/0?ooo`@00000 1@3oool2000000D0oooo1000000[0?ooo`030000003oool0oooo02/0oooo100000050?ooo`800000 1@3oool400000100oooo00<000000?ooo`3oool06P3oool5000000P0oooo000:0?ooo`050000003o ool0oooo0?ooo`000000;`3oool00`000000oooo0?ooo`040?ooo`800000103oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo02/0oooo00<000000?ooo`3oool0:`3oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo0080oooo0P0000040?ooo`030000003oool0oooo0080oooo 00<000000?ooo`3oool0:03oool00`000000oooo0?ooo`0Z0?ooo`030000003oool0oooo0080oooo 00<000000?ooo`3oool00P3oool2000000@0oooo00<000000?ooo`3oool00P3oool00`000000oooo 0?ooo`0>0?ooo`030000003oool0oooo01/0oooo00<000000?ooo`3oool0203oool000/0oooo00<0 00000?ooo`3oool0<03oool00`000000oooo0?ooo`0?0?ooo`030000003oool0oooo02/0oooo00<0 00000?ooo`3oool0:`3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00d0oooo00<0 00000?ooo`3oool0:03oool2000002/0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?oo o`0=0?ooo`030000003oool0oooo00h0oooo00<000000?ooo`3oool06`3oool00`000000oooo0?oo o`080?ooo`000P3oool6000000@0oooo00<000000?ooo`3oool0903oool6000000D0oooo00<00000 0?ooo`3oool03`3oool00`000000oooo0?ooo`0P0?ooo`H000001@3oool00`000000oooo0?ooo`0S 0?ooo`H000000P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00d0oooo00<00000 0?ooo`3oool0:03oool00`000000oooo0?ooo`0Z0?ooo`030000003oool0oooo0080oooo00<00000 0?ooo`3oool03@3oool00`000000oooo0?ooo`0>0?ooo`030000003oool0oooo01/0oooo00<00000 0?ooo`3oool0203oool000d0oooo00<000000?ooo`3oool0;P3oool00`000000oooo0?ooo`0;0?oo o`@00000;P3oool00`000000oooo0?ooo`0[0?ooo`030000003oool0oooo0080oooo00<000000?oo o`3oool02@3oool4000002/0oooo00<000000?ooo`3oool0:P3oool00`000000oooo0?ooo`020?oo o`030000003oool0oooo00T0oooo1000000B0?ooo`030000003oool0oooo01X0oooo00<000000?oo o`3oool0203oool000h0oooo00<000000?ooo`3oool0;@3oool00`000000oooo0?ooo`0;0?ooo`03 0000003oool0oooo02l0oooo00<000000?ooo`3oool0:`3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo00T0oooo00<000000?ooo`3oool0;03oool00`000000oooo0?ooo`0Z0?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`0C0?ooo`03 0000003oool0oooo01X0oooo00<000000?ooo`3oool0203oool000X0oooo00D000000?ooo`3oool0 oooo0000000]0?ooo`<000003@3oool00`000000oooo0?ooo`0]0?ooo`<00000;@3oool00`000000 oooo0?ooo`020?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool0;03oool00`000000 oooo0?ooo`0Z0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool02@3oool00`000000 oooo0?ooo`0D0?ooo`030000003oool0oooo01L0oooo0`00000:0?ooo`002`3oool300000300oooo 00<000000?ooo`3oool02`3oool5000002d0oooo00<000000?ooo`3oool0;03oool4000000`0oooo 1@00000Z0?ooo`030000003oool0oooo02/0oooo1000000<0?ooo`D000004P3oool00`000000oooo 0?ooo`0I0?ooo`030000003oool0oooo00P0oooo003/0?ooo`030000003oool0oooo0580oooo00<0 00000?ooo`3oool0903oool00>`0oooo0P00001D0?ooo`030000003oool0oooo02<0oooo003/0?oo o`030000003oool0oooo05<0oooo00<000000?ooo`3oool08`3oool00>`0oooo00<000000?ooo`3o ool0D`3oool00`000000oooo0?ooo`0S0?ooo`00k03oool00`000000oooo0?ooo`1D0?ooo`030000 003oool0oooo0280oooo003/0?ooo`030000003oool0oooo05@0oooo00<000000?ooo`3oool08P3o ool00>`0oooo00<000000?ooo`3oool0E03oool00`000000oooo0?ooo`0R0?ooo`00k03oool00`00 0000oooo0?ooo`1E0?ooo`030000003oool0oooo0240oooo00000`3oool000000000003o000006@0 00000P3oool000T0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`090?ooo`030000 003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`090?ooo`030000 003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`090?ooo`030000 003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`090?ooo`030000 003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`090?ooo`030000 003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`090?ooo`030000 003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`090?ooo`030000 003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`090?ooo`030000 003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`090?ooo`030000 003oool0oooo00P0oooo00<000000?ooo`3oool01P3oool00`000000oooo0000000;0?ooo`030000 003oool0oooo00P0oooo00<000000?ooo`3oool0203oool000T0oooo00<000000?ooo`3oool0=P3o ool00`000000oooo0?ooo`0e0?ooo`030000003oool0oooo03H0oooo00<000000?ooo`3oool0=P3o ool00`000000oooo0?ooo`0e0?ooo`030000003oool0oooo01d0oooo00<000000?ooo`3oool05P3o ool00`000000oooo0?ooo`080?ooo`00k03oool00`000000oooo0?ooo`1F0?ooo`030000003oool0 oooo0200oooo003/0?ooo`030000003oool0oooo05H0oooo00<000000?ooo`3oool0803oool00>`0 oooo00<000000?ooo`3oool0EP3oool00`000000oooo0?ooo`0P0?ooo`00k03oool00`000000oooo 0?ooo`1G0?ooo`030000003oool0oooo01l0oooo003/0?ooo`800000F03oool00`000000oooo0?oo o`0O0?ooo`00k03oool00`000000oooo0?ooo`1G0?ooo`030000003oool0oooo01l0oooo003/0?oo o`030000003oool0oooo05P0oooo00<000000?ooo`3oool07P3oool00>`0oooo00<000000?ooo`3o ool0F03oool00`000000oooo0?ooo`0N0?ooo`00k03oool00`000000oooo0?ooo`1H0?ooo`030000 003oool0oooo01h0oooo003/0?ooo`030000003oool0oooo05T0oooo00<000000?ooo`3oool07@3o ool00>`0oooo00<000000?ooo`3oool0F@3oool00`000000oooo0?ooo`0M0?ooo`00k03oool20000 05X0oooo00<000000?ooo`3oool07@3oool00>`0oooo00<000000?ooo`3oool0F@3oool00`000000 oooo0?ooo`0M0?ooo`00k03oool00`000000oooo0?ooo`1J0?ooo`030000003oool0oooo01`0oooo 003/0?ooo`030000003oool0oooo05X0oooo00<000000?ooo`3oool0703oool00>`0oooo00<00000 0?ooo`3oool0FP3oool00`000000oooo0?ooo`0L0?ooo`00k03oool00`000000oooo0?ooo`1J0?oo o`030000003oool0oooo01`0oooo003/0?ooo`030000003oool0oooo05/0oooo00<000000?ooo`3o ool06`3oool00>`0oooo0P00001L0?ooo`030000003oool0oooo01/0oooo003/0?ooo`030000003o ool0oooo05/0oooo00<000000?ooo`3oool06`3oool00>`0oooo00<000000?ooo`3oool0F`3oool0 0`000000oooo0?ooo`0K0?ooo`00k03oool00`000000oooo0?ooo`1K0?ooo`030000003oool0oooo 01/0oooo003/0?ooo`030000003oool0oooo05`0oooo00<000000?ooo`3oool06P3oool00>`0oooo 00<000000?ooo`3oool0G03oool00`000000oooo0?ooo`0J0?ooo`00k03oool00`000000oooo0?oo o`1L0?ooo`030000003oool0oooo01X0oooo003/0?ooo`800000G@3oool00`000000oooo0?ooo`0J 0?ooo`00k03oool00`000000oooo0?ooo`1M0?ooo`030000003oool0oooo01T0oooo003/0?ooo`03 0000003oool0oooo05d0oooo00<000000?ooo`3oool06@3oool00>`0oooo00<000000?ooo`3oool0 G@3oool00`000000oooo0?ooo`0I0?ooo`00d@3oool4000000D0oooo0P0000050?ooo`D000001P3o ool00`000000oooo0?ooo`1M0?ooo`030000003oool0oooo01T0oooo003@0?ooo`030000003oool0 oooo0080oooo00<000000?ooo`3oool00P3oool2000000L0oooo00<000000?ooo`3oool01P3oool0 0`000000oooo0?ooo`1N0?ooo`030000003oool0oooo01P0oooo003@0?ooo`030000003oool0oooo 0080oooo00<000000?ooo`3oool02`3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo 05h0oooo00<000000?ooo`3oool0603oool00=00oooo00<000000?ooo`3oool00P3oool00`000000 oooo0?ooo`0;0?ooo`030000003oool0oooo00H0oooo0`00001N0?ooo`030000003oool0oooo01P0 oooo003@0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool02`3oool00`000000oooo 0?ooo`060?ooo`030000003oool0oooo05h0oooo00<000000?ooo`3oool0603oool00=00oooo00<0 00000?ooo`3oool00P3oool00`000000oooo0?ooo`0;0?ooo`030000003oool0oooo00H0oooo00<0 00000?ooo`3oool0GP3oool00`000000oooo0?ooo`0H0?ooo`00d03oool00`000000oooo0?ooo`02 0?ooo`030000003oool0oooo00T0oooo0`0000080?ooo`030000003oool0oooo05l0oooo00<00000 0?ooo`3oool05`3oool00=40oooo1000000>0?ooo`030000003oool0oooo00H0oooo00<000000?oo o`3oool0G`3oool00`000000oooo0?ooo`0G0?ooo`00k03oool00`000000oooo0?ooo`1O0?ooo`03 0000003oool0oooo01L0oooo003/0?ooo`030000003oool0oooo05l0oooo00<000000?ooo`3oool0 5`3oool00>`0oooo0P00001Q0?ooo`030000003oool0oooo01H0oooo003/0?ooo`030000003oool0 oooo0600oooo00<000000?ooo`3oool05P3oool00>`0oooo00<000000?ooo`3oool0H03oool00`00 0000oooo0?ooo`0F0?ooo`00k03oool00`000000oooo0?ooo`1P0?ooo`030000003oool0oooo01H0 oooo003/0?ooo`030000003oool0oooo0600oooo00<000000?ooo`3oool05P3oool00>`0oooo00<0 00000?ooo`3oool0H@3oool00`000000oooo0?ooo`0E0?ooo`00k03oool00`000000oooo0?ooo`1Q 0?ooo`030000003oool0oooo01D0oooo003/0?ooo`800000HP3oool00`000000oooo0?ooo`0E0?oo o`00k03oool00`000000oooo0?ooo`1Q0?ooo`030000003oool0oooo01D0oooo003/0?ooo`030000 003oool0oooo0640oooo00<000000?ooo`3oool05@3oool00>`0oooo00<000000?ooo`3oool0H@3o ool00`000000oooo0?ooo`0E0?ooo`00k03oool00`000000oooo0?ooo`1R0?ooo`030000003oool0 oooo01@0oooo003/0?ooo`030000003oool0oooo0680oooo00<000000?ooo`3oool0503oool00>`0 oooo00<000000?ooo`3oool0HP3oool00`000000oooo0?ooo`0D0?ooo`00k03oool2000006<0oooo 00<000000?ooo`3oool0503oool00>`0oooo00<000000?ooo`3oool0HP3oool00`000000oooo0?oo o`0D0?ooo`00k03oool00`000000oooo0?ooo`1S0?ooo`030000003oool0oooo01<0oooo003/0?oo o`030000003oool0oooo06<0oooo00<000000?ooo`3oool04`3oool00>`0oooo00<000000?ooo`3o ool0H`3oool00`000000oooo0?ooo`0C0?ooo`00k03oool00`000000oooo0?ooo`1S0?ooo`030000 003oool0oooo01<0oooo003/0?ooo`030000003oool0oooo06<0oooo00<000000?ooo`3oool04`3o ool00>`0oooo0P00001T0?ooo`030000003oool0oooo01<0oooo003/0?ooo`030000003oool0oooo 06@0oooo00<000000?ooo`3oool04P3oool00>`0oooo00<000000?ooo`3oool0I03oool00`000000 oooo0?ooo`0B0?ooo`00k03oool00`000000oooo0?ooo`1T0?ooo`030000003oool0oooo0180oooo 003A0?ooo`@000001@3oool2000000@0oooo1@0000070?ooo`030000003oool0oooo06@0oooo00<0 00000?ooo`3oool04P3oool00=00oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`02 0?ooo`800000103oool01@000000oooo0?ooo`3oool0000000L0oooo00<000000?ooo`3oool0I03o ool00`000000oooo0?ooo`0B0?ooo`00d03oool00`000000oooo0?ooo`020?ooo`030000003oool0 oooo00T0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`1T0?ooo`030000003oool0 oooo0180oooo003@0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool02P3oool00`00 0000oooo0?ooo`070?ooo`<00000I@3oool00`000000oooo0?ooo`0A0?ooo`00d03oool00`000000 oooo0?ooo`020?ooo`030000003oool0oooo00/0oooo00<000000?ooo`3oool01P3oool00`000000 oooo0?ooo`1U0?ooo`030000003oool0oooo0140oooo003@0?ooo`030000003oool0oooo0080oooo 00<000000?ooo`3oool0303oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo06D0oooo 00<000000?ooo`3oool04@3oool00=00oooo00<000000?ooo`3oool00P3oool00`000000oooo0?oo o`080?ooo`050000003oool0oooo0?ooo`0000001`3oool00`000000oooo0?ooo`1U0?ooo`030000 003oool0oooo0140oooo003A0?ooo`@00000303oool3000000P0oooo00<000000?ooo`3oool0I@3o ool00`000000oooo0?ooo`0A0?ooo`00k03oool00`000000oooo0?ooo`1V0?ooo`030000003oool0 oooo0100oooo003/0?ooo`030000003oool0oooo06H0oooo00<000000?ooo`3oool0403oool00>`0 oooo0P00001W0?ooo`030000003oool0oooo0100oooo003/0?ooo`030000003oool0oooo06H0oooo 00<000000?ooo`3oool0403oool00>`0oooo00<000000?ooo`3oool0IP3oool00`000000oooo0?oo o`0@0?ooo`00k03oool00`000000oooo0?ooo`1V0?ooo`030000003oool0oooo0100oooo003/0?oo o`030000003oool0oooo06L0oooo00<000000?ooo`3oool03`3oool00>`0oooo00<000000?ooo`3o ool0I`3oool00`000000oooo0?ooo`0?0?ooo`00k03oool00`000000oooo0?ooo`1W0?ooo`030000 003oool0oooo00l0oooo003/0?ooo`800000J03oool00`000000oooo0?ooo`0?0?ooo`00k03oool0 0`000000oooo0?ooo`1W0?ooo`030000003oool0oooo00l0oooo003/0?ooo`030000003oool0oooo 06L0oooo00<000000?ooo`3oool03`3oool00>`0oooo00<000000?ooo`3oool0I`3oool00`000000 oooo0?ooo`0?0?ooo`00k03oool00`000000oooo0?ooo`1X0?ooo`030000003oool0oooo00h0oooo 003/0?ooo`030000003oool0oooo06P0oooo00<000000?ooo`3oool03P3oool00>`0oooo00<00000 0?ooo`3oool0J03oool00`000000oooo0?ooo`0>0?ooo`00k03oool2000006T0oooo00<000000?oo o`3oool03P3oool00>`0oooo00<000000?ooo`3oool0J03oool00`000000oooo0?ooo`0>0?ooo`00 k03oool00`000000oooo0?ooo`1X0?ooo`030000003oool0oooo00h0oooo003/0?ooo`030000003o ool0oooo06P0oooo00<000000?ooo`3oool03P3oool00>`0oooo00<000000?ooo`3oool0J03oool0 0`000000oooo0?ooo`0>0?ooo`00k03oool00`000000oooo0?ooo`1Y0?ooo`030000003oool0oooo 00d0oooo003/0?ooo`030000003oool0oooo06T0oooo00<000000?ooo`3oool03@3oool00>`0oooo 0P00001Z0?ooo`030000003oool0oooo00d0oooo003/0?ooo`030000003oool0oooo06T0oooo00<0 00000?ooo`3oool03@3oool00>`0oooo00<000000?ooo`3oool0J@3oool00`000000oooo0?ooo`0= 0?ooo`00k03oool00`000000oooo0?ooo`1Y0?ooo`030000003oool0oooo00d0oooo003A0?ooo`@0 00001@3oool2000000D0oooo0`0000080?ooo`030000003oool0oooo06T0oooo00<000000?ooo`3o ool03@3oool00=00oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`020?ooo`800000 103oool01@000000oooo0?ooo`3oool0000000L0oooo00<000000?ooo`3oool0J@3oool00`000000 oooo0?ooo`0=0?ooo`00d03oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00`0oooo 00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`1Z0?ooo`030000003oool0oooo00`0oooo 003@0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0303oool00`000000oooo0?oo o`050?ooo`<00000JP3oool00`000000oooo0?ooo`0<0?ooo`00d03oool00`000000oooo0?ooo`02 0?ooo`030000003oool0oooo00X0oooo0P0000080?ooo`030000003oool0oooo06X0oooo00<00000 0?ooo`3oool0303oool00=00oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`0<0?oo o`030000003oool0oooo00D0oooo00<000000?ooo`3oool0JP3oool00`000000oooo0?ooo`0<0?oo o`00d03oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00P0oooo00D000000?ooo`3o ool0oooo000000070?ooo`030000003oool0oooo06X0oooo00<000000?ooo`3oool0303oool00=40 oooo1000000<0?ooo`<00000203oool00`000000oooo0?ooo`1Z0?ooo`030000003oool0oooo00`0 oooo003/0?ooo`030000003oool0oooo06X0oooo00<000000?ooo`3oool0303oool00>`0oooo00<0 00000?ooo`3oool0JP3oool00`000000oooo0?ooo`0<0?ooo`00k03oool2000006`0oooo00<00000 0?ooo`3oool02`3oool00>`0oooo00<000000?ooo`3oool0J`3oool00`000000oooo0?ooo`0;0?oo o`00k03oool00`000000oooo0?ooo`1[0?ooo`030000003oool0oooo00/0oooo003/0?ooo`030000 003oool0oooo06/0oooo00<000000?ooo`3oool02`3oool00>`0oooo00<000000?ooo`3oool0J`3o ool00`000000oooo0?ooo`0;0?ooo`00k03oool00`000000oooo0?ooo`1[0?ooo`030000003oool0 oooo00/0oooo003/0?ooo`030000003oool0oooo06/0oooo00<000000?ooo`3oool02`3oool00>`0 oooo0P00001/0?ooo`030000003oool0oooo00/0oooo003/0?ooo`030000003oool0oooo06`0oooo 00<000000?ooo`3oool02P3oool00>`0oooo00<000000?ooo`3oool0K03oool00`000000oooo0?oo o`0:0?ooo`00k03oool00`000000oooo0?ooo`1/0?ooo`030000003oool0oooo00X0oooo003/0?oo o`030000003oool0oooo06`0oooo00<000000?ooo`3oool02P3oool00>`0oooo00<000000?ooo`3o ool0K03oool00`000000oooo0?ooo`0:0?ooo`00k03oool00`000000oooo0?ooo`1/0?ooo`030000 003oool0oooo00X0oooo003/0?ooo`800000K@3oool00`000000oooo0?ooo`0:0?ooo`00k03oool0 0`000000oooo0?ooo`1/0?ooo`030000003oool0oooo00X0oooo003/0?ooo`030000003oool0oooo 06d0oooo00<000000?ooo`3oool02@3oool00>`0oooo00<000000?ooo`3oool0K@3oool00`000000 oooo0?ooo`090?ooo`00k03oool00`000000oooo0?ooo`1]0?ooo`030000003oool0oooo00T0oooo 003/0?ooo`030000003oool0oooo06d0oooo00<000000?ooo`3oool02@3oool00>`0oooo00<00000 0?ooo`3oool0K@3oool00`000000oooo0?ooo`090?ooo`00k03oool2000006h0oooo00<000000?oo o`3oool02@3oool00>`0oooo00<000000?ooo`3oool0K@3oool00`000000oooo0?ooo`090?ooo`00 k03oool00`000000oooo0?ooo`1]0?ooo`030000003oool0oooo00T0oooo003/0?ooo`030000003o ool0oooo06h0oooo00<000000?ooo`3oool0203oool00=40oooo100000050?ooo`8000001`3oool3 000000H0oooo00<000000?ooo`3oool0KP3oool00`000000oooo0?ooo`080?ooo`00d03oool00`00 0000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo0P0000080?ooo`030000003oool0oooo 00D0oooo00<000000?ooo`3oool0KP3oool00`000000oooo0?ooo`080?ooo`00d03oool00`000000 oooo0?ooo`020?ooo`030000003oool0oooo00`0oooo00<000000?ooo`3oool01@3oool00`000000 oooo0?ooo`1^0?ooo`030000003oool0oooo00P0oooo003@0?ooo`030000003oool0oooo0080oooo 00<000000?ooo`3oool0203oool6000000H0oooo0`00001^0?ooo`030000003oool0oooo00P0oooo 003@0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool02@3oool010000000oooo0?oo o`0000070?ooo`030000003oool0oooo07T0oooo003@0?ooo`030000003oool0oooo0080oooo00<0 00000?ooo`3oool02@3oool010000000oooo0?ooo`0000070?ooo`030000003oool0oooo07T0oooo 003@0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool02P3oool00`000000oooo0000 00070?ooo`030000003oool0oooo07T0oooo003A0?ooo`@000003P3oool2000000L0oooo00<00000 0?ooo`3oool0N@3oool00>`0oooo00<000000?ooo`3oool0N@3oool00001\ \>"], ImageRangeCache->{{{0, 359}, {221.375, 0}} -> {-2.08391, -0.21607, 0.01103, \ 0.00356937}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ Teise n\[ADoubleDot]itena vaatame sumbuvat v\[OTilde]nkumist kirjeldavat v\ \[OTilde]rrandit koos algtingimustega. See on teist j\[ADoubleDot]rku \ lineaarne konstantsete kordajatega diferentsiaalv\[OTilde]rrand: y''(x)+0.01y'(x)+4y(x)==0.2 cos (3x), y'(0)=2, y(0)=10\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(lahendus = DSolve[{\(y''\)[x] + 0.15 \( y'\)[x] + 4 y[x] \[Equal] 5 Cos[3 x], \[IndentingNewLine]\(y'\)[0] \[Equal] 2, y[0] \[Equal] 10}, y[x], x]\)], "Input"], Cell[BoxData[ \(Less::"nord" \(\(:\)\(\ \)\) "Invalid comparison with \!\(\(\(0.` \[InvisibleSpace]\)\) - \ \(\(3.9971865105346285`\\ \[ImaginaryI]\)\)\) attempted."\)], "Message"], Cell[BoxData[ \({{y[ x] \[Rule] \((\(-1.2421551317942252`\) + 0.`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(-0.075`\)\ x\)\ \ \((\((\(-8.849108135915191`\) + 0.`\ \[ImaginaryI])\)\ Cos[ 1.9985932552673142`\ x] + \((\(\(1.`\)\(\[InvisibleSpace]\ \)\) + 0.`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(0.075`\ x\)\ Cos[ 1.0014067447326858`\ x]\ Cos[ 1.9985932552673142`\ x] - \((\(\(0.20141610541330285`\)\(\ \[InvisibleSpace]\)\) + 0.`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(0.075`\ x\)\ \ Cos[1.9985932552673142`\ x]\ Cos[ 4.9985932552673145`\ x] - \((\(\(0.0748946423563588`\)\(\ \[InvisibleSpace]\)\) + 2.0770120797523094`*^-19\ \[ImaginaryI])\)\ \ \[ExponentialE]\^\(0.075`\ x\)\ Cos[1.9985932552673142`\ x]\ Sin[ 1.0014067447326858`\ x] - \((\(\(1.029809493000439`\)\(\ \[InvisibleSpace]\)\) + 0.`\ \[ImaginaryI])\)\ Sin[ 1.9985932552673142`\ x] - \((\(\(0.0748946423563588`\)\(\ \[InvisibleSpace]\)\) + 2.0770120797523094`*^-19\ \[ImaginaryI])\)\ \ \[ExponentialE]\^\(0.075`\ x\)\ Cos[1.0014067447326858`\ x]\ Sin[ 1.9985932552673142`\ x] - \((\(\(0.0030220918435560655`\)\ \(\[InvisibleSpace]\)\) + 1.0029206814769075`*^-21\ \[ImaginaryI])\)\ \ \[ExponentialE]\^\(0.075`\ x\)\ Cos[4.9985932552673145`\ x]\ Sin[ 1.9985932552673142`\ x] - \((\(\(1.`\)\(\[InvisibleSpace]\ \)\) - 6.741972681052259`*^-18\ \[ImaginaryI])\)\ \[ExponentialE]\^\(0.075`\ \ x\)\ Sin[1.0014067447326858`\ x]\ Sin[ 1.9985932552673142`\ x] + \((\(\(0.0030220918435560655`\)\ \(\[InvisibleSpace]\)\) + 1.0029206814769075`*^-21\ \[ImaginaryI])\)\ \ \[ExponentialE]\^\(0.075`\ x\)\ Cos[1.9985932552673142`\ x]\ Sin[ 4.9985932552673145`\ x] - \((\(\(0.20141610541330288`\)\(\ \[InvisibleSpace]\)\) + 1.4458051232772747`*^-19\ \[ImaginaryI])\)\ \ \[ExponentialE]\^\(0.075`\ x\)\ Sin[1.9985932552673142`\ x]\ Sin[ 4.9985932552673145`\ x])\)}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[\(\(lahendus[\([1]\)]\)[\([1]\)]\)[\([2]\)], {x, 0, 70}, PlotPoints \[Rule] 100, PlotRange \[Rule] All]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0136054 0.309807 0.0291874 [ [.15986 .29731 -6 -9 ] [.15986 .29731 6 0 ] [.29592 .29731 -6 -9 ] [.29592 .29731 6 0 ] [.43197 .29731 -6 -9 ] [.43197 .29731 6 0 ] [.56803 .29731 -6 -9 ] [.56803 .29731 6 0 ] [.70408 .29731 -6 -9 ] [.70408 .29731 6 0 ] [.84014 .29731 -6 -9 ] [.84014 .29731 6 0 ] [.97619 .29731 -6 -9 ] [.97619 .29731 6 0 ] [.01131 .01793 -18 -4.5 ] [.01131 .01793 0 4.5 ] [.01131 .16387 -12 -4.5 ] [.01131 .16387 0 4.5 ] [.01131 .45574 -6 -4.5 ] [.01131 .45574 0 4.5 ] [.01131 .60168 -12 -4.5 ] [.01131 .60168 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15986 .30981 m .15986 .31606 L s [(10)] .15986 .29731 0 1 Mshowa .29592 .30981 m .29592 .31606 L s [(20)] .29592 .29731 0 1 Mshowa .43197 .30981 m .43197 .31606 L s [(30)] .43197 .29731 0 1 Mshowa .56803 .30981 m .56803 .31606 L s [(40)] .56803 .29731 0 1 Mshowa .70408 .30981 m .70408 .31606 L s [(50)] .70408 .29731 0 1 Mshowa .84014 .30981 m .84014 .31606 L s [(60)] .84014 .29731 0 1 Mshowa .97619 .30981 m .97619 .31606 L s [(70)] .97619 .29731 0 1 Mshowa .125 Mabswid .05102 .30981 m .05102 .31356 L s .07823 .30981 m .07823 .31356 L s .10544 .30981 m .10544 .31356 L s .13265 .30981 m .13265 .31356 L s .18707 .30981 m .18707 .31356 L s .21429 .30981 m .21429 .31356 L s .2415 .30981 m .2415 .31356 L s .26871 .30981 m .26871 .31356 L s .32313 .30981 m .32313 .31356 L s .35034 .30981 m .35034 .31356 L s .37755 .30981 m .37755 .31356 L s .40476 .30981 m .40476 .31356 L s .45918 .30981 m .45918 .31356 L s .48639 .30981 m .48639 .31356 L s .51361 .30981 m .51361 .31356 L s .54082 .30981 m .54082 .31356 L s .59524 .30981 m .59524 .31356 L s .62245 .30981 m .62245 .31356 L s .64966 .30981 m .64966 .31356 L s .67687 .30981 m .67687 .31356 L s .73129 .30981 m .73129 .31356 L s .7585 .30981 m .7585 .31356 L s .78571 .30981 m .78571 .31356 L s .81293 .30981 m .81293 .31356 L s .86735 .30981 m .86735 .31356 L s .89456 .30981 m .89456 .31356 L s .92177 .30981 m .92177 .31356 L s .94898 .30981 m .94898 .31356 L s .25 Mabswid 0 .30981 m 1 .30981 L s .02381 .01793 m .03006 .01793 L s [(-10)] .01131 .01793 1 0 Mshowa .02381 .16387 m .03006 .16387 L s [(-5)] .01131 .16387 1 0 Mshowa .02381 .45574 m .03006 .45574 L s [(5)] .01131 .45574 1 0 Mshowa .02381 .60168 m .03006 .60168 L s [(10)] .01131 .60168 1 0 Mshowa .125 Mabswid .02381 .04712 m .02756 .04712 L s .02381 .07631 m .02756 .07631 L s .02381 .1055 m .02756 .1055 L s .02381 .13468 m .02756 .13468 L s .02381 .19306 m .02756 .19306 L s .02381 .22224 m .02756 .22224 L s .02381 .25143 m .02756 .25143 L s .02381 .28062 m .02756 .28062 L s .02381 .33899 m .02756 .33899 L s .02381 .36818 m .02756 .36818 L s .02381 .39737 m .02756 .39737 L s .02381 .42656 m .02756 .42656 L s .02381 .48493 m .02756 .48493 L s .02381 .51412 m .02756 .51412 L s .02381 .54331 m .02756 .54331 L s .02381 .57249 m .02756 .57249 L s .25 Mabswid .02381 0 m .02381 .61803 L s .5 Mabswid .02381 .60168 m .02409 .60268 L .02435 .60319 L .02465 .60332 L .02494 .60298 L .0252 .60227 L .02544 .60128 L .0257 .59983 L .02599 .59786 L .02657 .59239 L .02712 .58561 L .02837 .56437 L .02958 .5366 L .03068 .50557 L .03318 .41965 L .03806 .22067 L .04064 .12458 L .04206 .08142 L .04275 .0636 L .04339 .0494 L .04399 .03814 L .04465 .02821 L .04531 .0209 L .04567 .01808 L .04583 .01709 L .04601 .0162 L .04632 .01514 L .04661 .01472 L .04689 .01484 L .04715 .01543 L .04744 .01658 L .04775 .01847 L .04808 .02114 L .04838 .02428 L .04895 .03171 L .04955 .04177 L .05061 .06521 L .05176 .0977 L .05302 .14076 L .05817 .36242 L .0606 .46354 L .06285 .53662 L .06398 .56309 L .06456 .57338 L .06519 .58221 L .06552 .58577 L .06582 .58838 L .06598 .58955 L .06616 .59061 L .06634 .5914 L Mistroke .06649 .59195 L .06681 .59252 L .06709 .59247 L .06724 .5922 L .06741 .59173 L .06772 .59037 L .06801 .58852 L .06827 .58629 L .06888 .57947 L .06948 .57055 L .07011 .55863 L .07231 .50071 L .07713 .32099 L .07966 .22585 L .08105 .18092 L .08235 .14557 L .08351 .12069 L .0841 .11042 L .08475 .10123 L .08542 .09398 L .08578 .09101 L .08612 .08887 L .08644 .0874 L .08673 .08651 L .08689 .0862 L .08707 .08602 L .08738 .08606 L .08767 .08654 L .08794 .08735 L .08824 .08864 L .08856 .09048 L .08921 .09565 L .0898 .10196 L .09094 .11805 L .09203 .13751 L .10131 .36957 L .10378 .42075 L .10499 .44088 L .1061 .4561 L .10726 .46848 L .10787 .47347 L .10852 .47757 L .10884 .47916 L .10918 .48052 L .10934 .48106 L .1095 .4815 L .10979 .48212 L .10996 .48236 L .11014 .48252 L .11029 .48259 L Mistroke .11046 .48258 L .11064 .48248 L .11084 .48226 L .11102 .48195 L .11119 .48158 L .1115 .48067 L .1118 .47954 L .11235 .47676 L .11294 .47277 L .11358 .46733 L .11473 .45458 L .1158 .43967 L .11824 .39498 L .12082 .33562 L .12564 .21509 L .12774 .17045 L .12885 .15148 L .13003 .13577 L .13063 .12974 L .13095 .12711 L .13129 .12474 L .13161 .12301 L .1319 .12179 L .13217 .12096 L .13246 .12045 L .13274 .1203 L .13303 .12052 L .13331 .12107 L .13356 .12188 L .13386 .12319 L .13418 .12507 L .13476 .12964 L .13537 .13603 L .13605 .14491 L .1374 .16843 L .13984 .22634 L .14495 .37721 L .14612 .40917 L .14737 .43917 L .14853 .4622 L .14962 .47893 L .1502 .48575 L .15051 .4887 L .15083 .49134 L .15111 .49317 L .15141 .49478 L .15168 .49586 L .15193 .49654 L .15209 .49681 L .15226 .49696 L Mistroke .15257 .49688 L .15287 .49636 L .15315 .49549 L .15345 .49415 L .15378 .49217 L .15445 .48664 L .15505 .48008 L .15559 .47278 L .15682 .4522 L .15904 .4034 L .16403 .27402 L .16528 .24509 L .16646 .22124 L .1676 .20188 L .16866 .18783 L .16971 .1777 L .17023 .17404 L .17053 .17241 L .17081 .17115 L .17112 .1701 L .17139 .16942 L .17169 .16897 L .17186 .16885 L .17201 .16883 L .17227 .16896 L .17256 .16936 L .17286 .17005 L .17314 .17095 L .17372 .17357 L .17434 .17738 L .17544 .1866 L .17662 .19949 L .17792 .21637 L .18307 .29541 L .18775 .35805 L .19008 .38056 L .1914 .39035 L .19261 .39748 L .19368 .4022 L .19428 .40425 L .19484 .40574 L .19515 .40637 L .19544 .40685 L .1957 .40719 L .19598 .40746 L .19629 .40762 L .19646 .40766 L .19662 .40766 L .19692 .40756 L .19721 .40734 L Mistroke .19749 .40701 L .19779 .40654 L .19834 .40534 L .19899 .40335 L .19958 .40097 L .20087 .39396 L .20208 .38493 L .20423 .36343 L .20656 .33281 L .21127 .25846 L .21377 .22184 L .21508 .20632 L .2158 .19937 L .21646 .19402 L .21705 .19022 L .21736 .18866 L .21769 .18726 L .21787 .1866 L .21805 .18609 L .21821 .1857 L .21839 .18535 L .2187 .18499 L .21887 .18492 L .21903 .18494 L .21933 .18519 L .21962 .1857 L .21988 .18639 L .22016 .18738 L .22079 .19053 L .22138 .19458 L .22244 .20464 L .22361 .21956 L .22599 .25995 L .22846 .31076 L .23106 .36457 L .23329 .4029 L .23455 .41918 L .23516 .42533 L .23572 .42993 L .23631 .43355 L .23662 .43498 L .23677 .43559 L .23694 .43614 L .23723 .43683 L .23749 .43722 L .23781 .43736 L .23809 .43718 L .23837 .43674 L .23862 .4361 L .2389 .43513 L Mistroke .2392 .43381 L .23975 .43058 L .24025 .4268 L .24145 .41469 L .24274 .39736 L .24509 .35799 L .24983 .27316 L .25113 .25439 L .25252 .23823 L .2532 .23206 L .25384 .22727 L .25441 .22386 L .25471 .22242 L .25503 .22112 L .25534 .22013 L .25563 .21943 L .2559 .21895 L .25618 .21864 L .25649 .21853 L .25678 .21863 L .2571 .21897 L .25728 .21926 L .25745 .21959 L .25777 .22042 L .25808 .22139 L .25876 .22425 L .26001 .23155 L .26224 .24976 L .26461 .27262 L .26707 .29615 L .26941 .31545 L .27151 .32924 L .2738 .34052 L .27624 .34917 L .27851 .35507 L .27978 .35771 L .28096 .3598 L .28162 .36076 L .28234 .36163 L .28265 .36194 L .28298 .36222 L .28329 .36244 L .28358 .36259 L .28387 .36271 L .28403 .36275 L .2842 .36277 L .28448 .36277 L .28478 .36271 L .28506 .3626 L .28535 .36242 L Mistroke .28563 .36219 L .28588 .36192 L .28649 .36106 L .28715 .35973 L .28777 .35807 L .28835 .35615 L .28948 .35132 L .2905 .34562 L .2928 .32835 L .29785 .27503 L .30007 .25164 L .30124 .24117 L .30189 .23626 L .3025 .23227 L .30309 .2291 L .3034 .22771 L .30373 .22646 L .30401 .2256 L .30431 .22484 L .30459 .22434 L .30485 .22403 L .30512 .22388 L .3054 .22391 L .30564 .22409 L .30591 .22445 L .30619 .22503 L .30649 .22587 L .30704 .22796 L .30766 .23122 L .30834 .23579 L .30956 .2467 L .31184 .27476 L .31656 .34622 L .31786 .36386 L .31925 .37975 L .31992 .38601 L .32056 .39098 L .32113 .39456 L .32176 .39749 L .32207 .39855 L .32223 .39901 L .3224 .39941 L .32272 .39993 L .32301 .40017 L .3233 .40017 L .32356 .39998 L .32385 .39956 L .32415 .39886 L .32448 .39783 L .32484 .39639 L Mistroke .32549 .39296 L .32671 .38385 L .32787 .37237 L .3291 .35786 L .3313 .32829 L .33358 .2976 L .33477 .28313 L .33603 .27002 L .33713 .26071 L .33772 .25673 L .33834 .25323 L .33892 .2507 L .33944 .249 L .33969 .24837 L .33997 .24785 L .34022 .24748 L .34046 .24727 L .34077 .24715 L .34105 .24721 L .34131 .24739 L .3416 .24773 L .3419 .24826 L .34223 .249 L .34281 .25076 L .34397 .25569 L .34501 .26153 L .35002 .29646 L .3523 .30996 L .35344 .3152 L .3547 .31962 L .35536 .32141 L .35606 .32294 L .35673 .32405 L .35733 .32481 L .35793 .32536 L .35827 .32559 L .35858 .32577 L .35915 .32601 L .35944 .32609 L .35975 .32616 L .36035 .32626 L .36101 .32634 L .36131 .32638 L .36163 .32643 L .36221 .32656 L .3625 .32665 L .36282 .32676 L .36339 .32704 L .36394 .32741 L .36446 .32783 L Mistroke .36563 .32917 L .36692 .33119 L .36952 .33641 L .37079 .33895 L .37141 .34005 L .37199 .34092 L .37252 .34156 L .37278 .34182 L .37307 .34205 L .37336 .34221 L .37363 .3423 L .37379 .34233 L .37395 .34233 L .37425 .34228 L .37456 .34214 L .37485 .34192 L .37519 .34156 L .3755 .34111 L .37606 .34005 L .37667 .3385 L .37734 .33628 L .37805 .33336 L .37932 .32666 L .3816 .31044 L .38406 .28936 L .38636 .26981 L .38749 .26161 L .3885 .25545 L .38907 .25263 L .38969 .25017 L .39003 .2491 L .39034 .2483 L .39064 .24771 L .39096 .24727 L .39127 .24702 L .39145 .24697 L .39162 .24698 L .39193 .24715 L .39223 .2475 L .3924 .24778 L .39258 .24813 L .3929 .24894 L .39325 .25005 L .39363 .25155 L .39484 .2582 L .39615 .26833 L .39851 .29268 L .40081 .32029 L .40328 .3481 L .40469 .36102 L Mistroke .40598 .36979 L .4066 .37285 L .40693 .37414 L .40727 .37525 L .40757 .376 L .40773 .37632 L .40791 .37659 L .40821 .37692 L .40849 .37704 L .4088 .37696 L .40896 .37684 L .40913 .37665 L .40944 .37614 L .40973 .37547 L .41006 .37447 L .41037 .37333 L .41107 .37006 L .41226 .36238 L .41352 .35188 L .41811 .30383 L .42042 .28239 L .42171 .27333 L .42232 .26996 L .42289 .26742 L .42342 .26553 L .42398 .26407 L .42428 .26354 L .42455 .26318 L .42485 .26294 L .42502 .26287 L .42518 .26285 L .42545 .26291 L .42571 .26308 L .42599 .26339 L .42628 .26385 L .42684 .26507 L .42734 .26655 L .42852 .27131 L .42977 .27785 L .43201 .29167 L .43444 .30647 L .43578 .31318 L .43644 .31593 L .43705 .31809 L .43762 .31978 L .43825 .32125 L .43888 .32233 L .43922 .32275 L .43938 .3229 L .43955 .32303 L Mistroke .43982 .3232 L .44012 .3233 L .44039 .32332 L .44064 .32328 L .44094 .32317 L .44121 .323 L .44152 .32274 L .44182 .32244 L .44293 .32083 L .44395 .31888 L .44626 .31406 L .4474 .3121 L .44803 .31126 L .44834 .31094 L .44862 .31069 L .44888 .31051 L .44916 .31036 L .44946 .31027 L .44974 .31024 L .45001 .31026 L .4503 .31035 L .45057 .31049 L .45081 .31067 L .45111 .31093 L .45142 .31129 L .45198 .31211 L .45264 .31337 L .45325 .31478 L .45582 .32263 L .45807 .33015 L .45921 .3333 L .45986 .33474 L .46046 .33575 L .46079 .33617 L .46111 .33647 L .46128 .33659 L .46144 .33667 L .46162 .33673 L .46181 .33676 L .46197 .33675 L .46215 .3367 L .46232 .33662 L .46247 .33652 L .46277 .33625 L .46308 .33585 L .46336 .33538 L .46367 .33476 L .46423 .33333 L .46489 .33115 L .46549 .32869 L Mistroke .4679 .3151 L .47012 .29886 L .47271 .27963 L .47398 .27169 L .47454 .26874 L .47515 .26597 L .47566 .26405 L .47621 .26243 L .47651 .26174 L .47679 .26125 L .47706 .26088 L .47733 .26065 L .47761 .26054 L .47791 .26058 L .47817 .26074 L .47845 .26106 L .47876 .26155 L .47908 .26227 L .47967 .26405 L .48031 .26667 L .48101 .27029 L .48228 .27877 L .48467 .29963 L .48733 .32587 L .48864 .33781 L .48984 .34729 L .49094 .35424 L .49149 .35704 L .49209 .35944 L .49241 .36044 L .49269 .36119 L .49298 .36178 L .49325 .3622 L .49357 .36251 L .49386 .36262 L .49402 .36261 L .49419 .36255 L .49436 .36243 L .49453 .36226 L .49482 .36185 L .49508 .36132 L .49569 .35964 L .49628 .35737 L .49691 .3543 L .4991 .33941 L .50402 .29624 L .50523 .28723 L .50651 .27957 L .50718 .27649 L .50753 .27513 L Mistroke .50791 .27388 L .50826 .27295 L .50858 .27226 L .5089 .27174 L .5092 .2714 L .50948 .27121 L .50979 .27115 L .50995 .27118 L .51011 .27125 L .51042 .27149 L .5107 .27185 L .511 .27235 L .51154 .27357 L .51217 .27549 L .51276 .27771 L .51409 .28404 L .51862 .31081 L .51987 .31708 L .52055 .31997 L .52118 .32227 L .52177 .324 L .52231 .32526 L .52259 .32579 L .5229 .32627 L .52307 .32648 L .52323 .32665 L .52354 .32689 L .52371 .32698 L .52387 .32703 L .52404 .32705 L .52422 .32704 L .52452 .32695 L .52469 .32685 L .52486 .32673 L .52516 .32643 L .52543 .32608 L .52604 .32504 L .5267 .32357 L .52741 .32161 L .52871 .31735 L .53103 .30891 L .53226 .3049 L .53291 .30311 L .53359 .30155 L .53421 .30046 L .53456 .29999 L .53488 .29965 L .53518 .29943 L .53545 .2993 L .53577 .29925 L Mistroke .53606 .29929 L .53635 .29941 L .53664 .29962 L .5369 .29987 L .53718 .30023 L .5378 .30128 L .53839 .3026 L .53967 .30648 L .54084 .31098 L .54348 .32257 L .54464 .32738 L .54587 .33167 L .54647 .33331 L .54704 .33454 L .54754 .33536 L .54783 .33569 L .54809 .33591 L .54838 .33606 L .5487 .33611 L .54899 .33603 L .54926 .33587 L .54957 .33556 L .54975 .33533 L .54992 .33508 L .55054 .33382 L .55113 .33215 L .55179 .3298 L .55312 .32356 L .5556 .30791 L .55821 .28966 L .55929 .28286 L .56044 .27669 L .56111 .27382 L .56171 .2717 L .562 .27086 L .56231 .27009 L .56261 .2695 L .56288 .26908 L .56316 .26876 L .56346 .26857 L .56374 .26852 L .56401 .26859 L .56432 .26883 L .56461 .26918 L .56492 .26973 L .56526 .27048 L .56587 .27235 L .56645 .27463 L .56777 .28163 L .56993 .29736 L Mistroke .57227 .31721 L .57349 .32729 L .57478 .33699 L .57599 .34439 L .57658 .34732 L .57712 .34957 L .57774 .35152 L .57806 .35231 L .5784 .35294 L .57869 .35332 L .57896 .35355 L .57925 .35365 L .57956 .3536 L .57974 .35349 L .57991 .35334 L .58009 .35313 L .58028 .35284 L .58064 .35213 L .58096 .35132 L .58162 .34914 L .58224 .34649 L .58337 .34033 L .58461 .33197 L .58711 .31234 L .58941 .29482 L .59054 .28763 L .59159 .28228 L .59215 .27999 L .59277 .278 L .59308 .27724 L .5934 .27657 L .59358 .27627 L .59374 .27604 L .5939 .27586 L .59406 .27571 L .59434 .27555 L .59459 .27551 L .59489 .27558 L .59516 .27577 L .59545 .27607 L .59576 .27654 L .59632 .27774 L .59693 .27951 L .5976 .28197 L .59896 .28835 L .60139 .30262 L .60381 .31679 L .60501 .32253 L .60611 .32666 L .60673 .32837 L Mistroke .60704 .32908 L .60738 .3297 L .60757 .33 L .60775 .33023 L .60792 .33041 L .6081 .33057 L .60842 .33074 L .6086 .33078 L .60876 .33079 L .60907 .33071 L .60937 .33052 L .60964 .33026 L .60993 .32988 L .61058 .3287 L .61118 .32722 L .61231 .32355 L .61352 .3186 L .61572 .30847 L .61705 .30255 L .61833 .29779 L .61888 .29611 L .61947 .29463 L .61981 .29393 L .62012 .2934 L .62043 .29297 L .62072 .29266 L .62099 .29246 L .62128 .29233 L .62144 .29231 L .6216 .29231 L .6219 .2924 L .62221 .29259 L .62249 .29288 L .62281 .29329 L .62314 .29386 L .62369 .29505 L .62421 .29645 L .62538 .30057 L .62784 .31212 L .63043 .32513 L .63156 .32989 L .63218 .33207 L .63276 .33379 L .63309 .3346 L .63346 .33533 L .63376 .33582 L .63393 .33605 L .63409 .33624 L .6344 .3365 L .63456 .33659 L Mistroke .63473 .33665 L .63504 .33665 L .63532 .33654 L .63559 .33634 L .63589 .336 L .63617 .33558 L .63642 .33511 L .63704 .33361 L .63762 .33176 L .63867 .3274 L .6398 .32144 L .64455 .29058 L .64585 .28328 L .64657 .27995 L .64724 .27735 L .64787 .27547 L .64823 .27465 L .64856 .27406 L .64883 .27369 L .64914 .27341 L .64946 .27327 L .64975 .27329 L .65004 .27343 L .65031 .27369 L .65061 .2741 L .65093 .27468 L .65157 .27636 L .65216 .2784 L .6533 .28368 L .65437 .29004 L .65678 .30758 L .65934 .32693 L .66045 .33426 L .66165 .34071 L .66234 .34358 L .66297 .34562 L .66327 .34639 L .6636 .34706 L .66391 .34754 L .6642 .34785 L .66445 .34802 L .66473 .34807 L .66499 .34801 L .66523 .34786 L .66549 .34759 L .66578 .34717 L .66608 .34658 L .66637 .34591 L .66695 .34415 L .66748 .34212 L Mistroke .66867 .33627 L .67112 .32016 L .67371 .30121 L .67592 .28763 L .67652 .28476 L .67718 .28218 L .67779 .28027 L .67835 .279 L .67866 .2785 L .67893 .27817 L .67924 .27792 L .67954 .27783 L .67981 .27785 L .68007 .27797 L .68034 .27821 L .68064 .27859 L .68094 .27909 L .68125 .27976 L .68183 .28131 L .68313 .28629 L .68551 .29915 L .68767 .31246 L .68884 .31914 L .69007 .32522 L .69113 .32927 L .69173 .33102 L .6923 .33226 L .69259 .33274 L .69291 .33315 L .69308 .3333 L .69325 .33342 L .69356 .33355 L .69387 .33355 L .69417 .33343 L .69443 .33323 L .69472 .33292 L .69504 .33245 L .69538 .3318 L .69608 .33007 L .69733 .32571 L .69995 .31305 L .70244 .30021 L .70353 .29549 L .70468 .29153 L .70534 .28987 L .70594 .2888 L .70623 .28843 L .70655 .28815 L .70684 .288 L .70711 .28795 L Mistroke .7074 .28801 L .70766 .28815 L .70796 .28841 L .70824 .28877 L .70875 .28964 L .7093 .29093 L .71054 .29506 L .7117 .30013 L .71419 .31356 L .71653 .32604 L .71765 .33089 L .71871 .3344 L .7193 .33578 L .71963 .33638 L .71994 .33681 L .72023 .3371 L .72048 .33726 L .72078 .33734 L .72106 .3373 L .72135 .33715 L .72167 .33685 L .72183 .33665 L .722 .3364 L .72231 .33584 L .72292 .33439 L .72346 .33266 L .7248 .32702 L .72606 .32011 L .73048 .2919 L .73168 .28542 L .73232 .28257 L .73299 .28008 L .73358 .27836 L .73389 .27764 L .73422 .27702 L .73453 .27659 L .7348 .27632 L .73508 .27616 L .73535 .27612 L .73563 .27619 L .73593 .2764 L .73625 .27677 L .73654 .27725 L .73708 .27843 L .73765 .28014 L .73895 .28564 L .74014 .29233 L .74278 .31055 L .74523 .32756 L .74638 .33421 L Mistroke .74746 .33918 L .74806 .34129 L .74838 .34221 L .74871 .34301 L .74899 .34357 L .7493 .34404 L .74958 .34435 L .74984 .34453 L .75015 .3446 L .75033 .34458 L .75049 .34451 L .75079 .34428 L .75111 .3439 L .75139 .34342 L .75166 .34287 L .75226 .34122 L .75292 .33889 L .75352 .33629 L .75486 .32901 L .75727 .31293 L .75985 .29561 L .76109 .28868 L .76171 .28586 L .76227 .28366 L .76278 .28203 L .76333 .28064 L .76362 .28009 L .76389 .27968 L .76417 .27936 L .76448 .27915 L .76478 .27908 L .76509 .27914 L .76539 .27933 L .76566 .27961 L .76598 .28008 L .76633 .28075 L .76696 .28235 L .76755 .28434 L .76818 .28688 L .76931 .29239 L .77372 .3189 L .77491 .32515 L .77603 .32994 L .77665 .33201 L .77698 .33291 L .77732 .33373 L .77761 .33429 L .77793 .33479 L .77823 .33512 L .7785 .33533 L Mistroke .77877 .33544 L .77907 .33544 L .77936 .33533 L .77962 .33514 L .77988 .33486 L .78011 .33453 L .78064 .33353 L .78121 .33206 L .78183 .33007 L .78295 .32548 L .78769 .29976 L .78898 .29357 L .7897 .29076 L .79038 .28858 L .79101 .28701 L .79136 .28633 L .79169 .28585 L .79197 .28555 L .79227 .28534 L .79259 .28524 L .79289 .28527 L .79318 .28541 L .79345 .28564 L .79374 .28601 L .79406 .28651 L .7947 .28794 L .79529 .28967 L .79642 .29405 L .79749 .29923 L .79991 .31302 L .80123 .32066 L .80246 .32711 L .80367 .33227 L .8042 .33406 L .80477 .33565 L .8051 .33637 L .8054 .33692 L .80569 .33732 L .806 .33764 L .80617 .33775 L .80635 .33784 L .80653 .33787 L .80669 .33787 L .80699 .33776 L .80714 .33766 L .80731 .33751 L .80761 .33714 L .8079 .33668 L .80843 .33553 L .809 .33388 L Mistroke .80963 .33164 L .81179 .3208 L .81405 .3064 L .81649 .29134 L .81718 .28779 L .81789 .28454 L .81856 .28204 L .81917 .28021 L .81975 .27896 L .82008 .27846 L .82037 .27813 L .82054 .27801 L .8207 .27793 L .82087 .27788 L .82105 .27787 L .82135 .27797 L .82152 .27809 L .82168 .27824 L .82199 .27863 L .82227 .27911 L .82292 .28062 L .82349 .28241 L .82409 .28477 L .82628 .2966 L .82865 .31264 L .8299 .32109 L .83122 .32913 L .83239 .33506 L .83301 .33757 L .83367 .33972 L .83399 .34053 L .83429 .34117 L .83457 .34167 L .83484 .34202 L .83509 .34225 L .83536 .3424 L .83563 .34244 L .83593 .34236 L .83622 .34214 L .83651 .34182 L .83676 .34144 L .83703 .34091 L .83765 .33936 L .83822 .33746 L .83925 .333 L .84036 .32704 L .8452 .29561 L .84653 .28854 L .84726 .28543 L .84793 .28309 L Mistroke .84851 .28157 L .84884 .28091 L .84913 .28044 L .84929 .28024 L .84945 .28007 L .84964 .27993 L .8498 .27984 L .85011 .27978 L .85028 .2798 L .85044 .27986 L .85074 .28007 L .85101 .28038 L .85131 .28083 L .85163 .28145 L .85229 .28315 L .85288 .28515 L .85404 .29013 L .85512 .29591 L .85757 .31096 L .85891 .31911 L .86016 .32589 L .86128 .33079 L .86185 .3328 L .86247 .33454 L .86283 .3353 L .86316 .33586 L .86347 .33627 L .86364 .33644 L .8638 .33655 L .8641 .33668 L .86427 .33669 L .86443 .33667 L .86471 .33655 L .86502 .3363 L .8653 .33596 L .86555 .33556 L .86612 .33436 L .86665 .33288 L .86715 .33119 L .86949 .32017 L .87162 .30766 L .87392 .2949 L .87459 .29178 L .87523 .2892 L .87586 .28711 L .87644 .28558 L .87698 .28451 L .87729 .28408 L .87757 .2838 L .87787 .28361 L Mistroke .87804 .28355 L .8782 .28354 L .87849 .2836 L .8788 .28379 L .8791 .2841 L .87937 .28449 L .87998 .2857 L .88055 .28724 L .88109 .28906 L .8823 .29421 L .88361 .30116 L .88603 .31572 L .88732 .32317 L .8887 .33006 L .88933 .33261 L .88999 .33483 L .89056 .33631 L .89088 .33698 L .89117 .33746 L .89147 .33784 L .89176 .33808 L .89205 .33822 L .89222 .33824 L .89238 .33823 L .89263 .33813 L .89292 .33792 L .89322 .33757 L .89349 .33714 L .89415 .3357 L .89478 .33382 L .89595 .32907 L .89859 .31406 L .90091 .29912 L .90219 .2917 L .90339 .28592 L .90394 .28379 L .90452 .28193 L .90482 .28112 L .90515 .28038 L .90546 .27983 L .90573 .27945 L .90601 .27917 L .90626 .27901 L .90654 .27895 L .90683 .279 L .90709 .27914 L .90736 .2794 L .9076 .27971 L .90785 .28014 L .90843 .28142 L Mistroke .90905 .28331 L .91031 .28857 L .91255 .30158 L .9152 .31922 L .91646 .32686 L .91761 .33281 L .91879 .33741 L .91941 .33913 L .91972 .3398 L .92006 .34038 L .92036 .34074 L .92064 .34097 L .92095 .34109 L .92125 .34106 L .92153 .34093 L .92179 .3407 L .92207 .34034 L .92237 .33983 L .92297 .33845 L .92362 .33643 L .92478 .33149 L .92745 .31582 L .92996 .29943 L .93119 .29236 L .9323 .28704 L .93287 .28486 L .93348 .28293 L .93382 .28208 L .93413 .28143 L .93443 .28093 L .93474 .28054 L .93506 .28029 L .93524 .28021 L .9354 .28018 L .93571 .28022 L .93601 .28039 L .93618 .28055 L .93636 .28075 L .93668 .28124 L .93707 .282 L .93741 .28286 L .9386 .28689 L .93985 .29278 L .94208 .306 L .94452 .32104 L .94586 .32807 L .94652 .33095 L .94713 .3332 L .94771 .33492 L .94832 .33628 L Mistroke .94864 .33679 L .94894 .33714 L .94911 .33729 L .94927 .33739 L .94944 .33746 L .94962 .33749 L .94989 .33745 L .95018 .33729 L .95046 .33704 L .9507 .33672 L .951 .33624 L .95131 .33559 L .95189 .33409 L .95301 .33003 L .9542 .32437 L .95634 .31202 L .95862 .29834 L .95988 .29188 L .96051 .28919 L .96108 .28705 L .96166 .28528 L .96219 .28403 L .96249 .28347 L .96278 .28306 L .96308 .28275 L .96325 .28262 L .9634 .28254 L .96366 .28249 L .96389 .28251 L .96415 .28263 L .96443 .28286 L .96473 .28321 L .965 .28365 L .96552 .28474 L .9661 .28636 L .96664 .28823 L .96787 .29364 L .97036 .3079 L .97269 .32206 L .97373 .32761 L .97483 .33245 L .97548 .33474 L .97619 .33664 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg`0oooo000J0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01`3oool00`000000 oooo0?ooo`020?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00P3oool00`000000 oooo0?ooo`090?ooo`040000003oool0oooo000000T0oooo00@000000?ooo`3oool000003@3oool0 0`000000oooo0000003/0?ooo`006P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo 00<0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo 00L0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 0080oooo00<000000?ooo`3oool02@3oool010000000oooo0?ooo`0000090?ooo`040000003oool0 oooo000000d0oooo00<000000?ooo`000000k03oool001X0oooo00<000000?ooo`3oool00P3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`070?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01@3oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo00P0oooo00<000000?ooo`3oool00P3oool0 0`000000oooo0?ooo`060?ooo`040000003oool0oooo000000d0oooo00<000000?ooo`000000k03o ool001X0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`030000003oool0 oooo00D0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`070?ooo`030000003oool0 oooo0080oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`020?ooo`030000003oool0 oooo00P0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`060?ooo`040000003oool0 oooo000000d0oooo00@000000?ooo`3oool00000j`3oool001X0oooo00<000000?ooo`3oool00P3o ool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3o ool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3o ool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00P0oooo00<000000?ooo`3oool00P3o ool00`000000oooo0?ooo`060?ooo`040000003oool0oooo000000`0oooo00D000000?ooo`3oool0 oooo000000090?ooo`8000003`3oool2000000?ooo`040000003oool0oooo000000L0oooo00@000000?ooo`3oool000003`3oool010000000 oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo0P0000070?ooo`040000003oool0 oooo000000H0oooo00@000000?ooo`3oool000001P3oool00`000000oooo000000060?ooo`040000 003oool0oooo000000H0oooo00@000000?ooo`3oool000001P3oool00`000000oooo000000060?oo o`040000003oool0oooo000000H0oooo00@000000?ooo`3oool000001P3oool00`000000oooo0000 000<0?ooo`006P3oool01@000000oooo0?ooo`3oool0000000H0oooo00<000000?ooo`3oool0103o ool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3o ool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3o ool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool00`3o ool00`000000oooo0?ooo`070?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01@3o ool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool00P3o ool00`000000oooo0?ooo`040?ooo`050000003oool0oooo0?ooo`000000303oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo00@0oooo00D000000?ooo`3oool0oooo0000000=0?ooo`05 0000003oool0oooo0?ooo`0000001P3oool010000000oooo0?ooo`0000060?ooo`8000001`3oool0 10000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00<000000?ooo`000000 1P3oool010000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00<000000?oo o`0000001P3oool010000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00<0 00000?ooo`0000001P3oool010000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0 oooo00<000000?ooo`000000303oool001X0oooo00D000000?ooo`3oool0oooo000000060?ooo`03 0000003oool0oooo00@0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`040?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo00@0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`090?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo00X0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`040?ooo`05 0000003oool0oooo0?ooo`0000003@3oool01@000000oooo0?ooo`3oool0000000H0oooo00@00000 0?ooo`3oool000001P3oool2000000L0oooo00@000000?ooo`3oool000001@3oool01@000000oooo 0?ooo`3oool0000000H0oooo00<000000?ooo`0000001P3oool010000000oooo0?ooo`0000060?oo o`040000003oool0oooo000000H0oooo00<000000?ooo`0000001P3oool010000000oooo0?ooo`00 00060?ooo`040000003oool0oooo000000H0oooo00<000000?ooo`0000001P3oool010000000oooo 0?ooo`0000060?ooo`040000003oool0oooo000000D0oooo00D000000?ooo`3oool0oooo0000000; 0?ooo`006P3oool01@000000oooo0?ooo`3oool0000000H0oooo00<000000?ooo`3oool0103oool0 0`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool0 0`000000oooo0?ooo`040?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`070?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0103oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool00P3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool02P3oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo00@0oooo00D000000?ooo`3oool0oooo0000 00050?ooo`8000001@3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00@0oooo00D0 00000?ooo`3oool0oooo000000050?ooo`030000003oool0000000H0oooo00@000000?ooo`3oool0 00001@3oool01@000000oooo0?ooo`3oool0000000D0oooo00@000000?ooo`3oool000001P3oool0 10000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000D0oooo00D000000?ooo`3oool0 oooo000000050?ooo`040000003oool0oooo000000H0oooo00@000000?ooo`3oool000001P3oool0 0`000000oooo000000060?ooo`050000003oool0oooo0?ooo`0000001@3oool010000000oooo0?oo o`0000050?ooo`050000003oool0oooo0?ooo`0000002`3oool001X0oooo00D000000?ooo`3oool0 oooo000000060?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool01@3oool00`000000 oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool00`000000 oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool0103oool00`000000 oooo0?ooo`040?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01`3oool00`000000 oooo0?ooo`030?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool00P3oool00`000000 oooo0?ooo`080?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`030?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool00P3oool00`000000 oooo0?ooo`040?ooo`050000003oool0oooo0?ooo`0000001@3oool2000000D0oooo00<000000?oo o`3oool00P3oool00`000000oooo0?ooo`040?ooo`050000003oool0oooo0?ooo`000000103oool0 10000000oooo0?ooo`0000050?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3o ool01@000000oooo0?ooo`3oool0000000D0oooo00@000000?ooo`3oool000001@3oool01@000000 oooo0?ooo`3oool0000000H0oooo00@000000?ooo`3oool000001@3oool01@000000oooo0?ooo`3o ool0000000@0oooo00D000000?ooo`3oool0oooo000000060?ooo`040000003oool0oooo000000D0 oooo00D000000?ooo`3oool0oooo000000050?ooo`050000003oool0oooo0?ooo`0000001@3oool0 1@000000oooo0?ooo`3oool0000000@0oooo00D000000?ooo`3oool0oooo0000000;0?ooo`006P3o ool01@000000oooo0?ooo`3oool0000000H0oooo00<000000?ooo`3oool0103oool00`000000oooo 0?ooo`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0103oool00`000000oooo 0?ooo`040?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo 0?ooo`040?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool00`3oool00`000000oooo 0?ooo`070?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0103oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo00P0oooo00<000000?ooo`3oool00`3oool00`000000oooo 0?ooo`030?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool02@3oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool00P3oool010000000oooo 0?ooo`3oool3000000D0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`0000050?oo o`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3oool01@000000oooo0?ooo`3oool0 000000D0oooo00@000000?ooo`3oool000001@3oool00`000000oooo0?ooo`020?ooo`030000003o ool0oooo0080oooo00D000000?ooo`3oool0oooo000000050?ooo`050000003oool0oooo0?ooo`00 0000103oool01@000000oooo0?ooo`3oool0000000D0oooo00<000000?ooo`3oool00P3oool00`00 0000oooo0?ooo`020?ooo`050000003oool0oooo0?ooo`0000001@3oool01@000000oooo0?ooo`3o ool0000000D0oooo00D000000?ooo`3oool0oooo000000040?ooo`050000003oool0oooo0?ooo`00 00002`3oool001X0oooo00D000000?ooo`3oool0oooo000000060?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00H0 oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo00<0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00P0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00<0 oooo00D000000?ooo`3oool0oooo000000020?ooo`030000003oool0oooo0080oooo00<000000?oo o`3oool00P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0080oooo00<000000?oo o`3oool00P3oool010000000oooo0?ooo`0000050?ooo`030000003oool0oooo0080oooo00<00000 0?ooo`3oool00P3oool00`000000oooo0?ooo`020?ooo`050000003oool0oooo0?ooo`0000000`3o ool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3o ool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo00D000000?ooo`3oool0oooo 000000040?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo0080oooo00D000000?ooo`3oool0oooo000000040?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`3oool00`3oool01@000000oooo0?ooo`3oool00000 00@0oooo00D000000?ooo`3oool0oooo0000000;0?ooo`004P3ooooo000005L00000000J0?ooo`05 0000003oool0oooo0?ooo`0000001@3oool00`000000oooo000000050?ooo`8000001P3oool00`00 0000oooo000000040?ooo`050000003oool0oooo0?ooo`0000000`3oool00`000000oooo0?ooo`03 0?ooo`030000003oool0oooo00D0oooo0P0000060?ooo`030000003oool0000000@0oooo00D00000 0?ooo`3oool0oooo000000020?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool01P3o ool00`000000oooo0?ooo`030?ooo`040000003oool0oooo00000080oooo00<000000?ooo`3oool0 0`3oool2000000P0oooo0P0000060?ooo`8000000`3oool00`000000oooo0?ooo`020?ooo`800000 0`3oool3000000050?ooo`000000oooo0?ooo`0000001@3oool2000000@0oooo00L000000?ooo`3o ool0oooo0000003oool0000000<0oooo00@000000?ooo`3oool00000103oool01`000000oooo0?oo o`3oool000000?ooo`000000103oool010000000oooo0?ooo`0000020?ooo`090000003oool0oooo 0?ooo`000000oooo0000003oool0000000@0oooo00<000000?ooo`0000000P3oool00`000000oooo 0?ooo`020?ooo`030000003oool000000080oooo00L000000?ooo`3oool0oooo0000003oool00000 0080oooo00<000000?ooo`3oool00P3oool2000000<0oooo00<000000?ooo`3oool00P3oool00`00 0000oooo0?ooo`020?ooo`040000003oool0oooo0?ooo`8000000`3oool00`000000oooo0?ooo`02 0?ooo`030000003oool0oooo0080oooo00@000000?ooo`3oool0oooo0P0000040?ooo`060000003o ool0oooo0000003oool00000103oool00`000000oooo0?ooo`02000000D0oooo00D000000?ooo`00 0000oooo000000040?ooo`030000003oool000000080oooo00L000000?ooo`3oool0oooo0000003o ool0000000T0oooo000J0?ooo`050000003oool0oooo0?ooo`0000001`3oool00`000000oooo0?oo o`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0103oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?oo o`040?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00D0oooo0P0000050?ooo`030000003oool0oooo00<0oooo00<0 00000?ooo`3oool0103oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo00@0oooo00<0 00000?ooo`3oool00P3oool00`000000oooo0?ooo`020?ooo`050000003oool000000?ooo`000000 0P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool0 0P3oool00`000000oooo0?ooo`030?ooo`040000003oool0oooo000000<0oooo00D000000?ooo`3o ool0oooo000000040?ooo`030000003oool0000000@0oooo00<000000?ooo`3oool00`3oool01000 0000oooo0?ooo`0000040?ooo`050000003oool0oooo0?ooo`0000001@3oool00`000000oooo0?oo o`020?ooo`030000003oool0oooo0080oooo00L000000?ooo`3oool0oooo0000003oool000000080 oooo00D000000?ooo`3oool0oooo000000050?ooo`030000003oool0oooo0080oooo00<000000?oo o`3oool00P3oool01@000000oooo0?ooo`3oool0000000@0oooo00D000000?ooo`3oool0oooo0000 00050?ooo`040000003oool0oooo0?ooo`800000103oool01@000000oooo0?ooo`3oool0000000D0 oooo00D000000?ooo`3oool0oooo000000050?ooo`050000003oool0oooo0?ooo`0000001@3oool0 1@000000oooo0?ooo`3oool0000000@0oooo0P0000090?ooo`006P3oool01@000000oooo0?ooo`3o ool0000000L0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003o ool0oooo00@0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003o ool0oooo00D0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`030000003o ool0oooo00<0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003o ool0oooo00@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003o ool0oooo00D0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`020?ooo`030000003o ool0oooo00@0oooo00<000000?ooo`0000000P3oool00`000000oooo0?ooo`020?ooo`030000003o ool0oooo00@0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`040000003o ool0oooo000000@0oooo00@000000?ooo`3oool000001P3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo00<0oooo00@000000?ooo`3oool00000103oool01@000000oooo0?ooo`3oool0 000000H0oooo00D000000?ooo`3oool0oooo000000050?ooo`030000003oool0000000D0oooo00D0 00000?ooo`3oool0oooo000000050?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0 0P3oool01@000000oooo0?ooo`3oool0000000D0oooo00@000000?ooo`3oool000001P3oool01@00 0000oooo0?ooo`3oool0000000@0oooo00D000000?ooo`3oool0oooo000000050?ooo`050000003o ool0oooo0?ooo`0000001@3oool01@000000oooo0?ooo`3oool0000000D0oooo00@000000?ooo`3o ool000001@3oool00`000000oooo0?ooo`080?ooo`006P3oool01@000000oooo0?ooo`3oool00000 00L0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 00@0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo 00D0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 00<0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 00@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 00D0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo 00@0oooo0`0000030?ooo`050000003oool0oooo0?ooo`0000001P3oool00`000000oooo0?ooo`02 0?ooo`030000003oool0oooo00<0oooo0P0000000`3oool000000?ooo`030?ooo`040000003oool0 oooo000000H0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`040000003o ool0oooo000000D0oooo00@000000?ooo`3oool000001P3oool01@000000oooo0?ooo`3oool00000 00D0oooo00<000000?ooo`0000001P3oool010000000oooo0?ooo`0000060?ooo`040000003oool0 oooo000000D0oooo00D000000?ooo`3oool0oooo000000050?ooo`040000003oool0oooo000000H0 oooo00@000000?ooo`3oool000001@3oool01@000000oooo0?ooo`3oool0000000D0oooo00@00000 0?ooo`3oool000001P3oool01@000000oooo0?ooo`3oool0000000D0oooo00@000000?ooo`3oool0 00001@3oool00`000000oooo0?ooo`080?ooo`006P3oool01@000000oooo0?ooo`3oool0000000L0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`8000001P3oool00`000000 oooo0?ooo`050?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01@3oool00`000000 oooo0?ooo`020?ooo`050000003oool0oooo0?ooo`0000001P3oool00`000000oooo0?ooo`020?oo o`030000003oool0oooo00@0oooo0P0000050?ooo`040000003oool0oooo000000H0oooo00D00000 0?ooo`3oool0oooo000000060?ooo`040000003oool0oooo000000D0oooo00@000000?ooo`3oool0 00001P3oool01@000000oooo0?ooo`3oool0000000D0oooo00<000000?ooo`0000001P3oool01000 0000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00@000000?ooo`3oool00000 1@3oool010000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00@000000?oo o`3oool000001@3oool010000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo 00@000000?ooo`3oool000001@3oool00`000000oooo0?ooo`080?ooo`006P3oool01@000000oooo 0?ooo`3oool0000000L0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`03 0000003oool0oooo00@0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo00D0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`040?ooo`03 0000003oool0oooo00@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`060?ooo`<0 0000103oool00`000000oooo0?ooo`050?ooo`050000003oool0oooo0?ooo`0000003P3oool01000 0000oooo0?ooo`0000060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0103oool2 000000H0oooo00<000000?ooo`0000001P3oool01@000000oooo0?ooo`3oool0000000H0oooo0`00 00060?ooo`040000003oool0oooo000000H0oooo00D000000?ooo`3oool0oooo000000050?ooo`03 0000003oool0000000H0oooo00@000000?ooo`3oool000001P3oool010000000oooo0?ooo`000006 0?ooo`030000003oool0000000H0oooo00@000000?ooo`3oool000001P3oool010000000oooo0?oo o`0000060?ooo`030000003oool0000000H0oooo00@000000?ooo`3oool000001P3oool010000000 oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00<000000?ooo`3oool01`3oool0 01X0oooo00D000000?ooo`3oool0oooo000000070?ooo`030000003oool0oooo00<0oooo00<00000 0?ooo`3oool01@3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00D0oooo00<00000 0?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00@0oooo00<00000 0?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<00000 0?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo0080oooo00<00000 0?ooo`3oool02@3oool01@000000oooo0?ooo`3oool0000000L0oooo00D000000?ooo`3oool0oooo 0000000>0?ooo`030000003oool0000000L0oooo00D000000?ooo`3oool0oooo0000000?0?ooo`03 0000003oool0000000H0oooo00D000000?ooo`3oool0oooo000000070?ooo`8000001P3oool00`00 0000oooo000000070?ooo`040000003oool0oooo000000H0oooo0`0000060?ooo`030000003oool0 000000L0oooo00@000000?ooo`3oool000001P3oool00`000000oooo000000060?ooo`040000003o ool0oooo000000H0oooo00@000000?ooo`3oool000001P3oool00`000000oooo000000070?ooo`03 0000003oool0000000H0oooo00@000000?ooo`3oool000001P3oool010000000oooo0?ooo`000006 0?ooo`030000003oool0oooo00L0oooo000J0?ooo`050000003oool0oooo0?ooo`0000001`3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0103oool0 0`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool0 0`000000oooo0?ooo`040?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`060?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool01@3oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo00T0oooo00D000000?ooo`3oool0oooo0000 00070?ooo`050000003oool0oooo0?ooo`0000003P3oool00`000000oooo000000070?ooo`050000 003oool0oooo0?ooo`0000003`3oool00`000000oooo000000070?ooo`040000003oool0oooo0000 00l0oooo0`0000070?ooo`040000003oool0oooo000000L0oooo0P0000070?ooo`8000001`3oool0 10000000oooo0?ooo`0000060?ooo`<000001`3oool2000000L0oooo00@000000?ooo`3oool00000 1P3oool3000000L0oooo00<000000?ooo`0000001P3oool010000000oooo0?ooo`0000070?ooo`80 00001`3oool00`000000oooo0?ooo`070?ooo`006P3oool01@000000oooo0?ooo`3oool0000000L0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0 oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`0:0?ooo`040000003oool0oooo0000 00L0oooo00D000000?ooo`3oool0oooo0000000?0?ooo`8000001`3oool01@000000oooo0?ooo`3o ool000000100oooo00<000000?ooo`3oool01P3oool010000000oooo0?ooo`00000@0?ooo`800000 1`3oool010000000oooo0?ooo`00000@0?ooo`8000001`3oool010000000oooo0?ooo`0000070?oo o`8000001`3oool2000000L0oooo0`0000080?ooo`8000001`3oool2000000P0oooo00<000000?oo o`0000001`3oool2000000L0oooo00<000000?ooo`3oool01`3oool001X0oooo0`0000000`3oool0 00000?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool00`000000 oooo0?ooo`040?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`050?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool01P3oool00`000000 oooo0?ooo`020?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool02P3oool3000000P0 oooo00D000000?ooo`3oool0oooo0000000H0?ooo`050000003oool0oooo0?ooo`0000006@3oool0 10000000oooo0?ooo`00000I0?ooo`030000003oool0000001/0oooo0P00000A0?ooo`800000203o ool200000180oooo00<000000?ooo`3oool01P3oool2000001/0oooo000J0?ooo`050000003oool0 oooo0?ooo`0000001`3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<0 00000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<0 00000?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<0 00000?ooo`3oool00P3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<0 00000?ooo`3oool01P3oool01@000000oooo0?ooo`3oool0000000h0oooo0P0000080?ooo`050000 003oool0oooo0?ooo`000000603oool01@000000oooo0?ooo`3oool0000001T0oooo00@000000?oo o`3oool000006@3oool00`000000oooo0000000K0?ooo`8000006`3oool2000001/0oooo0P00000K 0?ooo`006P3oool01@000000oooo0?ooo`3oool0000000L0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01P3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00D000000?ooo`3oool0oooo0000 000H0?ooo`050000003oool0oooo0?ooo`0000006@3oool010000000oooo0?ooo`00000I0?ooo`03 0000003oool0000001/0oooo0P00000K0?ooo`800000E@3oool001X0oooo00D000000?ooo`3oool0 oooo000000070?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000 oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000 oooo0?ooo`020?ooo`030000003oool0oooo00L0oooo00<000000?ooo`3oool00P3oool00`000000 oooo0?ooo`060?ooo`050000003oool0oooo0?ooo`000000603oool01@000000oooo0?ooo`3oool0 000001T0oooo00<000000?ooo`0000006P3oool00`000000oooo0000000K0?ooo`800000LP3oool0 01X0oooo00D000000?ooo`3oool0oooo000000070?ooo`030000003oool0oooo00<0oooo00<00000 0?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<00000 0?ooo`3oool00`3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<00000 0?ooo`3oool01P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00L0oooo00<00000 0?ooo`3oool00P3oool00`000000oooo0?ooo`060?ooo`050000003oool0oooo0?ooo`000000603o ool01@000000oooo0?ooo`3oool0000001T0oooo00<000000?ooo`0000006`3oool2000008l0oooo 000J0?ooo`050000003oool0oooo0?ooo`0000001`3oool00`000000oooo0?ooo`030?ooo`030000 003oool0oooo00H0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000 003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`030000 003oool0oooo00H0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`080?ooo`040000 003oool0oooo000000T0oooo00D000000?ooo`3oool0oooo0000000H0?ooo`050000003oool0oooo 0?ooo`0000006@3oool00`000000oooo0000000K0?ooo`800000S`3oool001X0oooo00D000000?oo o`3oool0oooo000000070?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo00P0oooo00@000000?ooo`3oool000002@3o ool01@000000oooo0?ooo`3oool0000001T0oooo00<000000?ooo`0000006P3oool00`000000oooo 0000002/0?ooo`006P3oool01@000000oooo0?ooo`3oool0000000L0oooo00<000000?ooo`3oool0 0`3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0 1@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool0 0`3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0 2@3oool00`000000oooo000000090?ooo`050000003oool0oooo0?ooo`0000006@3oool00`000000 oooo0000000K0?ooo`800000[03oool001X0oooo00D000000?ooo`3oool0oooo000000070?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`060?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo00T0oooo0P00000:0?ooo`050000003oool0oooo0?ooo`0000006@3oool00`00 0000oooo0000000K0?ooo`800000[03oool001X0oooo00D000000?ooo`3oool0oooo000000070?oo o`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`020?oo o`030000003oool0oooo00H0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`060?oo o`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`020?oo o`030000003oool0oooo01D0oooo00D000000?ooo`3oool0oooo0000000I0?ooo`030000003oool0 00000H0oooo000J0?ooo`040000003oool0oooo000000P0oooo00<000000?ooo`3oool00`3oool00`00 0000oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01P3oool00`00 0000oooo0?ooo`020?ooo`030000003oool0oooo00P0oooo00D000000?ooo`3oool0oooo0000000: 0?ooo`040000003oool0oooo000001T0oooo00<000000?ooo`000000iP3oool001X0oooo00@00000 0?ooo`3oool00000203oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<0 00000?ooo`3oool00P3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<0 00000?ooo`3oool0203oool01@000000oooo0?ooo`3oool0000000X0oooo00@000000?ooo`3oool0 00006@3oool00`000000oooo0000003V0?ooo`006P3oool010000000oooo0?ooo`0000080?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`080?ooo`05 0000003oool0oooo0?ooo`0000002P3oool010000000oooo0?ooo`00000I0?ooo`030000003oool0 00000>H0oooo000J0?ooo`040000003oool0oooo000000P0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01`3oool0 1@000000oooo0?ooo`3oool0000000/0oooo00@000000?ooo`3oool000002P3oool010000000oooo 0?ooo`00000I0?ooo`030000003oool000000>H0oooo000J0?ooo`@00000203oool00`000000oooo 0?ooo`030?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool00P3oool00`000000oooo 0?ooo`070?ooo`050000003oool0oooo0?ooo`0000002`3oool00`000000oooo0000000;0?ooo`04 0000003oool0oooo000001X0oooo0P00003V0?ooo`006P3oool010000000oooo0?ooo`0000080?oo o`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`020?oo o`030000003oool0oooo00L0oooo00D000000?ooo`3oool0oooo0000000;0?ooo`030000003oool0 000000/0oooo00@000000?ooo`3oool000006P3oool00`000000oooo0?ooo`3U0?ooo`006P3oool0 10000000oooo0?ooo`0000080?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3o ool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00L0oooo00D000000?ooo`3oool0oooo 0000000;0?ooo`030000003oool0000000/0oooo00@000000?ooo`3oool00000o`3oool30?ooo`00 6P3oool010000000oooo0?ooo`0000080?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3o ool01P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00L0oooo00D000000?ooo`3o ool0oooo0000000;0?ooo`<000002`3oool00`000000oooo0000003o0?ooo`@0oooo000J0?ooo`04 0000003oool0oooo000000P0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`060?oo o`030000003oool0oooo0080oooo00<000000?ooo`3oool01`3oool01@000000oooo0?ooo`3oool0 000001T0oooo00<000000?ooo`000000o`3oool40?ooo`006P3oool010000000oooo0?ooo`000008 0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`02 0?ooo`030000003oool0oooo00L0oooo00D000000?ooo`3oool0oooo0000000I0?ooo`030000003o ool000000?l0oooo103oool001X0oooo00@000000?ooo`3oool000002@3oool01@000000oooo0?oo o`3oool0000000T0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`070?ooo`050000 003oool0oooo0?ooo`0000006@3oool00`000000oooo0000003o0?ooo`@0oooo000J0?ooo`040000 003oool0oooo000000T0oooo00D000000?ooo`3oool0oooo000000090?ooo`030000003oool0oooo 0080oooo00<000000?ooo`3oool01`3oool01@000000oooo0?ooo`3oool0000001T0oooo00<00000 0?ooo`000000o`3oool40?ooo`006P3oool010000000oooo0?ooo`0000090?ooo`050000003oool0 oooo0?ooo`0000002@3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00L0oooo00D0 00000?ooo`3oool0oooo0000000I0?ooo`030000003oool000000?l0oooo103oool001X0oooo00@0 00000?ooo`3oool000002@3oool01@000000oooo0?ooo`3oool0000000T0oooo00<000000?ooo`3o ool00P3oool00`000000oooo0?ooo`070?ooo`050000003oool0oooo0?ooo`0000006@3oool00`00 0000oooo0000003o0?ooo`@0oooo000J0?ooo`@000002@3oool01@000000oooo0?ooo`3oool00000 00T0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`070?ooo`050000003oool0oooo 0?ooo`0000006@3oool00`000000oooo0000003o0?ooo`@0oooo000J0?ooo`040000003oool0oooo 000000T0oooo00D000000?ooo`3oool0oooo000000090?ooo`030000003oool0oooo0080oooo00<0 00000?ooo`3oool01`3oool01@000000oooo0?ooo`3oool0000001T0oooo00<000000?ooo`000000 o`3oool40?ooo`006P3oool010000000oooo0?ooo`0000090?ooo`050000003oool0oooo0?ooo`00 00002P3oool01@000000oooo0?ooo`3oool0000000T0oooo00D000000?ooo`3oool0oooo0000000J 0?ooo`800000o`3oool40?ooo`006P3oool010000000oooo0?ooo`0000090?ooo`050000003oool0 oooo0?ooo`0000002P3oool01@000000oooo0?ooo`3oool0000000T0oooo00D000000?ooo`3oool0 oooo0000000J0?ooo`030000003oool0oooo0?l0oooo0`3oool001X0oooo00@000000?ooo`3oool0 00002@3oool01@000000oooo0?ooo`3oool0000000X0oooo00D000000?ooo`3oool0oooo00000009 0?ooo`050000003oool0oooo0?ooo`000000o`3ooolP0?ooo`006P3oool010000000oooo0?ooo`00 00090?ooo`050000003oool0oooo0?ooo`0000002P3oool01@000000oooo0?ooo`3oool0000000T0 oooo00D000000?ooo`3oool0oooo0000003o0?ooob00oooo000J0?ooo`040000003oool0oooo0000 00T0oooo00D000000?ooo`3oool0oooo0000000:0?ooo`050000003oool0oooo0?ooo`0000002@3o ool01@000000oooo0?ooo`3oool000000?l0oooo803oool00100oooo100000060?ooo`040000003o ool0oooo000000T0oooo00D000000?ooo`3oool0oooo0000000:0?ooo`040000003oool0oooo0000 00X0oooo00D000000?ooo`3oool0oooo0000003o0?ooob00oooo000?0?ooo`030000003oool0oooo 0080oooo00<000000?ooo`3oool00`3oool010000000oooo0?ooo`0000090?ooo`050000003oool0 oooo0?ooo`0000002P3oool010000000oooo0?ooo`00000:0?ooo`050000003oool0oooo0?ooo`00 0000o`3ooolP0?ooo`00503oool00`000000oooo0?ooo`030?ooo`040000003oool0oooo000000T0 oooo00D000000?ooo`3oool0oooo0000000:0?ooo`040000003oool0oooo000000/0oooo00@00000 0?ooo`3oool00000o`3ooolP0?ooo`00503oool00`000000oooo0?ooo`030?ooo`@000002@3oool0 1@000000oooo0?ooo`3oool0000000X0oooo00@000000?ooo`3oool000002`3oool010000000oooo 0?ooo`00003o0?ooob00oooo000@0?ooo`@000001P3oool010000000oooo0?ooo`0000090?ooo`05 0000003oool0oooo0?ooo`0000002P3oool010000000oooo0?ooo`00000;0?ooo`040000003oool0 oooo00000?l0oooo803oool00100oooo00<000000?ooo`3oool01`3oool010000000oooo0?ooo`00 00090?ooo`050000003oool0oooo0?ooo`0000002P3oool010000000oooo0?ooo`00000;0?ooo`04 0000003oool0oooo00000?l0oooo803oool00100oooo00<000000?ooo`3oool01`3oool010000000 oooo0?ooo`0000090?ooo`050000003oool0oooo0?ooo`0000002`3oool00`000000oooo0000000; 0?ooo`030000003oool000000?l0oooo8@3oool00100oooo1@0000050?ooo`040000003oool0oooo 000000T0oooo00D000000?ooo`3oool0oooo0000000;0?ooo`030000003oool0000000/0oooo00<0 00000?ooo`000000o`3ooolQ0?ooo`006P3oool010000000oooo0?ooo`0000090?ooo`050000003o ool0oooo0?ooo`0000002`3oool00`000000oooo0000000;0?ooo`030000003oool000000?l0oooo 8@3oool001X0oooo00@000000?ooo`3oool000002@3oool01@000000oooo0?ooo`3oool0000000/0 oooo00<000000?ooo`0000002`3oool00`000000oooo0000003o0?ooob40oooo000J0?ooo`040000 003oool0oooo000000T0oooo00D000000?ooo`3oool0oooo0000000;0?ooo`800000303oool00`00 0000oooo0000003o0?ooob40oooo000J0?ooo`040000003oool0oooo000000T0oooo00D000000?oo o`3oool0oooo0000000;0?ooo`800000303oool00`000000oooo0000003o0?ooob40oooo000J0?oo o`040000003oool0oooo000000T0oooo00D000000?ooo`3oool0oooo0000000<0?ooo`030000003o ool0oooo00X0oooo00<000000?ooo`000000o`3ooolQ0?ooo`006P3oool4000000T0oooo00D00000 0?ooo`3oool0oooo0000000I0?ooo`030000003oool000000?l0oooo8@3oool001X0oooo00@00000 0?ooo`3oool000002@3oool01@000000oooo0?ooo`3oool0000001T0oooo0P00003o0?ooob80oooo 000J0?ooo`040000003oool0oooo000000T0oooo00D000000?ooo`3oool0oooo0000000I0?ooo`80 0000o`3ooolR0?ooo`006P3oool010000000oooo0?ooo`0000090?ooo`050000003oool0oooo0?oo o`0000006P3oool00`000000oooo0?ooo`3o0?ooob00oooo000J0?ooo`040000003oool0oooo0000 00T0oooo00D000000?ooo`3oool0oooo0000000J0?ooo`030000003oool0oooo0?l0oooo803oool0 01X0oooo00@000000?ooo`3oool000002P3oool010000000oooo0?ooo`00003o0?ooocd0oooo000J 0?ooo`040000003oool0oooo000000X0oooo00@000000?ooo`3oool00000o`3ooolm0?ooo`006P3o ool010000000oooo0?ooo`00000:0?ooo`040000003oool0oooo00000?l0oooo?@3oool001X0oooo 00@000000?ooo`3oool000002P3oool010000000oooo0?ooo`00003o0?ooocd0oooo000J0?ooo`04 0000003oool0oooo000000X0oooo00@000000?ooo`3oool00000o`3ooolm0?ooo`006P3oool40000 00X0oooo00@000000?ooo`3oool00000o`3ooolm0?ooo`006P3oool010000000oooo0?ooo`00000: 0?ooo`040000003oool0oooo00000?l0oooo?@3oool001X0oooo00<000000?ooo`0000002`3oool0 10000000oooo0?ooo`00003o0?ooocd0oooo000J0?ooo`030000003oool0000000/0oooo00@00000 0?ooo`3oool00000o`3ooolm0?ooo`006P3oool00`000000oooo0000000;0?ooo`040000003oool0 oooo00000?l0oooo?@3oool001X0oooo00<000000?ooo`0000002`3oool00`000000oooo0000003o 0?oooch0oooo000J0?ooo`030000003oool0000000/0oooo00<000000?ooo`000000o`3oooln0?oo o`006P3oool00`000000oooo0000000;0?ooo`030000003oool000000?l0oooo?P3oool001X0oooo 00<000000?ooo`0000002`3oool00`000000oooo0000003o0?oooch0oooo000J0?ooo`030000003o ool0000000/0oooo00<000000?ooo`000000o`3oooln0?ooo`006P3oool3000000/0oooo00<00000 0?ooo`000000o`3oooln0?ooo`006P3oool00`000000oooo0000000;0?ooo`030000003oool00000 0?l0oooo?P3oool001X0oooo00<000000?ooo`0000002`3oool00`000000oooo0000003o0?oooch0 oooo000J0?ooo`030000003oool0000000/0oooo00<000000?ooo`000000o`3oooln0?ooo`006P3o ool00`000000oooo0000000;0?ooo`030000003oool000000?l0oooo?P3oool001X0oooo00<00000 0?ooo`0000002`3oool00`000000oooo0000003o0?oooch0oooo000J0?ooo`030000003oool00000 00/0oooo00<000000?ooo`000000o`3oooln0?ooo`006P3oool00`000000oooo0000000;0?ooo`03 0000003oool000000?l0oooo?P3oool001X0oooo00<000000?ooo`0000002`3oool00`000000oooo 0000003o0?oooch0oooo000J0?ooo`<000002`3oool00`000000oooo0000003o0?oooch0oooo000J 0?ooo`030000003oool0000000/0oooo00<000000?ooo`000000o`3oooln0?ooo`006P3oool20000 00`0oooo00<000000?ooo`000000o`3oooln0?ooo`006P3oool2000000`0oooo00<000000?ooo`00 0000o`3oooln0?ooo`006P3oool2000000`0oooo0P00003o0?ooocl0oooo000J0?ooo`800000303o ool200000?l0oooo?`3oool001X0oooo0P00000=0?ooo`030000003oool0oooo0?l0oooo?@3oool0 00P0oooo1@0000030?ooo`@000001P3oool2000000d0oooo00<000000?ooo`3oool0o`3ooolm0?oo o`002P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo00<000000?ooo`3o ool00`3oool200000?l0ooooC@3oool000X0oooo00<000000?ooo`3oool00P3oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo00<0oooo0P00003o0?ooodd0oooo000:0?ooo`030000003o ool0oooo0080oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`<00000o`3o oom<0?ooo`002P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo00<00000 0?ooo`3oool00`3oool200000?l0ooooC@3oool000X0oooo00<000000?ooo`3oool00P3oool00`00 0000oooo0?ooo`020?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0o`3ooom<0?oo o`00203oool3000000@0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo0?l0ooooC03oool000X0oooo00<000000?ooo`3oool00`3oool4000000H0oooo 00<000000?ooo`3oool0o`3ooom<0?ooo`006P3oool00`000000oooo0?ooo`3o0?oood`0oooo000J 0?ooo`030000003oool0oooo0?l0ooooC03oool00?l0ooooJ@3oool00?l0ooooJ@3oool00?l0oooo J@3oool00?l0ooooJ@3oool00?l0ooooJ@3oool00001\ \>"], ImageRangeCache->{{{0, 359}, {221.375, 0}} -> {-5.77812, -11.1666, \ 0.269947, 0.125833}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ Kuigi lahendis on kompleksarvud sees, on lahend tegelikult reaalne. I ees \ olevad kordajad on arvutust\[ADoubleDot]psuse piiril. Nagu oli \ n\[ADoubleDot]ha, arvestas programm seda funktsiooni graafiku joonistamisel. \ Kuid selleks, et antud juhul neist neist lahti saada, v\[OTilde]ib kasutada \ funktsiooni Chop:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(lahend = Chop[%20]\)], "Input"], Cell[BoxData[ \({{y[ x] \[Rule] \(-1.2421551317942252`\)\ \[ExponentialE]\^\(\(-0.075`\ \)\ x\)\ \((\(-8.849108135915191`\)\ Cos[1.9985932552673142`\ x] + 1.`\ \[ExponentialE]\^\(0.075`\ x\)\ Cos[ 1.0014067447326858`\ x]\ Cos[1.9985932552673142`\ x] - 0.20141610541330285`\ \[ExponentialE]\^\(0.075`\ x\)\ Cos[ 1.9985932552673142`\ x]\ Cos[4.9985932552673145`\ x] - 0.0748946423563588`\ \[ExponentialE]\^\(0.075`\ x\)\ Cos[ 1.9985932552673142`\ x]\ Sin[1.0014067447326858`\ x] - 1.029809493000439`\ Sin[1.9985932552673142`\ x] - 0.0748946423563588`\ \[ExponentialE]\^\(0.075`\ x\)\ Cos[ 1.0014067447326858`\ x]\ Sin[1.9985932552673142`\ x] - 0.0030220918435560655`\ \[ExponentialE]\^\(0.075`\ x\)\ Cos[ 4.9985932552673145`\ x]\ Sin[1.9985932552673142`\ x] - 1.`\ \[ExponentialE]\^\(0.075`\ x\)\ Sin[ 1.0014067447326858`\ x]\ Sin[1.9985932552673142`\ x] + 0.0030220918435560655`\ \[ExponentialE]\^\(0.075`\ x\)\ Cos[ 1.9985932552673142`\ x]\ Sin[4.9985932552673145`\ x] - 0.20141610541330288`\ \[ExponentialE]\^\(0.075`\ x\)\ Sin[ 1.9985932552673142`\ x]\ Sin[ 4.9985932552673145`\ x])\)}}\)], "Output"] }, Open ]], Cell[TextData[{ "Chop[avaldis]\t\t\t\tviskab \[ADoubleDot]ra liikmed, mis on \ v\[ADoubleDot]iksemad kui ", Cell[BoxData[ \(TraditionalForm\`10\^\(-10\)\)]], "\nChop[avaldis, dx]\t\t\tviskab \[ADoubleDot]ra liikmed, mis on v\ \[ADoubleDot]iksemad kui dx\t" }], "Text", Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[\(\(lahend[\([1]\)]\)[\([1]\)]\)[\([2]\)], {x, 0, 70}, PlotPoints \[Rule] 100, PlotRange \[Rule] All]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0136054 0.309807 0.0291874 [ [.15986 .29731 -6 -9 ] [.15986 .29731 6 0 ] [.29592 .29731 -6 -9 ] [.29592 .29731 6 0 ] [.43197 .29731 -6 -9 ] [.43197 .29731 6 0 ] [.56803 .29731 -6 -9 ] [.56803 .29731 6 0 ] [.70408 .29731 -6 -9 ] [.70408 .29731 6 0 ] [.84014 .29731 -6 -9 ] [.84014 .29731 6 0 ] [.97619 .29731 -6 -9 ] [.97619 .29731 6 0 ] [.01131 .01793 -18 -4.5 ] [.01131 .01793 0 4.5 ] [.01131 .16387 -12 -4.5 ] [.01131 .16387 0 4.5 ] [.01131 .45574 -6 -4.5 ] [.01131 .45574 0 4.5 ] [.01131 .60168 -12 -4.5 ] [.01131 .60168 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15986 .30981 m .15986 .31606 L s [(10)] .15986 .29731 0 1 Mshowa .29592 .30981 m .29592 .31606 L s [(20)] .29592 .29731 0 1 Mshowa .43197 .30981 m .43197 .31606 L s [(30)] .43197 .29731 0 1 Mshowa .56803 .30981 m .56803 .31606 L s [(40)] .56803 .29731 0 1 Mshowa .70408 .30981 m .70408 .31606 L s [(50)] .70408 .29731 0 1 Mshowa .84014 .30981 m .84014 .31606 L s [(60)] .84014 .29731 0 1 Mshowa .97619 .30981 m .97619 .31606 L s [(70)] .97619 .29731 0 1 Mshowa .125 Mabswid .05102 .30981 m .05102 .31356 L s .07823 .30981 m .07823 .31356 L s .10544 .30981 m .10544 .31356 L s .13265 .30981 m .13265 .31356 L s .18707 .30981 m .18707 .31356 L s .21429 .30981 m .21429 .31356 L s .2415 .30981 m .2415 .31356 L s .26871 .30981 m .26871 .31356 L s .32313 .30981 m .32313 .31356 L s .35034 .30981 m .35034 .31356 L s .37755 .30981 m .37755 .31356 L s .40476 .30981 m .40476 .31356 L s .45918 .30981 m .45918 .31356 L s .48639 .30981 m .48639 .31356 L s .51361 .30981 m .51361 .31356 L s .54082 .30981 m .54082 .31356 L s .59524 .30981 m .59524 .31356 L s .62245 .30981 m .62245 .31356 L s .64966 .30981 m .64966 .31356 L s .67687 .30981 m .67687 .31356 L s .73129 .30981 m .73129 .31356 L s .7585 .30981 m .7585 .31356 L s .78571 .30981 m .78571 .31356 L s .81293 .30981 m .81293 .31356 L s .86735 .30981 m .86735 .31356 L s .89456 .30981 m .89456 .31356 L s .92177 .30981 m .92177 .31356 L s .94898 .30981 m .94898 .31356 L s .25 Mabswid 0 .30981 m 1 .30981 L s .02381 .01793 m .03006 .01793 L s [(-10)] .01131 .01793 1 0 Mshowa .02381 .16387 m .03006 .16387 L s [(-5)] .01131 .16387 1 0 Mshowa .02381 .45574 m .03006 .45574 L s [(5)] .01131 .45574 1 0 Mshowa .02381 .60168 m .03006 .60168 L s [(10)] .01131 .60168 1 0 Mshowa .125 Mabswid .02381 .04712 m .02756 .04712 L s .02381 .07631 m .02756 .07631 L s .02381 .1055 m .02756 .1055 L s .02381 .13468 m .02756 .13468 L s .02381 .19306 m .02756 .19306 L s .02381 .22224 m .02756 .22224 L s .02381 .25143 m .02756 .25143 L s .02381 .28062 m .02756 .28062 L s .02381 .33899 m .02756 .33899 L s .02381 .36818 m .02756 .36818 L s .02381 .39737 m .02756 .39737 L s .02381 .42656 m .02756 .42656 L s .02381 .48493 m .02756 .48493 L s .02381 .51412 m .02756 .51412 L s .02381 .54331 m .02756 .54331 L s .02381 .57249 m .02756 .57249 L s .25 Mabswid .02381 0 m .02381 .61803 L s .5 Mabswid .02381 .60168 m .02409 .60268 L .02435 .60319 L .02465 .60332 L .02494 .60298 L .0252 .60227 L .02544 .60128 L .0257 .59983 L .02599 .59786 L .02657 .59239 L .02712 .58561 L .02837 .56437 L .02958 .5366 L .03068 .50557 L .03318 .41965 L .03806 .22067 L .04064 .12458 L .04206 .08142 L .04275 .0636 L .04339 .0494 L .04399 .03814 L .04465 .02821 L .04531 .0209 L .04567 .01808 L .04583 .01709 L .04601 .0162 L .04632 .01514 L .04661 .01472 L .04689 .01484 L .04715 .01543 L .04744 .01658 L .04775 .01847 L .04808 .02114 L .04838 .02428 L .04895 .03171 L .04955 .04177 L .05061 .06521 L .05176 .0977 L .05302 .14076 L .05817 .36242 L .0606 .46354 L .06285 .53662 L .06398 .56309 L .06456 .57338 L .06519 .58221 L .06552 .58577 L .06582 .58838 L .06598 .58955 L .06616 .59061 L .06634 .5914 L Mistroke .06649 .59195 L .06681 .59252 L .06709 .59247 L .06724 .5922 L .06741 .59173 L .06772 .59037 L .06801 .58852 L .06827 .58629 L .06888 .57947 L .06948 .57055 L .07011 .55863 L .07231 .50071 L .07713 .32099 L .07966 .22585 L .08105 .18092 L .08235 .14557 L .08351 .12069 L .0841 .11042 L .08475 .10123 L .08542 .09398 L .08578 .09101 L .08612 .08887 L .08644 .0874 L .08673 .08651 L .08689 .0862 L .08707 .08602 L .08738 .08606 L .08767 .08654 L .08794 .08735 L .08824 .08864 L .08856 .09048 L .08921 .09565 L .0898 .10196 L .09094 .11805 L .09203 .13751 L .10131 .36957 L .10378 .42075 L .10499 .44088 L .1061 .4561 L .10726 .46848 L .10787 .47347 L .10852 .47757 L .10884 .47916 L .10918 .48052 L .10934 .48106 L .1095 .4815 L .10979 .48212 L .10996 .48236 L .11014 .48252 L .11029 .48259 L Mistroke .11046 .48258 L .11064 .48248 L .11084 .48226 L .11102 .48195 L .11119 .48158 L .1115 .48067 L .1118 .47954 L .11235 .47676 L .11294 .47277 L .11358 .46733 L .11473 .45458 L .1158 .43967 L .11824 .39498 L .12082 .33562 L .12564 .21509 L .12774 .17045 L .12885 .15148 L .13003 .13577 L .13063 .12974 L .13095 .12711 L .13129 .12474 L .13161 .12301 L .1319 .12179 L .13217 .12096 L .13246 .12045 L .13274 .1203 L .13303 .12052 L .13331 .12107 L .13356 .12188 L .13386 .12319 L .13418 .12507 L .13476 .12964 L .13537 .13603 L .13605 .14491 L .1374 .16843 L .13984 .22634 L .14495 .37721 L .14612 .40917 L .14737 .43917 L .14853 .4622 L .14962 .47893 L .1502 .48575 L .15051 .4887 L .15083 .49134 L .15111 .49317 L .15141 .49478 L .15168 .49586 L .15193 .49654 L .15209 .49681 L .15226 .49696 L Mistroke .15257 .49688 L .15287 .49636 L .15315 .49549 L .15345 .49415 L .15378 .49217 L .15445 .48664 L .15505 .48008 L .15559 .47278 L .15682 .4522 L .15904 .4034 L .16403 .27402 L .16528 .24509 L .16646 .22124 L .1676 .20188 L .16866 .18783 L .16971 .1777 L .17023 .17404 L .17053 .17241 L .17081 .17115 L .17112 .1701 L .17139 .16942 L .17169 .16897 L .17186 .16885 L .17201 .16883 L .17227 .16896 L .17256 .16936 L .17286 .17005 L .17314 .17095 L .17372 .17357 L .17434 .17738 L .17544 .1866 L .17662 .19949 L .17792 .21637 L .18307 .29541 L .18775 .35805 L .19008 .38056 L .1914 .39035 L .19261 .39748 L .19368 .4022 L .19428 .40425 L .19484 .40574 L .19515 .40637 L .19544 .40685 L .1957 .40719 L .19598 .40746 L .19629 .40762 L .19646 .40766 L .19662 .40766 L .19692 .40756 L .19721 .40734 L Mistroke .19749 .40701 L .19779 .40654 L .19834 .40534 L .19899 .40335 L .19958 .40097 L .20087 .39396 L .20208 .38493 L .20423 .36343 L .20656 .33281 L .21127 .25846 L .21377 .22184 L .21508 .20632 L .2158 .19937 L .21646 .19402 L .21705 .19022 L .21736 .18866 L .21769 .18726 L .21787 .1866 L .21805 .18609 L .21821 .1857 L .21839 .18535 L .2187 .18499 L .21887 .18492 L .21903 .18494 L .21933 .18519 L .21962 .1857 L .21988 .18639 L .22016 .18738 L .22079 .19053 L .22138 .19458 L .22244 .20464 L .22361 .21956 L .22599 .25995 L .22846 .31076 L .23106 .36457 L .23329 .4029 L .23455 .41918 L .23516 .42533 L .23572 .42993 L .23631 .43355 L .23662 .43498 L .23677 .43559 L .23694 .43614 L .23723 .43683 L .23749 .43722 L .23781 .43736 L .23809 .43718 L .23837 .43674 L .23862 .4361 L .2389 .43513 L Mistroke .2392 .43381 L .23975 .43058 L .24025 .4268 L .24145 .41469 L .24274 .39736 L .24509 .35799 L .24983 .27316 L .25113 .25439 L .25252 .23823 L .2532 .23206 L .25384 .22727 L .25441 .22386 L .25471 .22242 L .25503 .22112 L .25534 .22013 L .25563 .21943 L .2559 .21895 L .25618 .21864 L .25649 .21853 L .25678 .21863 L .2571 .21897 L .25728 .21926 L .25745 .21959 L .25777 .22042 L .25808 .22139 L .25876 .22425 L .26001 .23155 L .26224 .24976 L .26461 .27262 L .26707 .29615 L .26941 .31545 L .27151 .32924 L .2738 .34052 L .27624 .34917 L .27851 .35507 L .27978 .35771 L .28096 .3598 L .28162 .36076 L .28234 .36163 L .28265 .36194 L .28298 .36222 L .28329 .36244 L .28358 .36259 L .28387 .36271 L .28403 .36275 L .2842 .36277 L .28448 .36277 L .28478 .36271 L .28506 .3626 L .28535 .36242 L Mistroke .28563 .36219 L .28588 .36192 L .28649 .36106 L .28715 .35973 L .28777 .35807 L .28835 .35615 L .28948 .35132 L .2905 .34562 L .2928 .32835 L .29785 .27503 L .30007 .25164 L .30124 .24117 L .30189 .23626 L .3025 .23227 L .30309 .2291 L .3034 .22771 L .30373 .22646 L .30401 .2256 L .30431 .22484 L .30459 .22434 L .30485 .22403 L .30512 .22388 L .3054 .22391 L .30564 .22409 L .30591 .22445 L .30619 .22503 L .30649 .22587 L .30704 .22796 L .30766 .23122 L .30834 .23579 L .30956 .2467 L .31184 .27476 L .31656 .34622 L .31786 .36386 L .31925 .37975 L .31992 .38601 L .32056 .39098 L .32113 .39456 L .32176 .39749 L .32207 .39855 L .32223 .39901 L .3224 .39941 L .32272 .39993 L .32301 .40017 L .3233 .40017 L .32356 .39998 L .32385 .39956 L .32415 .39886 L .32448 .39783 L .32484 .39639 L Mistroke .32549 .39296 L .32671 .38385 L .32787 .37237 L .3291 .35786 L .3313 .32829 L .33358 .2976 L .33477 .28313 L .33603 .27002 L .33713 .26071 L .33772 .25673 L .33834 .25323 L .33892 .2507 L .33944 .249 L .33969 .24837 L .33997 .24785 L .34022 .24748 L .34046 .24727 L .34077 .24715 L .34105 .24721 L .34131 .24739 L .3416 .24773 L .3419 .24826 L .34223 .249 L .34281 .25076 L .34397 .25569 L .34501 .26153 L .35002 .29646 L .3523 .30996 L .35344 .3152 L .3547 .31962 L .35536 .32141 L .35606 .32294 L .35673 .32405 L .35733 .32481 L .35793 .32536 L .35827 .32559 L .35858 .32577 L .35915 .32601 L .35944 .32609 L .35975 .32616 L .36035 .32626 L .36101 .32634 L .36131 .32638 L .36163 .32643 L .36221 .32656 L .3625 .32665 L .36282 .32676 L .36339 .32704 L .36394 .32741 L .36446 .32783 L Mistroke .36563 .32917 L .36692 .33119 L .36952 .33641 L .37079 .33895 L .37141 .34005 L .37199 .34092 L .37252 .34156 L .37278 .34182 L .37307 .34205 L .37336 .34221 L .37363 .3423 L .37379 .34233 L .37395 .34233 L .37425 .34228 L .37456 .34214 L .37485 .34192 L .37519 .34156 L .3755 .34111 L .37606 .34005 L .37667 .3385 L .37734 .33628 L .37805 .33336 L .37932 .32666 L .3816 .31044 L .38406 .28936 L .38636 .26981 L .38749 .26161 L .3885 .25545 L .38907 .25263 L .38969 .25017 L .39003 .2491 L .39034 .2483 L .39064 .24771 L .39096 .24727 L .39127 .24702 L .39145 .24697 L .39162 .24698 L .39193 .24715 L .39223 .2475 L .3924 .24778 L .39258 .24813 L .3929 .24894 L .39325 .25005 L .39363 .25155 L .39484 .2582 L .39615 .26833 L .39851 .29268 L .40081 .32029 L .40328 .3481 L .40469 .36102 L Mistroke .40598 .36979 L .4066 .37285 L .40693 .37414 L .40727 .37525 L .40757 .376 L .40773 .37632 L .40791 .37659 L .40821 .37692 L .40849 .37704 L .4088 .37696 L .40896 .37684 L .40913 .37665 L .40944 .37614 L .40973 .37547 L .41006 .37447 L .41037 .37333 L .41107 .37006 L .41226 .36238 L .41352 .35188 L .41811 .30383 L .42042 .28239 L .42171 .27333 L .42232 .26996 L .42289 .26742 L .42342 .26553 L .42398 .26407 L .42428 .26354 L .42455 .26318 L .42485 .26294 L .42502 .26287 L .42518 .26285 L .42545 .26291 L .42571 .26308 L .42599 .26339 L .42628 .26385 L .42684 .26507 L .42734 .26655 L .42852 .27131 L .42977 .27785 L .43201 .29167 L .43444 .30647 L .43578 .31318 L .43644 .31593 L .43705 .31809 L .43762 .31978 L .43825 .32125 L .43888 .32233 L .43922 .32275 L .43938 .3229 L .43955 .32303 L Mistroke .43982 .3232 L .44012 .3233 L .44039 .32332 L .44064 .32328 L .44094 .32317 L .44121 .323 L .44152 .32274 L .44182 .32244 L .44293 .32083 L .44395 .31888 L .44626 .31406 L .4474 .3121 L .44803 .31126 L .44834 .31094 L .44862 .31069 L .44888 .31051 L .44916 .31036 L .44946 .31027 L .44974 .31024 L .45001 .31026 L .4503 .31035 L .45057 .31049 L .45081 .31067 L .45111 .31093 L .45142 .31129 L .45198 .31211 L .45264 .31337 L .45325 .31478 L .45582 .32263 L .45807 .33015 L .45921 .3333 L .45986 .33474 L .46046 .33575 L .46079 .33617 L .46111 .33647 L .46128 .33659 L .46144 .33667 L .46162 .33673 L .46181 .33676 L .46197 .33675 L .46215 .3367 L .46232 .33662 L .46247 .33652 L .46277 .33625 L .46308 .33585 L .46336 .33538 L .46367 .33476 L .46423 .33333 L .46489 .33115 L .46549 .32869 L Mistroke .4679 .3151 L .47012 .29886 L .47271 .27963 L .47398 .27169 L .47454 .26874 L .47515 .26597 L .47566 .26405 L .47621 .26243 L .47651 .26174 L .47679 .26125 L .47706 .26088 L .47733 .26065 L .47761 .26054 L .47791 .26058 L .47817 .26074 L .47845 .26106 L .47876 .26155 L .47908 .26227 L .47967 .26405 L .48031 .26667 L .48101 .27029 L .48228 .27877 L .48467 .29963 L .48733 .32587 L .48864 .33781 L .48984 .34729 L .49094 .35424 L .49149 .35704 L .49209 .35944 L .49241 .36044 L .49269 .36119 L .49298 .36178 L .49325 .3622 L .49357 .36251 L .49386 .36262 L .49402 .36261 L .49419 .36255 L .49436 .36243 L .49453 .36226 L .49482 .36185 L .49508 .36132 L .49569 .35964 L .49628 .35737 L .49691 .3543 L .4991 .33941 L .50402 .29624 L .50523 .28723 L .50651 .27957 L .50718 .27649 L .50753 .27513 L Mistroke .50791 .27388 L .50826 .27295 L .50858 .27226 L .5089 .27174 L .5092 .2714 L .50948 .27121 L .50979 .27115 L .50995 .27118 L .51011 .27125 L .51042 .27149 L .5107 .27185 L .511 .27235 L .51154 .27357 L .51217 .27549 L .51276 .27771 L .51409 .28404 L .51862 .31081 L .51987 .31708 L .52055 .31997 L .52118 .32227 L .52177 .324 L .52231 .32526 L .52259 .32579 L .5229 .32627 L .52307 .32648 L .52323 .32665 L .52354 .32689 L .52371 .32698 L .52387 .32703 L .52404 .32705 L .52422 .32704 L .52452 .32695 L .52469 .32685 L .52486 .32673 L .52516 .32643 L .52543 .32608 L .52604 .32504 L .5267 .32357 L .52741 .32161 L .52871 .31735 L .53103 .30891 L .53226 .3049 L .53291 .30311 L .53359 .30155 L .53421 .30046 L .53456 .29999 L .53488 .29965 L .53518 .29943 L .53545 .2993 L .53577 .29925 L Mistroke .53606 .29929 L .53635 .29941 L .53664 .29962 L .5369 .29987 L .53718 .30023 L .5378 .30128 L .53839 .3026 L .53967 .30648 L .54084 .31098 L .54348 .32257 L .54464 .32738 L .54587 .33167 L .54647 .33331 L .54704 .33454 L .54754 .33536 L .54783 .33569 L .54809 .33591 L .54838 .33606 L .5487 .33611 L .54899 .33603 L .54926 .33587 L .54957 .33556 L .54975 .33533 L .54992 .33508 L .55054 .33382 L .55113 .33215 L .55179 .3298 L .55312 .32356 L .5556 .30791 L .55821 .28966 L .55929 .28286 L .56044 .27669 L .56111 .27382 L .56171 .2717 L .562 .27086 L .56231 .27009 L .56261 .2695 L .56288 .26908 L .56316 .26876 L .56346 .26857 L .56374 .26852 L .56401 .26859 L .56432 .26883 L .56461 .26918 L .56492 .26973 L .56526 .27048 L .56587 .27235 L .56645 .27463 L .56777 .28163 L .56993 .29736 L Mistroke .57227 .31721 L .57349 .32729 L .57478 .33699 L .57599 .34439 L .57658 .34732 L .57712 .34957 L .57774 .35152 L .57806 .35231 L .5784 .35294 L .57869 .35332 L .57896 .35355 L .57925 .35365 L .57956 .3536 L .57974 .35349 L .57991 .35334 L .58009 .35313 L .58028 .35284 L .58064 .35213 L .58096 .35132 L .58162 .34914 L .58224 .34649 L .58337 .34033 L .58461 .33197 L .58711 .31234 L .58941 .29482 L .59054 .28763 L .59159 .28228 L .59215 .27999 L .59277 .278 L .59308 .27724 L .5934 .27657 L .59358 .27627 L .59374 .27604 L .5939 .27586 L .59406 .27571 L .59434 .27555 L .59459 .27551 L .59489 .27558 L .59516 .27577 L .59545 .27607 L .59576 .27654 L .59632 .27774 L .59693 .27951 L .5976 .28197 L .59896 .28835 L .60139 .30262 L .60381 .31679 L .60501 .32253 L .60611 .32666 L .60673 .32837 L Mistroke .60704 .32908 L .60738 .3297 L .60757 .33 L .60775 .33023 L .60792 .33041 L .6081 .33057 L .60842 .33074 L .6086 .33078 L .60876 .33079 L .60907 .33071 L .60937 .33052 L .60964 .33026 L .60993 .32988 L .61058 .3287 L .61118 .32722 L .61231 .32355 L .61352 .3186 L .61572 .30847 L .61705 .30255 L .61833 .29779 L .61888 .29611 L .61947 .29463 L .61981 .29393 L .62012 .2934 L .62043 .29297 L .62072 .29266 L .62099 .29246 L .62128 .29233 L .62144 .29231 L .6216 .29231 L .6219 .2924 L .62221 .29259 L .62249 .29288 L .62281 .29329 L .62314 .29386 L .62369 .29505 L .62421 .29645 L .62538 .30057 L .62784 .31212 L .63043 .32513 L .63156 .32989 L .63218 .33207 L .63276 .33379 L .63309 .3346 L .63346 .33533 L .63376 .33582 L .63393 .33605 L .63409 .33624 L .6344 .3365 L .63456 .33659 L Mistroke .63473 .33665 L .63504 .33665 L .63532 .33654 L .63559 .33634 L .63589 .336 L .63617 .33558 L .63642 .33511 L .63704 .33361 L .63762 .33176 L .63867 .3274 L .6398 .32144 L .64455 .29058 L .64585 .28328 L .64657 .27995 L .64724 .27735 L .64787 .27547 L .64823 .27465 L .64856 .27406 L .64883 .27369 L .64914 .27341 L .64946 .27327 L .64975 .27329 L .65004 .27343 L .65031 .27369 L .65061 .2741 L .65093 .27468 L .65157 .27636 L .65216 .2784 L .6533 .28368 L .65437 .29004 L .65678 .30758 L .65934 .32693 L .66045 .33426 L .66165 .34071 L .66234 .34358 L .66297 .34562 L .66327 .34639 L .6636 .34706 L .66391 .34754 L .6642 .34785 L .66445 .34802 L .66473 .34807 L .66499 .34801 L .66523 .34786 L .66549 .34759 L .66578 .34717 L .66608 .34658 L .66637 .34591 L .66695 .34415 L .66748 .34212 L Mistroke .66867 .33627 L .67112 .32016 L .67371 .30121 L .67592 .28763 L .67652 .28476 L .67718 .28218 L .67779 .28027 L .67835 .279 L .67866 .2785 L .67893 .27817 L .67924 .27792 L .67954 .27783 L .67981 .27785 L .68007 .27797 L .68034 .27821 L .68064 .27859 L .68094 .27909 L .68125 .27976 L .68183 .28131 L .68313 .28629 L .68551 .29915 L .68767 .31246 L .68884 .31914 L .69007 .32522 L .69113 .32927 L .69173 .33102 L .6923 .33226 L .69259 .33274 L .69291 .33315 L .69308 .3333 L .69325 .33342 L .69356 .33355 L .69387 .33355 L .69417 .33343 L .69443 .33323 L .69472 .33292 L .69504 .33245 L .69538 .3318 L .69608 .33007 L .69733 .32571 L .69995 .31305 L .70244 .30021 L .70353 .29549 L .70468 .29153 L .70534 .28987 L .70594 .2888 L .70623 .28843 L .70655 .28815 L .70684 .288 L .70711 .28795 L Mistroke .7074 .28801 L .70766 .28815 L .70796 .28841 L .70824 .28877 L .70875 .28964 L .7093 .29093 L .71054 .29506 L .7117 .30013 L .71419 .31356 L .71653 .32604 L .71765 .33089 L .71871 .3344 L .7193 .33578 L .71963 .33638 L .71994 .33681 L .72023 .3371 L .72048 .33726 L .72078 .33734 L .72106 .3373 L .72135 .33715 L .72167 .33685 L .72183 .33665 L .722 .3364 L .72231 .33584 L .72292 .33439 L .72346 .33266 L .7248 .32702 L .72606 .32011 L .73048 .2919 L .73168 .28542 L .73232 .28257 L .73299 .28008 L .73358 .27836 L .73389 .27764 L .73422 .27702 L .73453 .27659 L .7348 .27632 L .73508 .27616 L .73535 .27612 L .73563 .27619 L .73593 .2764 L .73625 .27677 L .73654 .27725 L .73708 .27843 L .73765 .28014 L .73895 .28564 L .74014 .29233 L .74278 .31055 L .74523 .32756 L .74638 .33421 L Mistroke .74746 .33918 L .74806 .34129 L .74838 .34221 L .74871 .34301 L .74899 .34357 L .7493 .34404 L .74958 .34435 L .74984 .34453 L .75015 .3446 L .75033 .34458 L .75049 .34451 L .75079 .34428 L .75111 .3439 L .75139 .34342 L .75166 .34287 L .75226 .34122 L .75292 .33889 L .75352 .33629 L .75486 .32901 L .75727 .31293 L .75985 .29561 L .76109 .28868 L .76171 .28586 L .76227 .28366 L .76278 .28203 L .76333 .28064 L .76362 .28009 L .76389 .27968 L .76417 .27936 L .76448 .27915 L .76478 .27908 L .76509 .27914 L .76539 .27933 L .76566 .27961 L .76598 .28008 L .76633 .28075 L .76696 .28235 L .76755 .28434 L .76818 .28688 L .76931 .29239 L .77372 .3189 L .77491 .32515 L .77603 .32994 L .77665 .33201 L .77698 .33291 L .77732 .33373 L .77761 .33429 L .77793 .33479 L .77823 .33512 L .7785 .33533 L Mistroke .77877 .33544 L .77907 .33544 L .77936 .33533 L .77962 .33514 L .77988 .33486 L .78011 .33453 L .78064 .33353 L .78121 .33206 L .78183 .33007 L .78295 .32548 L .78769 .29976 L .78898 .29357 L .7897 .29076 L .79038 .28858 L .79101 .28701 L .79136 .28633 L .79169 .28585 L .79197 .28555 L .79227 .28534 L .79259 .28524 L .79289 .28527 L .79318 .28541 L .79345 .28564 L .79374 .28601 L .79406 .28651 L .7947 .28794 L .79529 .28967 L .79642 .29405 L .79749 .29923 L .79991 .31302 L .80123 .32066 L .80246 .32711 L .80367 .33227 L .8042 .33406 L .80477 .33565 L .8051 .33637 L .8054 .33692 L .80569 .33732 L .806 .33764 L .80617 .33775 L .80635 .33784 L .80653 .33787 L .80669 .33787 L .80699 .33776 L .80714 .33766 L .80731 .33751 L .80761 .33714 L .8079 .33668 L .80843 .33553 L .809 .33388 L Mistroke .80963 .33164 L .81179 .3208 L .81405 .3064 L .81649 .29134 L .81718 .28779 L .81789 .28454 L .81856 .28204 L .81917 .28021 L .81975 .27896 L .82008 .27846 L .82037 .27813 L .82054 .27801 L .8207 .27793 L .82087 .27788 L .82105 .27787 L .82135 .27797 L .82152 .27809 L .82168 .27824 L .82199 .27863 L .82227 .27911 L .82292 .28062 L .82349 .28241 L .82409 .28477 L .82628 .2966 L .82865 .31264 L .8299 .32109 L .83122 .32913 L .83239 .33506 L .83301 .33757 L .83367 .33972 L .83399 .34053 L .83429 .34117 L .83457 .34167 L .83484 .34202 L .83509 .34225 L .83536 .3424 L .83563 .34244 L .83593 .34236 L .83622 .34214 L .83651 .34182 L .83676 .34144 L .83703 .34091 L .83765 .33936 L .83822 .33746 L .83925 .333 L .84036 .32704 L .8452 .29561 L .84653 .28854 L .84726 .28543 L .84793 .28309 L Mistroke .84851 .28157 L .84884 .28091 L .84913 .28044 L .84929 .28024 L .84945 .28007 L .84964 .27993 L .8498 .27984 L .85011 .27978 L .85028 .2798 L .85044 .27986 L .85074 .28007 L .85101 .28038 L .85131 .28083 L .85163 .28145 L .85229 .28315 L .85288 .28515 L .85404 .29013 L .85512 .29591 L .85757 .31096 L .85891 .31911 L .86016 .32589 L .86128 .33079 L .86185 .3328 L .86247 .33454 L .86283 .3353 L .86316 .33586 L .86347 .33627 L .86364 .33644 L .8638 .33655 L .8641 .33668 L .86427 .33669 L .86443 .33667 L .86471 .33655 L .86502 .3363 L .8653 .33596 L .86555 .33556 L .86612 .33436 L .86665 .33288 L .86715 .33119 L .86949 .32017 L .87162 .30766 L .87392 .2949 L .87459 .29178 L .87523 .2892 L .87586 .28711 L .87644 .28558 L .87698 .28451 L .87729 .28408 L .87757 .2838 L .87787 .28361 L Mistroke .87804 .28355 L .8782 .28354 L .87849 .2836 L .8788 .28379 L .8791 .2841 L .87937 .28449 L .87998 .2857 L .88055 .28724 L .88109 .28906 L .8823 .29421 L .88361 .30116 L .88603 .31572 L .88732 .32317 L .8887 .33006 L .88933 .33261 L .88999 .33483 L .89056 .33631 L .89088 .33698 L .89117 .33746 L .89147 .33784 L .89176 .33808 L .89205 .33822 L .89222 .33824 L .89238 .33823 L .89263 .33813 L .89292 .33792 L .89322 .33757 L .89349 .33714 L .89415 .3357 L .89478 .33382 L .89595 .32907 L .89859 .31406 L .90091 .29912 L .90219 .2917 L .90339 .28592 L .90394 .28379 L .90452 .28193 L .90482 .28112 L .90515 .28038 L .90546 .27983 L .90573 .27945 L .90601 .27917 L .90626 .27901 L .90654 .27895 L .90683 .279 L .90709 .27914 L .90736 .2794 L .9076 .27971 L .90785 .28014 L .90843 .28142 L Mistroke .90905 .28331 L .91031 .28857 L .91255 .30158 L .9152 .31922 L .91646 .32686 L .91761 .33281 L .91879 .33741 L .91941 .33913 L .91972 .3398 L .92006 .34038 L .92036 .34074 L .92064 .34097 L .92095 .34109 L .92125 .34106 L .92153 .34093 L .92179 .3407 L .92207 .34034 L .92237 .33983 L .92297 .33845 L .92362 .33643 L .92478 .33149 L .92745 .31582 L .92996 .29943 L .93119 .29236 L .9323 .28704 L .93287 .28486 L .93348 .28293 L .93382 .28208 L .93413 .28143 L .93443 .28093 L .93474 .28054 L .93506 .28029 L .93524 .28021 L .9354 .28018 L .93571 .28022 L .93601 .28039 L .93618 .28055 L .93636 .28075 L .93668 .28124 L .93707 .282 L .93741 .28286 L .9386 .28689 L .93985 .29278 L .94208 .306 L .94452 .32104 L .94586 .32807 L .94652 .33095 L .94713 .3332 L .94771 .33492 L .94832 .33628 L Mistroke .94864 .33679 L .94894 .33714 L .94911 .33729 L .94927 .33739 L .94944 .33746 L .94962 .33749 L .94989 .33745 L .95018 .33729 L .95046 .33704 L .9507 .33672 L .951 .33624 L .95131 .33559 L .95189 .33409 L .95301 .33003 L .9542 .32437 L .95634 .31202 L .95862 .29834 L .95988 .29188 L .96051 .28919 L .96108 .28705 L .96166 .28528 L .96219 .28403 L .96249 .28347 L .96278 .28306 L .96308 .28275 L .96325 .28262 L .9634 .28254 L .96366 .28249 L .96389 .28251 L .96415 .28263 L .96443 .28286 L .96473 .28321 L .965 .28365 L .96552 .28474 L .9661 .28636 L .96664 .28823 L .96787 .29364 L .97036 .3079 L .97269 .32206 L .97373 .32761 L .97483 .33245 L .97548 .33474 L .97619 .33664 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg`0oooo000J0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01`3oool00`000000 oooo0?ooo`020?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00P3oool00`000000 oooo0?ooo`090?ooo`040000003oool0oooo000000T0oooo00@000000?ooo`3oool000003@3oool0 0`000000oooo0000003/0?ooo`006P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo 00<0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo 00L0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 0080oooo00<000000?ooo`3oool02@3oool010000000oooo0?ooo`0000090?ooo`040000003oool0 oooo000000d0oooo00<000000?ooo`000000k03oool001X0oooo00<000000?ooo`3oool00P3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`070?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01@3oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo00P0oooo00<000000?ooo`3oool00P3oool0 0`000000oooo0?ooo`060?ooo`040000003oool0oooo000000d0oooo00<000000?ooo`000000k03o ool001X0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`030000003oool0 oooo00D0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`070?ooo`030000003oool0 oooo0080oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`020?ooo`030000003oool0 oooo00P0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`060?ooo`040000003oool0 oooo000000d0oooo00@000000?ooo`3oool00000j`3oool001X0oooo00<000000?ooo`3oool00P3o ool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3o ool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3o ool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00P0oooo00<000000?ooo`3oool00P3o ool00`000000oooo0?ooo`060?ooo`040000003oool0oooo000000`0oooo00D000000?ooo`3oool0 oooo000000090?ooo`8000003`3oool2000000?ooo`040000003oool0oooo000000L0oooo00@000000?ooo`3oool000003`3oool010000000 oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo0P0000070?ooo`040000003oool0 oooo000000H0oooo00@000000?ooo`3oool000001P3oool00`000000oooo000000060?ooo`040000 003oool0oooo000000H0oooo00@000000?ooo`3oool000001P3oool00`000000oooo000000060?oo o`040000003oool0oooo000000H0oooo00@000000?ooo`3oool000001P3oool00`000000oooo0000 000<0?ooo`006P3oool01@000000oooo0?ooo`3oool0000000H0oooo00<000000?ooo`3oool0103o ool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3o ool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3o ool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool00`3o ool00`000000oooo0?ooo`070?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01@3o ool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool00P3o ool00`000000oooo0?ooo`040?ooo`050000003oool0oooo0?ooo`000000303oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo00@0oooo00D000000?ooo`3oool0oooo0000000=0?ooo`05 0000003oool0oooo0?ooo`0000001P3oool010000000oooo0?ooo`0000060?ooo`8000001`3oool0 10000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00<000000?ooo`000000 1P3oool010000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00<000000?oo o`0000001P3oool010000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00<0 00000?ooo`0000001P3oool010000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0 oooo00<000000?ooo`000000303oool001X0oooo00D000000?ooo`3oool0oooo000000060?ooo`03 0000003oool0oooo00@0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`040?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo00@0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`090?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo00X0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`040?ooo`05 0000003oool0oooo0?ooo`0000003@3oool01@000000oooo0?ooo`3oool0000000H0oooo00@00000 0?ooo`3oool000001P3oool2000000L0oooo00@000000?ooo`3oool000001@3oool01@000000oooo 0?ooo`3oool0000000H0oooo00<000000?ooo`0000001P3oool010000000oooo0?ooo`0000060?oo o`040000003oool0oooo000000H0oooo00<000000?ooo`0000001P3oool010000000oooo0?ooo`00 00060?ooo`040000003oool0oooo000000H0oooo00<000000?ooo`0000001P3oool010000000oooo 0?ooo`0000060?ooo`040000003oool0oooo000000D0oooo00D000000?ooo`3oool0oooo0000000; 0?ooo`006P3oool01@000000oooo0?ooo`3oool0000000H0oooo00<000000?ooo`3oool0103oool0 0`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool0 0`000000oooo0?ooo`040?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`070?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0103oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool00P3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool02P3oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo00@0oooo00D000000?ooo`3oool0oooo0000 00050?ooo`8000001@3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00@0oooo00D0 00000?ooo`3oool0oooo000000050?ooo`030000003oool0000000H0oooo00@000000?ooo`3oool0 00001@3oool01@000000oooo0?ooo`3oool0000000D0oooo00@000000?ooo`3oool000001P3oool0 10000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000D0oooo00D000000?ooo`3oool0 oooo000000050?ooo`040000003oool0oooo000000H0oooo00@000000?ooo`3oool000001P3oool0 0`000000oooo000000060?ooo`050000003oool0oooo0?ooo`0000001@3oool010000000oooo0?oo o`0000050?ooo`050000003oool0oooo0?ooo`0000002`3oool001X0oooo00D000000?ooo`3oool0 oooo000000060?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool01@3oool00`000000 oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool00`000000 oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool0103oool00`000000 oooo0?ooo`040?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01`3oool00`000000 oooo0?ooo`030?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool00P3oool00`000000 oooo0?ooo`080?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`030?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool00P3oool00`000000 oooo0?ooo`040?ooo`050000003oool0oooo0?ooo`0000001@3oool2000000D0oooo00<000000?oo o`3oool00P3oool00`000000oooo0?ooo`040?ooo`050000003oool0oooo0?ooo`000000103oool0 10000000oooo0?ooo`0000050?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3o ool01@000000oooo0?ooo`3oool0000000D0oooo00@000000?ooo`3oool000001@3oool01@000000 oooo0?ooo`3oool0000000H0oooo00@000000?ooo`3oool000001@3oool01@000000oooo0?ooo`3o ool0000000@0oooo00D000000?ooo`3oool0oooo000000060?ooo`040000003oool0oooo000000D0 oooo00D000000?ooo`3oool0oooo000000050?ooo`050000003oool0oooo0?ooo`0000001@3oool0 1@000000oooo0?ooo`3oool0000000@0oooo00D000000?ooo`3oool0oooo0000000;0?ooo`006P3o ool01@000000oooo0?ooo`3oool0000000H0oooo00<000000?ooo`3oool0103oool00`000000oooo 0?ooo`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0103oool00`000000oooo 0?ooo`040?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo 0?ooo`040?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool00`3oool00`000000oooo 0?ooo`070?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0103oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo00P0oooo00<000000?ooo`3oool00`3oool00`000000oooo 0?ooo`030?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool02@3oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool00P3oool010000000oooo 0?ooo`3oool3000000D0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`0000050?oo o`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3oool01@000000oooo0?ooo`3oool0 000000D0oooo00@000000?ooo`3oool000001@3oool00`000000oooo0?ooo`020?ooo`030000003o ool0oooo0080oooo00D000000?ooo`3oool0oooo000000050?ooo`050000003oool0oooo0?ooo`00 0000103oool01@000000oooo0?ooo`3oool0000000D0oooo00<000000?ooo`3oool00P3oool00`00 0000oooo0?ooo`020?ooo`050000003oool0oooo0?ooo`0000001@3oool01@000000oooo0?ooo`3o ool0000000D0oooo00D000000?ooo`3oool0oooo000000040?ooo`050000003oool0oooo0?ooo`00 00002`3oool001X0oooo00D000000?ooo`3oool0oooo000000060?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00H0 oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo00<0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00P0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00<0 oooo00D000000?ooo`3oool0oooo000000020?ooo`030000003oool0oooo0080oooo00<000000?oo o`3oool00P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0080oooo00<000000?oo o`3oool00P3oool010000000oooo0?ooo`0000050?ooo`030000003oool0oooo0080oooo00<00000 0?ooo`3oool00P3oool00`000000oooo0?ooo`020?ooo`050000003oool0oooo0?ooo`0000000`3o ool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3o ool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo00D000000?ooo`3oool0oooo 000000040?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo0080oooo00D000000?ooo`3oool0oooo000000040?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`3oool00`3oool01@000000oooo0?ooo`3oool00000 00@0oooo00D000000?ooo`3oool0oooo0000000;0?ooo`004P3ooooo000005L00000000J0?ooo`05 0000003oool0oooo0?ooo`0000001@3oool00`000000oooo000000050?ooo`8000001P3oool00`00 0000oooo000000040?ooo`050000003oool0oooo0?ooo`0000000`3oool00`000000oooo0?ooo`03 0?ooo`030000003oool0oooo00D0oooo0P0000060?ooo`030000003oool0000000@0oooo00D00000 0?ooo`3oool0oooo000000020?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool01P3o ool00`000000oooo0?ooo`030?ooo`040000003oool0oooo00000080oooo00<000000?ooo`3oool0 0`3oool2000000P0oooo0P0000060?ooo`8000000`3oool00`000000oooo0?ooo`020?ooo`800000 0`3oool3000000050?ooo`000000oooo0?ooo`0000001@3oool2000000@0oooo00L000000?ooo`3o ool0oooo0000003oool0000000<0oooo00@000000?ooo`3oool00000103oool01`000000oooo0?oo o`3oool000000?ooo`000000103oool010000000oooo0?ooo`0000020?ooo`090000003oool0oooo 0?ooo`000000oooo0000003oool0000000@0oooo00<000000?ooo`0000000P3oool00`000000oooo 0?ooo`020?ooo`030000003oool000000080oooo00L000000?ooo`3oool0oooo0000003oool00000 0080oooo00<000000?ooo`3oool00P3oool2000000<0oooo00<000000?ooo`3oool00P3oool00`00 0000oooo0?ooo`020?ooo`040000003oool0oooo0?ooo`8000000`3oool00`000000oooo0?ooo`02 0?ooo`030000003oool0oooo0080oooo00@000000?ooo`3oool0oooo0P0000040?ooo`060000003o ool0oooo0000003oool00000103oool00`000000oooo0?ooo`02000000D0oooo00D000000?ooo`00 0000oooo000000040?ooo`030000003oool000000080oooo00L000000?ooo`3oool0oooo0000003o ool0000000T0oooo000J0?ooo`050000003oool0oooo0?ooo`0000001`3oool00`000000oooo0?oo o`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0103oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?oo o`040?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00D0oooo0P0000050?ooo`030000003oool0oooo00<0oooo00<0 00000?ooo`3oool0103oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo00@0oooo00<0 00000?ooo`3oool00P3oool00`000000oooo0?ooo`020?ooo`050000003oool000000?ooo`000000 0P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool0 0P3oool00`000000oooo0?ooo`030?ooo`040000003oool0oooo000000<0oooo00D000000?ooo`3o ool0oooo000000040?ooo`030000003oool0000000@0oooo00<000000?ooo`3oool00`3oool01000 0000oooo0?ooo`0000040?ooo`050000003oool0oooo0?ooo`0000001@3oool00`000000oooo0?oo o`020?ooo`030000003oool0oooo0080oooo00L000000?ooo`3oool0oooo0000003oool000000080 oooo00D000000?ooo`3oool0oooo000000050?ooo`030000003oool0oooo0080oooo00<000000?oo o`3oool00P3oool01@000000oooo0?ooo`3oool0000000@0oooo00D000000?ooo`3oool0oooo0000 00050?ooo`040000003oool0oooo0?ooo`800000103oool01@000000oooo0?ooo`3oool0000000D0 oooo00D000000?ooo`3oool0oooo000000050?ooo`050000003oool0oooo0?ooo`0000001@3oool0 1@000000oooo0?ooo`3oool0000000@0oooo0P0000090?ooo`006P3oool01@000000oooo0?ooo`3o ool0000000L0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003o ool0oooo00@0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003o ool0oooo00D0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`030000003o ool0oooo00<0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003o ool0oooo00@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003o ool0oooo00D0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`020?ooo`030000003o ool0oooo00@0oooo00<000000?ooo`0000000P3oool00`000000oooo0?ooo`020?ooo`030000003o ool0oooo00@0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`040000003o ool0oooo000000@0oooo00@000000?ooo`3oool000001P3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo00<0oooo00@000000?ooo`3oool00000103oool01@000000oooo0?ooo`3oool0 000000H0oooo00D000000?ooo`3oool0oooo000000050?ooo`030000003oool0000000D0oooo00D0 00000?ooo`3oool0oooo000000050?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0 0P3oool01@000000oooo0?ooo`3oool0000000D0oooo00@000000?ooo`3oool000001P3oool01@00 0000oooo0?ooo`3oool0000000@0oooo00D000000?ooo`3oool0oooo000000050?ooo`050000003o ool0oooo0?ooo`0000001@3oool01@000000oooo0?ooo`3oool0000000D0oooo00@000000?ooo`3o ool000001@3oool00`000000oooo0?ooo`080?ooo`006P3oool01@000000oooo0?ooo`3oool00000 00L0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 00@0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo 00D0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 00<0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 00@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 00D0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo 00@0oooo0`0000030?ooo`050000003oool0oooo0?ooo`0000001P3oool00`000000oooo0?ooo`02 0?ooo`030000003oool0oooo00<0oooo0P0000000`3oool000000?ooo`030?ooo`040000003oool0 oooo000000H0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`040000003o ool0oooo000000D0oooo00@000000?ooo`3oool000001P3oool01@000000oooo0?ooo`3oool00000 00D0oooo00<000000?ooo`0000001P3oool010000000oooo0?ooo`0000060?ooo`040000003oool0 oooo000000D0oooo00D000000?ooo`3oool0oooo000000050?ooo`040000003oool0oooo000000H0 oooo00@000000?ooo`3oool000001@3oool01@000000oooo0?ooo`3oool0000000D0oooo00@00000 0?ooo`3oool000001P3oool01@000000oooo0?ooo`3oool0000000D0oooo00@000000?ooo`3oool0 00001@3oool00`000000oooo0?ooo`080?ooo`006P3oool01@000000oooo0?ooo`3oool0000000L0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`8000001P3oool00`000000 oooo0?ooo`050?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01@3oool00`000000 oooo0?ooo`020?ooo`050000003oool0oooo0?ooo`0000001P3oool00`000000oooo0?ooo`020?oo o`030000003oool0oooo00@0oooo0P0000050?ooo`040000003oool0oooo000000H0oooo00D00000 0?ooo`3oool0oooo000000060?ooo`040000003oool0oooo000000D0oooo00@000000?ooo`3oool0 00001P3oool01@000000oooo0?ooo`3oool0000000D0oooo00<000000?ooo`0000001P3oool01000 0000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00@000000?ooo`3oool00000 1@3oool010000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00@000000?oo o`3oool000001@3oool010000000oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo 00@000000?ooo`3oool000001@3oool00`000000oooo0?ooo`080?ooo`006P3oool01@000000oooo 0?ooo`3oool0000000L0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`03 0000003oool0oooo00@0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo00D0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`040?ooo`03 0000003oool0oooo00@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`060?ooo`<0 0000103oool00`000000oooo0?ooo`050?ooo`050000003oool0oooo0?ooo`0000003P3oool01000 0000oooo0?ooo`0000060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0103oool2 000000H0oooo00<000000?ooo`0000001P3oool01@000000oooo0?ooo`3oool0000000H0oooo0`00 00060?ooo`040000003oool0oooo000000H0oooo00D000000?ooo`3oool0oooo000000050?ooo`03 0000003oool0000000H0oooo00@000000?ooo`3oool000001P3oool010000000oooo0?ooo`000006 0?ooo`030000003oool0000000H0oooo00@000000?ooo`3oool000001P3oool010000000oooo0?oo o`0000060?ooo`030000003oool0000000H0oooo00@000000?ooo`3oool000001P3oool010000000 oooo0?ooo`0000060?ooo`040000003oool0oooo000000H0oooo00<000000?ooo`3oool01`3oool0 01X0oooo00D000000?ooo`3oool0oooo000000070?ooo`030000003oool0oooo00<0oooo00<00000 0?ooo`3oool01@3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00D0oooo00<00000 0?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00@0oooo00<00000 0?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<00000 0?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo0080oooo00<00000 0?ooo`3oool02@3oool01@000000oooo0?ooo`3oool0000000L0oooo00D000000?ooo`3oool0oooo 0000000>0?ooo`030000003oool0000000L0oooo00D000000?ooo`3oool0oooo0000000?0?ooo`03 0000003oool0000000H0oooo00D000000?ooo`3oool0oooo000000070?ooo`8000001P3oool00`00 0000oooo000000070?ooo`040000003oool0oooo000000H0oooo0`0000060?ooo`030000003oool0 000000L0oooo00@000000?ooo`3oool000001P3oool00`000000oooo000000060?ooo`040000003o ool0oooo000000H0oooo00@000000?ooo`3oool000001P3oool00`000000oooo000000070?ooo`03 0000003oool0000000H0oooo00@000000?ooo`3oool000001P3oool010000000oooo0?ooo`000006 0?ooo`030000003oool0oooo00L0oooo000J0?ooo`050000003oool0oooo0?ooo`0000001`3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0103oool0 0`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool0 0`000000oooo0?ooo`040?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`060?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool01@3oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo00T0oooo00D000000?ooo`3oool0oooo0000 00070?ooo`050000003oool0oooo0?ooo`0000003P3oool00`000000oooo000000070?ooo`050000 003oool0oooo0?ooo`0000003`3oool00`000000oooo000000070?ooo`040000003oool0oooo0000 00l0oooo0`0000070?ooo`040000003oool0oooo000000L0oooo0P0000070?ooo`8000001`3oool0 10000000oooo0?ooo`0000060?ooo`<000001`3oool2000000L0oooo00@000000?ooo`3oool00000 1P3oool3000000L0oooo00<000000?ooo`0000001P3oool010000000oooo0?ooo`0000070?ooo`80 00001`3oool00`000000oooo0?ooo`070?ooo`006P3oool01@000000oooo0?ooo`3oool0000000L0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00@0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0 oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`0:0?ooo`040000003oool0oooo0000 00L0oooo00D000000?ooo`3oool0oooo0000000?0?ooo`8000001`3oool01@000000oooo0?ooo`3o ool000000100oooo00<000000?ooo`3oool01P3oool010000000oooo0?ooo`00000@0?ooo`800000 1`3oool010000000oooo0?ooo`00000@0?ooo`8000001`3oool010000000oooo0?ooo`0000070?oo o`8000001`3oool2000000L0oooo0`0000080?ooo`8000001`3oool2000000P0oooo00<000000?oo o`0000001`3oool2000000L0oooo00<000000?ooo`3oool01`3oool001X0oooo0`0000000`3oool0 00000?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool00`000000 oooo0?ooo`040?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`050?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool01P3oool00`000000 oooo0?ooo`020?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool02P3oool3000000P0 oooo00D000000?ooo`3oool0oooo0000000H0?ooo`050000003oool0oooo0?ooo`0000006@3oool0 10000000oooo0?ooo`00000I0?ooo`030000003oool0000001/0oooo0P00000A0?ooo`800000203o ool200000180oooo00<000000?ooo`3oool01P3oool2000001/0oooo000J0?ooo`050000003oool0 oooo0?ooo`0000001`3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<0 00000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00<0 00000?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<0 00000?ooo`3oool00P3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<0 00000?ooo`3oool01P3oool01@000000oooo0?ooo`3oool0000000h0oooo0P0000080?ooo`050000 003oool0oooo0?ooo`000000603oool01@000000oooo0?ooo`3oool0000001T0oooo00@000000?oo o`3oool000006@3oool00`000000oooo0000000K0?ooo`8000006`3oool2000001/0oooo0P00000K 0?ooo`006P3oool01@000000oooo0?ooo`3oool0000000L0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01@3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01P3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00D000000?ooo`3oool0oooo0000 000H0?ooo`050000003oool0oooo0?ooo`0000006@3oool010000000oooo0?ooo`00000I0?ooo`03 0000003oool0000001/0oooo0P00000K0?ooo`800000E@3oool001X0oooo00D000000?ooo`3oool0 oooo000000070?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000 oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000 oooo0?ooo`020?ooo`030000003oool0oooo00L0oooo00<000000?ooo`3oool00P3oool00`000000 oooo0?ooo`060?ooo`050000003oool0oooo0?ooo`000000603oool01@000000oooo0?ooo`3oool0 000001T0oooo00<000000?ooo`0000006P3oool00`000000oooo0000000K0?ooo`800000LP3oool0 01X0oooo00D000000?ooo`3oool0oooo000000070?ooo`030000003oool0oooo00<0oooo00<00000 0?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<00000 0?ooo`3oool00`3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<00000 0?ooo`3oool01P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00L0oooo00<00000 0?ooo`3oool00P3oool00`000000oooo0?ooo`060?ooo`050000003oool0oooo0?ooo`000000603o ool01@000000oooo0?ooo`3oool0000001T0oooo00<000000?ooo`0000006`3oool2000008l0oooo 000J0?ooo`050000003oool0oooo0?ooo`0000001`3oool00`000000oooo0?ooo`030?ooo`030000 003oool0oooo00H0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`050?ooo`030000 003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`030000 003oool0oooo00H0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`080?ooo`040000 003oool0oooo000000T0oooo00D000000?ooo`3oool0oooo0000000H0?ooo`050000003oool0oooo 0?ooo`0000006@3oool00`000000oooo0000000K0?ooo`800000S`3oool001X0oooo00D000000?oo o`3oool0oooo000000070?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo00P0oooo00@000000?ooo`3oool000002@3o ool01@000000oooo0?ooo`3oool0000001T0oooo00<000000?ooo`0000006P3oool00`000000oooo 0000002/0?ooo`006P3oool01@000000oooo0?ooo`3oool0000000L0oooo00<000000?ooo`3oool0 0`3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0 1@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool0 0`3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0 2@3oool00`000000oooo000000090?ooo`050000003oool0oooo0?ooo`0000006@3oool00`000000 oooo0000000K0?ooo`800000[03oool001X0oooo00D000000?ooo`3oool0oooo000000070?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`060?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo00T0oooo0P00000:0?ooo`050000003oool0oooo0?ooo`0000006@3oool00`00 0000oooo0000000K0?ooo`800000[03oool001X0oooo00D000000?ooo`3oool0oooo000000070?oo o`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`020?oo o`030000003oool0oooo00H0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`060?oo o`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`020?oo o`030000003oool0oooo01D0oooo00D000000?ooo`3oool0oooo0000000I0?ooo`030000003oool0 00000H0oooo000J0?ooo`040000003oool0oooo000000P0oooo00<000000?ooo`3oool00`3oool00`00 0000oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01P3oool00`00 0000oooo0?ooo`020?ooo`030000003oool0oooo00P0oooo00D000000?ooo`3oool0oooo0000000: 0?ooo`040000003oool0oooo000001T0oooo00<000000?ooo`000000iP3oool001X0oooo00@00000 0?ooo`3oool00000203oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00H0oooo00<0 00000?ooo`3oool00P3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<0 00000?ooo`3oool0203oool01@000000oooo0?ooo`3oool0000000X0oooo00@000000?ooo`3oool0 00006@3oool00`000000oooo0000003V0?ooo`006P3oool010000000oooo0?ooo`0000080?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`080?ooo`05 0000003oool0oooo0?ooo`0000002P3oool010000000oooo0?ooo`00000I0?ooo`030000003oool0 00000>H0oooo000J0?ooo`040000003oool0oooo000000P0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01`3oool0 1@000000oooo0?ooo`3oool0000000/0oooo00@000000?ooo`3oool000002P3oool010000000oooo 0?ooo`00000I0?ooo`030000003oool000000>H0oooo000J0?ooo`@00000203oool00`000000oooo 0?ooo`030?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool00P3oool00`000000oooo 0?ooo`070?ooo`050000003oool0oooo0?ooo`0000002`3oool00`000000oooo0000000;0?ooo`04 0000003oool0oooo000001X0oooo0P00003V0?ooo`006P3oool010000000oooo0?ooo`0000080?oo o`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`020?oo o`030000003oool0oooo00L0oooo00D000000?ooo`3oool0oooo0000000;0?ooo`030000003oool0 000000/0oooo00@000000?ooo`3oool000006P3oool00`000000oooo0?ooo`3U0?ooo`006P3oool0 10000000oooo0?ooo`0000080?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool01P3o ool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00L0oooo00D000000?ooo`3oool0oooo 0000000;0?ooo`030000003oool0000000/0oooo00@000000?ooo`3oool00000o`3oool30?ooo`00 6P3oool010000000oooo0?ooo`0000080?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3o ool01P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00L0oooo00D000000?ooo`3o ool0oooo0000000;0?ooo`<000002`3oool00`000000oooo0000003o0?ooo`@0oooo000J0?ooo`04 0000003oool0oooo000000P0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`060?oo o`030000003oool0oooo0080oooo00<000000?ooo`3oool01`3oool01@000000oooo0?ooo`3oool0 000001T0oooo00<000000?ooo`000000o`3oool40?ooo`006P3oool010000000oooo0?ooo`000008 0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`02 0?ooo`030000003oool0oooo00L0oooo00D000000?ooo`3oool0oooo0000000I0?ooo`030000003o ool000000?l0oooo103oool001X0oooo00@000000?ooo`3oool000002@3oool01@000000oooo0?oo o`3oool0000000T0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`070?ooo`050000 003oool0oooo0?ooo`0000006@3oool00`000000oooo0000003o0?ooo`@0oooo000J0?ooo`040000 003oool0oooo000000T0oooo00D000000?ooo`3oool0oooo000000090?ooo`030000003oool0oooo 0080oooo00<000000?ooo`3oool01`3oool01@000000oooo0?ooo`3oool0000001T0oooo00<00000 0?ooo`000000o`3oool40?ooo`006P3oool010000000oooo0?ooo`0000090?ooo`050000003oool0 oooo0?ooo`0000002@3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo00L0oooo00D0 00000?ooo`3oool0oooo0000000I0?ooo`030000003oool000000?l0oooo103oool001X0oooo00@0 00000?ooo`3oool000002@3oool01@000000oooo0?ooo`3oool0000000T0oooo00<000000?ooo`3o ool00P3oool00`000000oooo0?ooo`070?ooo`050000003oool0oooo0?ooo`0000006@3oool00`00 0000oooo0000003o0?ooo`@0oooo000J0?ooo`@000002@3oool01@000000oooo0?ooo`3oool00000 00T0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`070?ooo`050000003oool0oooo 0?ooo`0000006@3oool00`000000oooo0000003o0?ooo`@0oooo000J0?ooo`040000003oool0oooo 000000T0oooo00D000000?ooo`3oool0oooo000000090?ooo`030000003oool0oooo0080oooo00<0 00000?ooo`3oool01`3oool01@000000oooo0?ooo`3oool0000001T0oooo00<000000?ooo`000000 o`3oool40?ooo`006P3oool010000000oooo0?ooo`0000090?ooo`050000003oool0oooo0?ooo`00 00002P3oool01@000000oooo0?ooo`3oool0000000T0oooo00D000000?ooo`3oool0oooo0000000J 0?ooo`800000o`3oool40?ooo`006P3oool010000000oooo0?ooo`0000090?ooo`050000003oool0 oooo0?ooo`0000002P3oool01@000000oooo0?ooo`3oool0000000T0oooo00D000000?ooo`3oool0 oooo0000000J0?ooo`030000003oool0oooo0?l0oooo0`3oool001X0oooo00@000000?ooo`3oool0 00002@3oool01@000000oooo0?ooo`3oool0000000X0oooo00D000000?ooo`3oool0oooo00000009 0?ooo`050000003oool0oooo0?ooo`000000o`3ooolP0?ooo`006P3oool010000000oooo0?ooo`00 00090?ooo`050000003oool0oooo0?ooo`0000002P3oool01@000000oooo0?ooo`3oool0000000T0 oooo00D000000?ooo`3oool0oooo0000003o0?ooob00oooo000J0?ooo`040000003oool0oooo0000 00T0oooo00D000000?ooo`3oool0oooo0000000:0?ooo`050000003oool0oooo0?ooo`0000002@3o ool01@000000oooo0?ooo`3oool000000?l0oooo803oool00100oooo100000060?ooo`040000003o ool0oooo000000T0oooo00D000000?ooo`3oool0oooo0000000:0?ooo`040000003oool0oooo0000 00X0oooo00D000000?ooo`3oool0oooo0000003o0?ooob00oooo000?0?ooo`030000003oool0oooo 0080oooo00<000000?ooo`3oool00`3oool010000000oooo0?ooo`0000090?ooo`050000003oool0 oooo0?ooo`0000002P3oool010000000oooo0?ooo`00000:0?ooo`050000003oool0oooo0?ooo`00 0000o`3ooolP0?ooo`00503oool00`000000oooo0?ooo`030?ooo`040000003oool0oooo000000T0 oooo00D000000?ooo`3oool0oooo0000000:0?ooo`040000003oool0oooo000000/0oooo00@00000 0?ooo`3oool00000o`3ooolP0?ooo`00503oool00`000000oooo0?ooo`030?ooo`@000002@3oool0 1@000000oooo0?ooo`3oool0000000X0oooo00@000000?ooo`3oool000002`3oool010000000oooo 0?ooo`00003o0?ooob00oooo000@0?ooo`@000001P3oool010000000oooo0?ooo`0000090?ooo`05 0000003oool0oooo0?ooo`0000002P3oool010000000oooo0?ooo`00000;0?ooo`040000003oool0 oooo00000?l0oooo803oool00100oooo00<000000?ooo`3oool01`3oool010000000oooo0?ooo`00 00090?ooo`050000003oool0oooo0?ooo`0000002P3oool010000000oooo0?ooo`00000;0?ooo`04 0000003oool0oooo00000?l0oooo803oool00100oooo00<000000?ooo`3oool01`3oool010000000 oooo0?ooo`0000090?ooo`050000003oool0oooo0?ooo`0000002`3oool00`000000oooo0000000; 0?ooo`030000003oool000000?l0oooo8@3oool00100oooo1@0000050?ooo`040000003oool0oooo 000000T0oooo00D000000?ooo`3oool0oooo0000000;0?ooo`030000003oool0000000/0oooo00<0 00000?ooo`000000o`3ooolQ0?ooo`006P3oool010000000oooo0?ooo`0000090?ooo`050000003o ool0oooo0?ooo`0000002`3oool00`000000oooo0000000;0?ooo`030000003oool000000?l0oooo 8@3oool001X0oooo00@000000?ooo`3oool000002@3oool01@000000oooo0?ooo`3oool0000000/0 oooo00<000000?ooo`0000002`3oool00`000000oooo0000003o0?ooob40oooo000J0?ooo`040000 003oool0oooo000000T0oooo00D000000?ooo`3oool0oooo0000000;0?ooo`800000303oool00`00 0000oooo0000003o0?ooob40oooo000J0?ooo`040000003oool0oooo000000T0oooo00D000000?oo o`3oool0oooo0000000;0?ooo`800000303oool00`000000oooo0000003o0?ooob40oooo000J0?oo o`040000003oool0oooo000000T0oooo00D000000?ooo`3oool0oooo0000000<0?ooo`030000003o ool0oooo00X0oooo00<000000?ooo`000000o`3ooolQ0?ooo`006P3oool4000000T0oooo00D00000 0?ooo`3oool0oooo0000000I0?ooo`030000003oool000000?l0oooo8@3oool001X0oooo00@00000 0?ooo`3oool000002@3oool01@000000oooo0?ooo`3oool0000001T0oooo0P00003o0?ooob80oooo 000J0?ooo`040000003oool0oooo000000T0oooo00D000000?ooo`3oool0oooo0000000I0?ooo`80 0000o`3ooolR0?ooo`006P3oool010000000oooo0?ooo`0000090?ooo`050000003oool0oooo0?oo o`0000006P3oool00`000000oooo0?ooo`3o0?ooob00oooo000J0?ooo`040000003oool0oooo0000 00T0oooo00D000000?ooo`3oool0oooo0000000J0?ooo`030000003oool0oooo0?l0oooo803oool0 01X0oooo00@000000?ooo`3oool000002P3oool010000000oooo0?ooo`00003o0?ooocd0oooo000J 0?ooo`040000003oool0oooo000000X0oooo00@000000?ooo`3oool00000o`3ooolm0?ooo`006P3o ool010000000oooo0?ooo`00000:0?ooo`040000003oool0oooo00000?l0oooo?@3oool001X0oooo 00@000000?ooo`3oool000002P3oool010000000oooo0?ooo`00003o0?ooocd0oooo000J0?ooo`04 0000003oool0oooo000000X0oooo00@000000?ooo`3oool00000o`3ooolm0?ooo`006P3oool40000 00X0oooo00@000000?ooo`3oool00000o`3ooolm0?ooo`006P3oool010000000oooo0?ooo`00000: 0?ooo`040000003oool0oooo00000?l0oooo?@3oool001X0oooo00<000000?ooo`0000002`3oool0 10000000oooo0?ooo`00003o0?ooocd0oooo000J0?ooo`030000003oool0000000/0oooo00@00000 0?ooo`3oool00000o`3ooolm0?ooo`006P3oool00`000000oooo0000000;0?ooo`040000003oool0 oooo00000?l0oooo?@3oool001X0oooo00<000000?ooo`0000002`3oool00`000000oooo0000003o 0?oooch0oooo000J0?ooo`030000003oool0000000/0oooo00<000000?ooo`000000o`3oooln0?oo o`006P3oool00`000000oooo0000000;0?ooo`030000003oool000000?l0oooo?P3oool001X0oooo 00<000000?ooo`0000002`3oool00`000000oooo0000003o0?oooch0oooo000J0?ooo`030000003o ool0000000/0oooo00<000000?ooo`000000o`3oooln0?ooo`006P3oool3000000/0oooo00<00000 0?ooo`000000o`3oooln0?ooo`006P3oool00`000000oooo0000000;0?ooo`030000003oool00000 0?l0oooo?P3oool001X0oooo00<000000?ooo`0000002`3oool00`000000oooo0000003o0?oooch0 oooo000J0?ooo`030000003oool0000000/0oooo00<000000?ooo`000000o`3oooln0?ooo`006P3o ool00`000000oooo0000000;0?ooo`030000003oool000000?l0oooo?P3oool001X0oooo00<00000 0?ooo`0000002`3oool00`000000oooo0000003o0?oooch0oooo000J0?ooo`030000003oool00000 00/0oooo00<000000?ooo`000000o`3oooln0?ooo`006P3oool00`000000oooo0000000;0?ooo`03 0000003oool000000?l0oooo?P3oool001X0oooo00<000000?ooo`0000002`3oool00`000000oooo 0000003o0?oooch0oooo000J0?ooo`<000002`3oool00`000000oooo0000003o0?oooch0oooo000J 0?ooo`030000003oool0000000/0oooo00<000000?ooo`000000o`3oooln0?ooo`006P3oool20000 00`0oooo00<000000?ooo`000000o`3oooln0?ooo`006P3oool2000000`0oooo00<000000?ooo`00 0000o`3oooln0?ooo`006P3oool2000000`0oooo0P00003o0?ooocl0oooo000J0?ooo`800000303o ool200000?l0oooo?`3oool001X0oooo0P00000=0?ooo`030000003oool0oooo0?l0oooo?@3oool0 00P0oooo1@0000030?ooo`@000001P3oool2000000d0oooo00<000000?ooo`3oool0o`3ooolm0?oo o`002P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo00<000000?ooo`3o ool00`3oool200000?l0ooooC@3oool000X0oooo00<000000?ooo`3oool00P3oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo00<0oooo0P00003o0?ooodd0oooo000:0?ooo`030000003o ool0oooo0080oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`<00000o`3o oom<0?ooo`002P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo00<00000 0?ooo`3oool00`3oool200000?l0ooooC@3oool000X0oooo00<000000?ooo`3oool00P3oool00`00 0000oooo0?ooo`020?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0o`3ooom<0?oo o`00203oool3000000@0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo0?l0ooooC03oool000X0oooo00<000000?ooo`3oool00`3oool4000000H0oooo 00<000000?ooo`3oool0o`3ooom<0?ooo`006P3oool00`000000oooo0?ooo`3o0?oood`0oooo000J 0?ooo`030000003oool0oooo0?l0ooooC03oool00?l0ooooJ@3oool00?l0ooooJ@3oool00?l0oooo J@3oool00?l0ooooJ@3oool00?l0ooooJ@3oool00001\ \>"], ImageRangeCache->{{{0, 359}, {221.375, 0}} -> {-5.77812, -11.1666, \ 0.269947, 0.125833}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[BoxData[ \(Clear[x, u, t, y]\)], "Input"], Cell["\<\ Tihti pole v\[OTilde]imalik leida diferentsiaalv\[OTilde]rrandi v\[OTilde]i v\ \[OTilde]rrandite s\[UDoubleDot]steemi lahendit \ anal\[UDoubleDot]\[UDoubleDot]tiliselt. Sel juhul tuleb alati ette anda ka algtingimused. Tulemuseks saame funktsiooni, mis on \ esitatud interpoleeritud funktsioonina. Viimast saame omakorda \ l\[ADoubleDot]hemalt uurida graafiku abil.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(funkt = NDSolve[{\(u'\)[t] \[Equal] 2 - \((u[t])\)\^2 + Sin[t], u[0] \[Equal] 2}, u, {t, 0, 15}]\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"u", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 15.`}}, "<>"]\), False, Editable->False]}], "}"}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[ Evaluate[u[t] /. \(funkt[\([1]\)]\)[\([1]\)]], {t, 0, 15}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0634921 -0.623795 0.613557 [ [.15079 .59082 -3 -9 ] [.15079 .59082 3 0 ] [.27778 .59082 -3 -9 ] [.27778 .59082 3 0 ] [.40476 .59082 -3 -9 ] [.40476 .59082 3 0 ] [.53175 .59082 -3 -9 ] [.53175 .59082 3 0 ] [.65873 .59082 -6 -9 ] [.65873 .59082 6 0 ] [.78571 .59082 -6 -9 ] [.78571 .59082 6 0 ] [.9127 .59082 -6 -9 ] [.9127 .59082 6 0 ] [.01131 .11247 -18 -4.5 ] [.01131 .11247 0 4.5 ] [.01131 .23519 -18 -4.5 ] [.01131 .23519 0 4.5 ] [.01131 .3579 -18 -4.5 ] [.01131 .3579 0 4.5 ] [.01131 .48061 -18 -4.5 ] [.01131 .48061 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 .60332 m .15079 .60957 L s [(2)] .15079 .59082 0 1 Mshowa .27778 .60332 m .27778 .60957 L s [(4)] .27778 .59082 0 1 Mshowa .40476 .60332 m .40476 .60957 L s [(6)] .40476 .59082 0 1 Mshowa .53175 .60332 m .53175 .60957 L s [(8)] .53175 .59082 0 1 Mshowa .65873 .60332 m .65873 .60957 L s [(10)] .65873 .59082 0 1 Mshowa .78571 .60332 m .78571 .60957 L s [(12)] .78571 .59082 0 1 Mshowa .9127 .60332 m .9127 .60957 L s [(14)] .9127 .59082 0 1 Mshowa .125 Mabswid .05556 .60332 m .05556 .60707 L s .0873 .60332 m .0873 .60707 L s .11905 .60332 m .11905 .60707 L s .18254 .60332 m .18254 .60707 L s .21429 .60332 m .21429 .60707 L s .24603 .60332 m .24603 .60707 L s .30952 .60332 m .30952 .60707 L s .34127 .60332 m .34127 .60707 L s .37302 .60332 m .37302 .60707 L s .43651 .60332 m .43651 .60707 L s .46825 .60332 m .46825 .60707 L s .5 .60332 m .5 .60707 L s .56349 .60332 m .56349 .60707 L s .59524 .60332 m .59524 .60707 L s .62698 .60332 m .62698 .60707 L s .69048 .60332 m .69048 .60707 L s .72222 .60332 m .72222 .60707 L s .75397 .60332 m .75397 .60707 L s .81746 .60332 m .81746 .60707 L s .84921 .60332 m .84921 .60707 L s .88095 .60332 m .88095 .60707 L s .94444 .60332 m .94444 .60707 L s .97619 .60332 m .97619 .60707 L s .25 Mabswid 0 .60332 m 1 .60332 L s .02381 .11247 m .03006 .11247 L s [(1.2)] .01131 .11247 1 0 Mshowa .02381 .23519 m .03006 .23519 L s [(1.4)] .01131 .23519 1 0 Mshowa .02381 .3579 m .03006 .3579 L s [(1.6)] .01131 .3579 1 0 Mshowa .02381 .48061 m .03006 .48061 L s [(1.8)] .01131 .48061 1 0 Mshowa .125 Mabswid .02381 .14315 m .02756 .14315 L s .02381 .17383 m .02756 .17383 L s .02381 .20451 m .02756 .20451 L s .02381 .26586 m .02756 .26586 L s .02381 .29654 m .02756 .29654 L s .02381 .32722 m .02756 .32722 L s .02381 .38857 m .02756 .38857 L s .02381 .41925 m .02756 .41925 L s .02381 .44993 m .02756 .44993 L s .02381 .51129 m .02756 .51129 L s .02381 .54196 m .02756 .54196 L s .02381 .57264 m .02756 .57264 L s .02381 .0818 m .02756 .0818 L s .02381 .05112 m .02756 .05112 L s .02381 .02044 m .02756 .02044 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .60332 m .02846 .52672 L .03279 .47465 L .03754 .43328 L .0402 .41573 L .04262 .40263 L .04499 .3921 L .0475 .3831 L .05026 .37545 L .05281 .37017 L .05395 .36829 L .05518 .36658 L .05624 .36534 L .05739 .36423 L .05875 .36323 L .06003 .36256 L .06128 .36213 L .06244 .36194 L .06311 .36191 L .06382 .36193 L .06509 .36213 L .0658 .36231 L .06645 .36253 L .06795 .36319 L .07046 .36474 L .07314 .36693 L .08284 .37798 L .09325 .39237 L .10458 .40762 L .10993 .414 L .11561 .41991 L .12088 .42446 L .12582 .42785 L .13042 .43018 L .13301 .43113 L .13538 .43177 L .13666 .43202 L .13784 .43219 L .13914 .43231 L .13987 .43235 L .14053 .43237 L .14122 .43237 L .14186 .43235 L .14257 .43231 L .14331 .43225 L .14456 .43209 L .14528 .43197 L .14594 .43184 L .14852 .43116 L .15092 .43028 L Mistroke .15355 .42905 L .15635 .42742 L .16153 .42357 L .16623 .41915 L .17578 .4075 L .18476 .39343 L .20488 .35209 L .22337 .30422 L .26291 .18461 L .30093 .07719 L .31098 .05518 L .32048 .03815 L .32573 .03054 L .33143 .02387 L .33395 .02148 L .33662 .01932 L .33891 .01779 L .34141 .01647 L .3438 .01555 L .3451 .01518 L .34631 .01494 L .34745 .01479 L .34849 .01472 L .34968 .01472 L .3508 .0148 L .35203 .01498 L .35333 .01527 L .35444 .0156 L .35566 .01604 L .35838 .01737 L .36092 .01902 L .36553 .02304 L .36974 .02783 L .37921 .04244 L .38911 .06303 L .39827 .08638 L .41902 .15063 L .45826 .28537 L .47793 .34387 L .49598 .38605 L .50539 .40286 L .5153 .41644 L .52045 .42179 L .52525 .4257 L .52796 .42745 L .53052 .4288 L .53193 .42942 L .53347 .43 L .53487 .43043 L .53615 .43075 L Mistroke .53735 .43098 L .5385 .43115 L .53971 .43126 L .54103 .4313 L .54217 .43128 L .5434 .43119 L .54455 .43104 L .5456 .43086 L .54694 .43056 L .54817 .43021 L .55095 .42919 L .55341 .42801 L .556 .42649 L .56119 .4226 L .56603 .41797 L .57703 .404 L .5875 .38654 L .5974 .36658 L .61596 .3215 L .65431 .20801 L .67371 .1484 L .69511 .08882 L .70487 .06575 L .71538 .04488 L .72022 .0369 L .72531 .02971 L .72998 .02426 L .7344 .0202 L .7368 .01845 L .73941 .01692 L .74056 .01637 L .74177 .01588 L .74291 .01549 L .74395 .0152 L .74517 .01495 L .74647 .01478 L .74767 .01472 L .74881 .01473 L .74946 .01478 L .75014 .01485 L .75137 .01506 L .75212 .01523 L .75283 .01543 L .75416 .01587 L .7564 .01687 L .75876 .01826 L .76299 .02161 L .76754 .02643 L .77253 .03315 L .78277 .05142 L Mistroke .79209 .07288 L .81302 .13428 L .85294 .27143 L .87121 .32826 L .88161 .35615 L .89134 .37873 L .9017 .39855 L .91117 .41271 L .91601 .41842 L .9213 .42347 L .9242 .42571 L .92689 .42744 L .92965 .4289 L .9322 .42993 L .93466 .43066 L .93591 .43092 L .93661 .43104 L .93727 .43113 L .93799 .4312 L .93864 .43126 L .93934 .43129 L .94011 .4313 L .94078 .43129 L .94149 .43126 L .94276 .43114 L .94393 .43097 L .9452 .43072 L .94749 .43009 L .95021 .42905 L .95271 .42781 L .95704 .42504 L .96177 .42112 L .97132 .41047 L .97619 .40366 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`006P3oool00`00 0000oooo0?ooo`1T0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0M@3oool00`00 0000oooo0?ooo`0<0?ooo`030000003oool0oooo04d0oooo000J0?ooo`030000003oool0oooo06<0 oooo00<000000?ooo`3oool03P3oool00`000000oooo0?ooo`1d0?ooo`030000003oool0oooo00h0 oooo00<000000?ooo`3oool0C03oool001X0oooo00<000000?ooo`3oool0H`3oool00`000000oooo 0?ooo`0?0?ooo`030000003oool0oooo0780oooo00<000000?ooo`3oool0403oool00`000000oooo 0?ooo`1;0?ooo`006P3oool00`000000oooo0?ooo`1R0?ooo`030000003oool0oooo0100oooo00<0 00000?ooo`3oool0LP3oool00`000000oooo0?ooo`0@0?ooo`030000003oool0oooo04/0oooo000J 0?ooo`030000003oool0oooo0640oooo00<000000?ooo`3oool04P3oool00`000000oooo0?ooo`1` 0?ooo`030000003oool0oooo0180oooo00<000000?ooo`3oool0BP3oool001X0oooo00<000000?oo o`3oool0H@3oool00`000000oooo0?ooo`0C0?ooo`030000003oool0oooo06l0oooo00<000000?oo o`3oool04`3oool00`000000oooo0?ooo`190?ooo`006P3oool00`000000oooo0?ooo`1P0?ooo`03 0000003oool0oooo01@0oooo00<000000?ooo`3oool0KP3oool00`000000oooo0?ooo`0D0?ooo`03 0000003oool0oooo04T0oooo000J0?ooo`<00000H03oool00`000000oooo0?ooo`0E0?ooo`030000 003oool0oooo06d0oooo00<000000?ooo`3oool05@3oool00`000000oooo0?ooo`180?ooo`006P3o ool00`000000oooo0?ooo`1O0?ooo`030000003oool0oooo01H0oooo00<000000?ooo`3oool0K03o ool00`000000oooo0?ooo`0F0?ooo`030000003oool0oooo04P0oooo000J0?ooo`030000003oool0 oooo05l0oooo00<000000?ooo`3oool05`3oool00`000000oooo0?ooo`1[0?ooo`030000003oool0 oooo01L0oooo00<000000?ooo`3oool0A`3oool001X0oooo00<000000?ooo`3oool0GP3oool00`00 0000oooo0?ooo`0H0?ooo`030000003oool0oooo06X0oooo00<000000?ooo`3oool0603oool00`00 0000oooo0?ooo`170?ooo`006P3oool00`000000oooo0?ooo`1N0?ooo`030000003oool0oooo01T0 oooo00<000000?ooo`3oool0J@3oool00`000000oooo0?ooo`0I0?ooo`030000003oool0oooo04H0 oooo000J0?ooo`030000003oool0oooo05d0oooo00<000000?ooo`3oool06P3oool00`000000oooo 0?ooo`1X0?ooo`030000003oool0oooo01X0oooo00<000000?ooo`3oool0AP3oool001X0oooo00<0 00000?ooo`3oool0G@3oool00`000000oooo0?ooo`0K0?ooo`030000003oool0oooo06L0oooo00<0 00000?ooo`3oool06`3oool00`000000oooo0?ooo`150?ooo`006P3oool00`000000oooo0?ooo`1M 0?ooo`030000003oool0oooo01/0oooo00<000000?ooo`3oool0IP3oool00`000000oooo0?ooo`0L 0?ooo`030000003oool0oooo04D0oooo000J0?ooo`030000003oool0oooo05`0oooo00<000000?oo o`3oool0703oool00`000000oooo0?ooo`1V0?ooo`030000003oool0oooo01`0oooo00<000000?oo o`3oool0A@3oool001X0oooo00<000000?ooo`3oool0G03oool00`000000oooo0?ooo`0M0?ooo`03 0000003oool0oooo06@0oooo00<000000?ooo`3oool07P3oool00`000000oooo0?ooo`140?ooo`00 6P3oool3000005`0oooo00<000000?ooo`3oool07@3oool00`000000oooo0?ooo`1T0?ooo`030000 003oool0oooo01h0oooo00<000000?ooo`3oool0A03oool001X0oooo00<000000?ooo`3oool0F`3o ool00`000000oooo0?ooo`0O0?ooo`030000003oool0oooo06<0oooo00<000000?ooo`3oool07P3o ool00`000000oooo0?ooo`140?ooo`006P3oool00`000000oooo0?ooo`1K0?ooo`030000003oool0 oooo01l0oooo00<000000?ooo`3oool0HP3oool00`000000oooo0?ooo`0P0?ooo`030000003oool0 oooo04<0oooo000J0?ooo`030000003oool0oooo05/0oooo00<000000?ooo`3oool07`3oool00`00 0000oooo0?ooo`1R0?ooo`030000003oool0oooo0200oooo00<000000?ooo`3oool0@`3oool001X0 oooo00<000000?ooo`3oool0FP3oool00`000000oooo0?ooo`0Q0?ooo`030000003oool0oooo0640 oooo00<000000?ooo`3oool0803oool00`000000oooo0?ooo`130?ooo`006P3oool00`000000oooo 0?ooo`1J0?ooo`030000003oool0oooo0240oooo00<000000?ooo`3oool0H03oool00`000000oooo 0?ooo`0R0?ooo`030000003oool0oooo0480oooo000J0?ooo`030000003oool0oooo05T0oooo00<0 00000?ooo`3oool08P3oool00`000000oooo0?ooo`1P0?ooo`030000003oool0oooo0280oooo00<0 00000?ooo`3oool0@P3oool001X0oooo00<000000?ooo`3oool0F@3oool00`000000oooo0?ooo`0S 0?ooo`030000003oool0oooo05h0oooo00<000000?ooo`3oool08`3oool00`000000oooo0?ooo`12 0?ooo`001@0000040?ooo`800000103oool5000000H0oooo00<000000?ooo`3oool0F@3oool00`00 0000oooo0?ooo`0S0?ooo`030000003oool0oooo05h0oooo00<000000?ooo`3oool0903oool00`00 0000oooo0?ooo`110?ooo`000P3oool00`000000oooo0?ooo`040?ooo`800000103oool01@000000 oooo0?ooo`3oool0000000H0oooo00<000000?ooo`3oool0F03oool00`000000oooo0?ooo`0T0?oo o`030000003oool0oooo05h0oooo00<000000?ooo`3oool0903oool00`000000oooo0?ooo`110?oo o`000P3oool00`000000oooo0?ooo`0;0?ooo`030000003oool0oooo00L0oooo00<000000?ooo`3o ool0F03oool00`000000oooo0?ooo`0U0?ooo`030000003oool0oooo05`0oooo00<000000?ooo`3o ool09@3oool00`000000oooo0?ooo`110?ooo`000P3oool00`000000oooo0?ooo`0<0?ooo`030000 003oool0oooo00H0oooo0`00001H0?ooo`030000003oool0oooo02D0oooo00<000000?ooo`3oool0 G03oool00`000000oooo0?ooo`0V0?ooo`030000003oool0oooo0400oooo00020?ooo`030000003o ool0oooo00d0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`1G0?ooo`030000003o ool0oooo02H0oooo00<000000?ooo`3oool0F`3oool00`000000oooo0?ooo`0W0?ooo`030000003o ool0oooo0400oooo00020?ooo`030000003oool0oooo00h0oooo00<000000?ooo`3oool0103oool0 0`000000oooo0?ooo`1G0?ooo`030000003oool0oooo02H0oooo00<000000?ooo`3oool0F`3oool0 0`000000oooo0?ooo`0W0?ooo`030000003oool0oooo0400oooo0003000000`0oooo00D000000?oo o`3oool0oooo000000060?ooo`030000003oool0oooo05L0oooo00<000000?ooo`3oool09`3oool0 0`000000oooo0?ooo`1J0?ooo`030000003oool0oooo02P0oooo00<000000?ooo`3oool0?`3oool0 0080oooo00<000000?ooo`3oool02`3oool3000000L0oooo00<000000?ooo`3oool0EP3oool00`00 0000oooo0?ooo`0X0?ooo`030000003oool0oooo05T0oooo00<000000?ooo`3oool0:@3oool00`00 0000oooo0?ooo`0o0?ooo`006P3oool00`000000oooo0?ooo`1F0?ooo`030000003oool0oooo02P0 oooo00<000000?ooo`3oool0F@3oool00`000000oooo0?ooo`0Y0?ooo`030000003oool0oooo03l0 oooo000J0?ooo`030000003oool0oooo05D0oooo00<000000?ooo`3oool0:P3oool00`000000oooo 0?ooo`1G0?ooo`030000003oool0oooo02/0oooo00<000000?ooo`3oool0?P3oool001X0oooo00<0 00000?ooo`3oool0E@3oool00`000000oooo0?ooo`0Z0?ooo`030000003oool0oooo05L0oooo00<0 00000?ooo`3oool0:`3oool00`000000oooo0?ooo`0n0?ooo`006P3oool00`000000oooo0?ooo`1E 0?ooo`030000003oool0oooo02X0oooo00<000000?ooo`3oool0E`3oool00`000000oooo0?ooo`0[ 0?ooo`030000003oool0oooo03h0oooo000J0?ooo`030000003oool0oooo05@0oooo00<000000?oo o`3oool0;03oool00`000000oooo0?ooo`1E0?ooo`030000003oool0oooo02d0oooo00<000000?oo o`3oool0?@3oool001X0oooo0`00001D0?ooo`030000003oool0oooo02`0oooo00<000000?ooo`3o ool0E@3oool00`000000oooo0?ooo`0]0?ooo`030000003oool0oooo03d0oooo000J0?ooo`030000 003oool0oooo05@0oooo00<000000?ooo`3oool0;03oool00`000000oooo0?ooo`1D0?ooo`030000 003oool0oooo02h0oooo00<000000?ooo`3oool0?@3oool001X0oooo00<000000?ooo`3oool0D`3o ool00`000000oooo0?ooo`0^0?ooo`030000003oool0oooo05<0oooo00<000000?ooo`3oool0;P3o ool00`000000oooo0?ooo`0m0?ooo`006P3oool00`000000oooo0?ooo`1C0?ooo`030000003oool0 oooo02h0oooo00<000000?ooo`3oool0D`3oool00`000000oooo0?ooo`0_0?ooo`030000003oool0 oooo03`0oooo000J0?ooo`030000003oool0oooo05<0oooo00<000000?ooo`3oool0;P3oool00`00 0000oooo0?ooo`1B0?ooo`030000003oool0oooo0300oooo00<000000?ooo`3oool0?03oool001X0 oooo00<000000?ooo`3oool0DP3oool00`000000oooo0?ooo`0`0?ooo`030000003oool0oooo0540 oooo00<000000?ooo`3oool0<03oool00`000000oooo0?ooo`0l0?ooo`006P3oool00`000000oooo 0?ooo`1B0?ooo`030000003oool0oooo0300oooo00<000000?ooo`3oool0D@3oool00`000000oooo 0?ooo`0`0?ooo`030000003oool0oooo03`0oooo000J0?ooo`030000003oool0oooo0580oooo00<0 00000?ooo`3oool0<03oool00`000000oooo0?ooo`1@0?ooo`030000003oool0oooo0380oooo00<0 00000?ooo`3oool0>`3oool001X0oooo00<000000?ooo`3oool0D@3oool00`000000oooo0?ooo`0a 0?ooo`030000003oool0oooo0500oooo00<000000?ooo`3oool0P3oool001X0oooo0`00001@0?ooo`030000 003oool0oooo03<0oooo00<000000?ooo`3oool0CP3oool00`000000oooo0?ooo`0d0?ooo`030000 003oool0oooo03X0oooo000J0?ooo`030000003oool0oooo0500oooo00<000000?ooo`3oool0=03o ool00`000000oooo0?ooo`1=0?ooo`030000003oool0oooo03@0oooo00<000000?ooo`3oool0>P3o ool001X0oooo00<000000?ooo`3oool0C`3oool00`000000oooo0?ooo`0e0?ooo`030000003oool0 oooo04d0oooo00<000000?ooo`3oool0=03oool00`000000oooo0?ooo`0j0?ooo`006P3oool00`00 0000oooo0?ooo`1?0?ooo`030000003oool0oooo03D0oooo00<000000?ooo`3oool0C03oool00`00 0000oooo0?ooo`0f0?ooo`030000003oool0oooo03T0oooo000J0?ooo`030000003oool0oooo04l0 oooo00<000000?ooo`3oool0=@3oool00`000000oooo0?ooo`1<0?ooo`030000003oool0oooo03H0 oooo00<000000?ooo`3oool0>@3oool001X0oooo00<000000?ooo`3oool0CP3oool00`000000oooo 0?ooo`0g0?ooo`030000003oool0oooo04/0oooo00<000000?ooo`3oool0=P3oool00`000000oooo 0?ooo`0i0?ooo`006P3oool00`000000oooo0?ooo`1>0?ooo`030000003oool0oooo03L0oooo00<0 00000?ooo`3oool0BP3oool00`000000oooo0?ooo`0h0?ooo`030000003oool0oooo03P0oooo000J 0?ooo`030000003oool0oooo04h0oooo00<000000?ooo`3oool0=`3oool00`000000oooo0?ooo`1: 0?ooo`030000003oool0oooo03P0oooo00<000000?ooo`3oool0>03oool001X0oooo00<000000?oo o`3oool0C@3oool00`000000oooo0?ooo`0i0?ooo`030000003oool0oooo04T0oooo00<000000?oo o`3oool0>03oool00`000000oooo0?ooo`0h0?ooo`006P3oool00`000000oooo0?ooo`1=0?ooo`03 0000003oool0oooo03T0oooo00<000000?ooo`3oool0B@3oool00`000000oooo0?ooo`0h0?ooo`03 0000003oool0oooo03P0oooo000J0?ooo`<00000C@3oool00`000000oooo0?ooo`0i0?ooo`030000 003oool0oooo04P0oooo00<000000?ooo`3oool0>P3oool00`000000oooo0?ooo`0g0?ooo`006P3o ool00`000000oooo0?ooo`1<0?ooo`030000003oool0oooo03X0oooo00<000000?ooo`3oool0B03o ool00`000000oooo0?ooo`0j0?ooo`030000003oool0oooo03L0oooo000J0?ooo`030000003oool0 oooo04`0oooo00<000000?ooo`3oool0>`3oool00`000000oooo0?ooo`170?ooo`030000003oool0 oooo03X0oooo00<000000?ooo`3oool0=`3oool001X0oooo00<000000?ooo`3oool0C03oool00`00 0000oooo0?ooo`0k0?ooo`030000003oool0oooo04H0oooo00<000000?ooo`3oool0>`3oool00`00 0000oooo0?ooo`0g0?ooo`006P3oool00`000000oooo0?ooo`1;0?ooo`030000003oool0oooo03`0 oooo00<000000?ooo`3oool0AP3oool00`000000oooo0?ooo`0l0?ooo`030000003oool0oooo03H0 oooo000J0?ooo`030000003oool0oooo04/0oooo00<000000?ooo`3oool0?03oool00`000000oooo 0?ooo`160?ooo`030000003oool0oooo03`0oooo00<000000?ooo`3oool0=P3oool001X0oooo00<0 00000?ooo`3oool0B`3oool00`000000oooo0?ooo`0m0?ooo`030000003oool0oooo04@0oooo00<0 00000?ooo`3oool0?@3oool00`000000oooo0?ooo`0f0?ooo`006P3oool00`000000oooo0?ooo`1: 0?ooo`030000003oool0oooo03h0oooo00<000000?ooo`3oool0A03oool00`000000oooo0?ooo`0n 0?ooo`030000003oool0oooo03D0oooo0005000000@0oooo0P0000070?ooo`<000001@3oool00`00 0000oooo0?ooo`1:0?ooo`030000003oool0oooo03h0oooo00<000000?ooo`3oool0A03oool00`00 0000oooo0?ooo`0n0?ooo`030000003oool0oooo03D0oooo00020?ooo`030000003oool0oooo00@0 oooo0P0000080?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool0BP3oool00`000000 oooo0?ooo`0o0?ooo`030000003oool0oooo0480oooo00<000000?ooo`3oool0?`3oool00`000000 oooo0?ooo`0e0?ooo`000P3oool00`000000oooo0?ooo`0>0?ooo`030000003oool0oooo00@0oooo 00<000000?ooo`3oool0B@3oool00`000000oooo0?ooo`100?ooo`030000003oool0oooo0480oooo 00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`0e0?ooo`000P3oool00`000000oooo0?oo o`0:0?ooo`H000001@3oool3000004T0oooo00<000000?ooo`3oool0@03oool00`000000oooo0?oo o`120?ooo`030000003oool0oooo0400oooo00<000000?ooo`3oool0=03oool00080oooo00<00000 0?ooo`3oool02`3oool010000000oooo0?ooo`0000060?ooo`030000003oool0oooo04T0oooo00<0 00000?ooo`3oool0@03oool00`000000oooo0?ooo`110?ooo`030000003oool0oooo0440oooo00<0 00000?ooo`3oool0=03oool00080oooo00<000000?ooo`3oool02`3oool010000000oooo0?ooo`00 00060?ooo`030000003oool0oooo04P0oooo00<000000?ooo`3oool0@P3oool00`000000oooo0?oo o`100?ooo`030000003oool0oooo0440oooo00<000000?ooo`3oool0=03oool000<000003P3oool0 0`000000oooo000000060?ooo`030000003oool0oooo04P0oooo00<000000?ooo`3oool0@P3oool0 0`000000oooo0?ooo`100?ooo`030000003oool0oooo0480oooo00<000000?ooo`3oool0<`3oool0 0080oooo00<000000?ooo`3oool03@3oool2000000H0oooo00<000000?ooo`3oool0A`3oool00`00 0000oooo0?ooo`130?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0@`3oool00`00 0000oooo0?ooo`0c0?ooo`006P3oool00`000000oooo0?ooo`170?ooo`030000003oool0oooo04@0 oooo00<000000?ooo`3oool0?P3oool00`000000oooo0?ooo`130?ooo`030000003oool0oooo03<0 oooo000J0?ooo`030000003oool0oooo04L0oooo00<000000?ooo`3oool0A03oool00`000000oooo 0?ooo`0n0?ooo`030000003oool0oooo04<0oooo00<000000?ooo`3oool0<`3oool001X0oooo00<0 00000?ooo`3oool0AP3oool00`000000oooo0?ooo`150?ooo`030000003oool0oooo03d0oooo00<0 00000?ooo`3oool0A@3oool00`000000oooo0?ooo`0b0?ooo`006P3oool00`000000oooo0?ooo`16 0?ooo`030000003oool0oooo04D0oooo00<000000?ooo`3oool0?@3oool00`000000oooo0?ooo`15 0?ooo`030000003oool0oooo0380oooo000J0?ooo`030000003oool0oooo04H0oooo00<000000?oo o`3oool0AP3oool00`000000oooo0?ooo`0l0?ooo`030000003oool0oooo04D0oooo00<000000?oo o`3oool0`3oool00`000000oooo0?ooo`160?ooo`030000003oool0oooo0380oooo000J0?ooo`030000 003oool0oooo04D0oooo00<000000?ooo`3oool0A`3oool00`000000oooo0?ooo`0k0?ooo`030000 003oool0oooo04L0oooo00<000000?ooo`3oool0<@3oool001X0oooo00<000000?ooo`3oool0A@3o ool00`000000oooo0?ooo`180?ooo`030000003oool0oooo03X0oooo00<000000?ooo`3oool0A`3o ool00`000000oooo0?ooo`0a0?ooo`006P3oool00`000000oooo0?ooo`140?ooo`030000003oool0 oooo04T0oooo00<000000?ooo`3oool0>@3oool00`000000oooo0?ooo`180?ooo`030000003oool0 oooo0340oooo000J0?ooo`030000003oool0oooo04@0oooo00<000000?ooo`3oool0B@3oool00`00 0000oooo0?ooo`0i0?ooo`030000003oool0oooo04T0oooo00<000000?ooo`3oool0<03oool001X0 oooo00<000000?ooo`3oool0A03oool00`000000oooo0?ooo`190?ooo`030000003oool0oooo03T0 oooo00<000000?ooo`3oool0B@3oool00`000000oooo0?ooo`0`0?ooo`006P3oool00`000000oooo 0?ooo`130?ooo`030000003oool0oooo04/0oooo00<000000?ooo`3oool0=`3oool00`000000oooo 0?ooo`1:0?ooo`030000003oool0oooo0300oooo000J0?ooo`030000003oool0oooo04<0oooo00<0 00000?ooo`3oool0B`3oool00`000000oooo0?ooo`0g0?ooo`030000003oool0oooo04/0oooo00<0 00000?ooo`3oool0;`3oool001X0oooo00<000000?ooo`3oool0@`3oool00`000000oooo0?ooo`1; 0?ooo`030000003oool0oooo03L0oooo00<000000?ooo`3oool0B`3oool00`000000oooo0?ooo`0_ 0?ooo`006P3oool00`000000oooo0?ooo`120?ooo`030000003oool0oooo04d0oooo00<000000?oo o`3oool0=@3oool00`000000oooo0?ooo`1=0?ooo`030000003oool0oooo02h0oooo000J0?ooo`03 0000003oool0oooo0480oooo00<000000?ooo`3oool0C@3oool00`000000oooo0?ooo`0e0?ooo`03 0000003oool0oooo04d0oooo00<000000?ooo`3oool0;P3oool001X0oooo0`0000120?ooo`030000 003oool0oooo04d0oooo00<000000?ooo`3oool0=@3oool00`000000oooo0?ooo`1=0?ooo`030000 003oool0oooo02h0oooo000J0?ooo`030000003oool0oooo0440oooo00<000000?ooo`3oool0C`3o ool00`000000oooo0?ooo`0c0?ooo`030000003oool0oooo04l0oooo00<000000?ooo`3oool0;@3o ool001X0oooo00<000000?ooo`3oool0@@3oool00`000000oooo0?ooo`1?0?ooo`030000003oool0 oooo03<0oooo00<000000?ooo`3oool0C`3oool00`000000oooo0?ooo`0]0?ooo`006P3oool00`00 0000oooo0?ooo`110?ooo`030000003oool0oooo04l0oooo00<000000?ooo`3oool0<`3oool00`00 0000oooo0?ooo`1?0?ooo`030000003oool0oooo02d0oooo000J0?ooo`030000003oool0oooo0400 oooo00<000000?ooo`3oool0D@3oool00`000000oooo0?ooo`0a0?ooo`030000003oool0oooo0540 oooo00<000000?ooo`3oool0;03oool001X0oooo00<000000?ooo`3oool0@03oool00`000000oooo 0?ooo`1A0?ooo`030000003oool0oooo0340oooo00<000000?ooo`3oool0D@3oool00`000000oooo 0?ooo`0/0?ooo`006P3oool00`000000oooo0?ooo`0o0?ooo`030000003oool0oooo0580oooo00<0 00000?ooo`3oool0<@3oool00`000000oooo0?ooo`1B0?ooo`030000003oool0oooo02/0oooo000J 0?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0D`3oool00`000000oooo0?ooo`0_ 0?ooo`030000003oool0oooo05<0oooo00<000000?ooo`3oool0:`3oool001X0oooo00<000000?oo o`3oool0?`3oool00`000000oooo0?ooo`1C0?ooo`030000003oool0oooo02l0oooo00<000000?oo o`3oool0D`3oool00`000000oooo0?ooo`0[0?ooo`006P3oool00`000000oooo0?ooo`0n0?ooo`03 0000003oool0oooo05D0oooo00<000000?ooo`3oool0;P3oool00`000000oooo0?ooo`1D0?ooo`03 0000003oool0oooo02X0oooo000J0?ooo`<00000?P3oool00`000000oooo0?ooo`1E0?ooo`030000 003oool0oooo02d0oooo00<000000?ooo`3oool0E@3oool00`000000oooo0?ooo`0Z0?ooo`006P3o ool00`000000oooo0?ooo`0n0?ooo`030000003oool0oooo05D0oooo00<000000?ooo`3oool0;@3o ool00`000000oooo0?ooo`1E0?ooo`030000003oool0oooo02X0oooo000J0?ooo`030000003oool0 oooo03d0oooo00<000000?ooo`3oool0E`3oool00`000000oooo0?ooo`0[0?ooo`030000003oool0 oooo05L0oooo00<000000?ooo`3oool0:@3oool001X0oooo00<000000?ooo`3oool0?@3oool00`00 0000oooo0?ooo`1G0?ooo`030000003oool0oooo02/0oooo00<000000?ooo`3oool0E`3oool00`00 0000oooo0?ooo`0Y0?ooo`006P3oool00`000000oooo0?ooo`0l0?ooo`030000003oool0oooo05P0 oooo00<000000?ooo`3oool0:P3oool00`000000oooo0?ooo`1H0?ooo`030000003oool0oooo02T0 oooo000J0?ooo`030000003oool0oooo03`0oooo00<000000?ooo`3oool0F@3oool00`000000oooo 0?ooo`0Y0?ooo`030000003oool0oooo05P0oooo00<000000?ooo`3oool0:@3oool001X0oooo00<0 00000?ooo`3oool0?03oool00`000000oooo0?ooo`1I0?ooo`030000003oool0oooo02P0oooo00<0 00000?ooo`3oool0FP3oool00`000000oooo0?ooo`0X0?ooo`001@0000040?ooo`8000001P3oool3 000000H0oooo00<000000?ooo`3oool0>`3oool00`000000oooo0?ooo`1J0?ooo`030000003oool0 oooo02P0oooo00<000000?ooo`3oool0FP3oool00`000000oooo0?ooo`0X0?ooo`000P3oool00`00 0000oooo0?ooo`040?ooo`8000001@3oool01@000000oooo0?ooo`3oool0000000D0oooo00<00000 0?ooo`3oool0>`3oool00`000000oooo0?ooo`1K0?ooo`030000003oool0oooo02H0oooo00<00000 0?ooo`3oool0F`3oool00`000000oooo0?ooo`0X0?ooo`000P3oool00`000000oooo0?ooo`0;0?oo o`050000003oool0oooo0?ooo`0000001@3oool00`000000oooo0?ooo`0k0?ooo`030000003oool0 oooo05/0oooo00<000000?ooo`3oool09P3oool00`000000oooo0?ooo`1L0?ooo`030000003oool0 oooo02L0oooo00020?ooo`030000003oool0oooo00/0oooo00D000000?ooo`3oool0oooo00000005 0?ooo`<00000>P3oool00`000000oooo0?ooo`1M0?ooo`030000003oool0oooo02@0oooo00<00000 0?ooo`3oool0G@3oool00`000000oooo0?ooo`0W0?ooo`000P3oool00`000000oooo0?ooo`0;0?oo o`@000001P3oool00`000000oooo0?ooo`0j0?ooo`030000003oool0oooo05d0oooo00<000000?oo o`3oool0903oool00`000000oooo0?ooo`1M0?ooo`030000003oool0oooo02L0oooo00020?ooo`03 0000003oool0oooo00/0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`090?ooo`@0 0000;03oool00`000000oooo0?ooo`1O0?ooo`030000003oool0oooo0280oooo00<000000?ooo`3o ool0G`3oool00`000000oooo0?ooo`0V0?ooo`000`00000>0?ooo`030000003oool0oooo00H0oooo 00<000000?ooo`3oool0203oool2000000<0oooo00<000000?ooo`3oool0:@3oool00`000000oooo 0?ooo`1O0?ooo`030000003oool0oooo0280oooo00<000000?ooo`3oool0G`3oool00`000000oooo 0?ooo`0V0?ooo`000P3oool00`000000oooo0?ooo`0=0?ooo`<000001@3oool00`000000oooo0?oo o`080?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool09`3oool00`000000oooo0?oo o`1P0?ooo`030000003oool0oooo0280oooo00<000000?ooo`3oool0H03oool00`000000oooo0?oo o`0U0?ooo`006P3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo00D0oooo00<00000 0?ooo`3oool09P3oool00`000000oooo0?ooo`1Q0?ooo`030000003oool0oooo0200oooo00<00000 0?ooo`3oool0H@3oool00`000000oooo0?ooo`0U0?ooo`006P3oool00`000000oooo0?ooo`060?oo o`030000003oool0oooo00L0oooo00<000000?ooo`3oool0903oool00`000000oooo0?ooo`1R0?oo o`030000003oool0oooo0200oooo00<000000?ooo`3oool0HP3oool00`000000oooo0?ooo`0T0?oo o`006P3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00P0oooo00<000000?ooo`3o ool08`3oool00`000000oooo0?ooo`1S0?ooo`030000003oool0oooo01h0oooo00<000000?ooo`3o ool0H`3oool00`000000oooo0?ooo`0T0?ooo`006P3oool00`000000oooo0?ooo`050?ooo`030000 003oool0oooo00X0oooo00<000000?ooo`3oool08@3oool00`000000oooo0?ooo`1T0?ooo`030000 003oool0oooo01h0oooo00<000000?ooo`3oool0I03oool00`000000oooo0?ooo`0S0?ooo`006P3o ool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00/0oooo00<000000?ooo`3oool0803o ool00`000000oooo0?ooo`1U0?ooo`030000003oool0oooo01`0oooo00<000000?ooo`3oool0I@3o ool00`000000oooo0?ooo`0S0?ooo`006P3oool00`000000oooo0?ooo`050?ooo`030000003oool0 oooo00/0oooo00<000000?ooo`3oool07`3oool00`000000oooo0?ooo`1V0?ooo`030000003oool0 oooo01`0oooo00<000000?ooo`3oool0IP3oool00`000000oooo0?ooo`0R0?ooo`006P3oool30000 00@0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0N0?ooo`030000003oool0oooo 06H0oooo00<000000?ooo`3oool06`3oool00`000000oooo0?ooo`1W0?ooo`030000003oool0oooo 0280oooo000J0?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool03P3oool00`000000 oooo0?ooo`0L0?ooo`030000003oool0oooo06P0oooo00<000000?ooo`3oool06P3oool00`000000 oooo0?ooo`1X0?ooo`030000003oool0oooo0240oooo000J0?ooo`030000003oool0oooo00@0oooo 00<000000?ooo`3oool03`3oool00`000000oooo0?ooo`0K0?ooo`030000003oool0oooo06P0oooo 00<000000?ooo`3oool06@3oool00`000000oooo0?ooo`1Y0?ooo`030000003oool0oooo0240oooo 000J0?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool0403oool00`000000oooo0?oo o`0I0?ooo`030000003oool0oooo06X0oooo00<000000?ooo`3oool0603oool00`000000oooo0?oo o`1Z0?ooo`030000003oool0oooo0200oooo000J0?ooo`030000003oool0oooo00@0oooo00<00000 0?ooo`3oool0403oool00`000000oooo0?ooo`0H0?ooo`030000003oool0oooo06/0oooo00<00000 0?ooo`3oool05`3oool00`000000oooo0?ooo`1/0?ooo`030000003oool0oooo01l0oooo000J0?oo o`030000003oool0oooo00@0oooo00<000000?ooo`3oool04@3oool00`000000oooo0?ooo`0G0?oo o`030000003oool0oooo06`0oooo00<000000?ooo`3oool05P3oool00`000000oooo0?ooo`1/0?oo o`030000003oool0oooo01D0oooo00<000000?ooo`3oool01`3oool001X0oooo00<000000?ooo`3o ool0103oool00`000000oooo0?ooo`0B0?ooo`030000003oool0oooo01D0oooo00<000000?ooo`3o ool0KP3oool00`000000oooo0?ooo`0D0?ooo`030000003oool0oooo06h0oooo00<000000?ooo`3o ool04`3oool00`000000oooo0?ooo`080?ooo`006P3oool00`000000oooo0?ooo`030?ooo`030000 003oool0oooo01@0oooo00<000000?ooo`3oool04`3oool00`000000oooo0?ooo`1`0?ooo`030000 003oool0oooo0180oooo00<000000?ooo`3oool0K`3oool00`000000oooo0?ooo`0C0?ooo`030000 003oool0oooo00P0oooo000J0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0503o ool00`000000oooo0?ooo`0B0?ooo`030000003oool0oooo0780oooo00<000000?ooo`3oool04@3o ool00`000000oooo0?ooo`1`0?ooo`030000003oool0oooo0140oooo00<000000?ooo`3oool02@3o ool001X0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`0E0?ooo`030000003oool0 oooo0140oooo00<000000?ooo`3oool0L`3oool00`000000oooo0?ooo`0?0?ooo`030000003oool0 oooo0780oooo00<000000?ooo`3oool03`3oool00`000000oooo0?ooo`0:0?ooo`006P3oool30000 00<0oooo00<000000?ooo`3oool05P3oool00`000000oooo0?ooo`0?0?ooo`030000003oool0oooo 07@0oooo00<000000?ooo`3oool03P3oool00`000000oooo0?ooo`1d0?ooo`030000003oool0oooo 00d0oooo00<000000?ooo`3oool02`3oool001X0oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`0G0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0MP3oool00`000000 oooo0?ooo`0;0?ooo`800000N03oool00`000000oooo0?ooo`0;0?ooo`030000003oool0oooo00`0 oooo000J0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool06@3oool00`000000oooo 0?ooo`0;0?ooo`030000003oool0oooo07P0oooo00<000000?ooo`3oool02@3oool00`000000oooo 0?ooo`1i0?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool03@3oool001X0oooo00<0 00000?ooo`3oool00P3oool00`000000oooo0?ooo`0J0?ooo`8000002@3oool2000007`0oooo0P00 00080?ooo`030000003oool0oooo07/0oooo0P0000070?ooo`800000403oool001X0oooo00<00000 0?ooo`3oool00P3oool00`000000oooo0?ooo`0L0?ooo`8000001@3oool200000800oooo20000020 0?ooo`P000004@3oool001X0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`0N0?oo o`D00000o`3ooolT0?ooo`006P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0?l0 ooooA`3oool001X0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`3o0?ooodL0oooo 000J0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0o`3ooom70?ooo`006P3oool0 1@000000oooo0?ooo`3oool000000?l0ooooBP3oool001X0oooo00D000000?ooo`3oool0oooo0000 003o0?ooodX0oooo000J0?ooo`<0000000<0oooo0000003oool0o`3ooom90?ooo`006P3oool01@00 0000oooo0?ooo`3oool000000?l0ooooBP3oool001X0oooo00D000000?ooo`3oool0oooo0000003o 0?ooodX0oooo000J0?ooo`050000003oool0oooo0?ooo`000000o`3ooom:0?ooo`006P3oool01@00 0000oooo0?ooo`3oool000000?l0ooooBP3oool001X0oooo00@000000?ooo`3oool00000o`3ooom; 0?ooo`006P3oool010000000oooo0?ooo`00003o0?oood/0oooo0005000000@0oooo0P0000050?oo o`@000001P3oool010000000oooo0?ooo`00003o0?oood/0oooo00020?ooo`030000003oool0oooo 00@0oooo0P0000040?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00`3oool01000 0000oooo0?ooo`00003o0?oood/0oooo00020?ooo`030000003oool0oooo00X0oooo00<000000?oo o`3oool00P3oool00`000000oooo0?ooo`030?ooo`040000003oool0oooo00000?l0ooooB`3oool0 0080oooo00<000000?ooo`3oool02P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo 00<0oooo1000003o0?oood/0oooo00020?ooo`030000003oool0oooo00/0oooo100000060?ooo`04 0000003oool0oooo00000?l0ooooB`3oool00080oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`020?ooo`030000003oool0oooo00<0oooo00@000000?ooo`3oool00000o`3ooom;0?oo o`000`00000<0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00`3oool010000000 oooo0?ooo`00003o0?oood/0oooo00020?ooo`030000003oool0oooo00/0oooo100000060?ooo`04 0000003oool0oooo00000?l0ooooB`3oool001X0oooo00@000000?ooo`3oool00000o`3ooom;0?oo o`006P3oool010000000oooo0?ooo`00003o0?oood/0oooo000J0?ooo`030000003oool000000?l0 ooooC03oool001X0oooo00<000000?ooo`000000o`3ooom<0?ooo`006P3oool00`000000oooo0000 003o0?oood`0oooo000J0?ooo`030000003oool000000?l0ooooC03oool001X0oooo0`00003o0?oo od`0oooo000J0?ooo`030000003oool000000?l0ooooC03oool001X0oooo00<000000?ooo`000000 o`3ooom<0?ooo`006P3oool00`000000oooo0000003o0?oood`0oooo000J0?ooo`030000003oool0 00000?l0ooooC03oool001X0oooo00<000000?ooo`000000o`3ooom<0?ooo`006P3oool00`000000 oooo0000003o0?oood`0oooo000J0?ooo`030000003oool000000?l0ooooC03oool001X0oooo00<0 00000?ooo`000000o`3ooom<0?ooo`006P3oool00`000000oooo0000003o0?oood`0oooo000J0?oo o`<00000o`3ooom<0?ooo`006P3oool00`000000oooo0000003o0?oood`0oooo000J0?ooo`800000 o`3ooom=0?ooo`006P3oool200000?l0ooooC@3oool001X0oooo0P00003o0?ooodd0oooo000J0?oo o`800000o`3ooom=0?ooo`006P3oool2000002H0oooo1@00000Z0?ooo`<000009`3oool3000002L0 oooo1000000S0?ooo`D000000`3oool400000200oooo1@0000020?ooo`D000007`3oool5000000D0 oooo0`00000H0?ooo`006P3oool2000002H0oooo00D000000?ooo`3oool0oooo0000000[0?ooo`03 0000003oool0oooo02D0oooo00D000000?ooo`3oool0oooo0000000U0?ooo`030000003oool0oooo 0080oooo00<000000?ooo`3oool08P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo 0080oooo00<000000?ooo`3oool07`3oool00`000000oooo0?ooo`020?ooo`050000003oool0oooo 0?ooo`0000008@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo01L0oooo000J0?oo o`8000009`3oool00`000000oooo0?ooo`0/0?ooo`030000003oool0oooo02D0oooo00D000000?oo o`3oool0oooo0000000U0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool08P3oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool07`3oool0 0`000000oooo0?ooo`030?ooo`030000003oool0oooo0280oooo00<000000?ooo`3oool01P3oool0 0`000000oooo0?ooo`0G0?ooo`006P3oool2000002P0oooo00<000000?ooo`3oool09`3oool60000 02H0oooo00D000000?ooo`3oool0oooo0000000U0?ooo`030000003oool0oooo0080oooo00<00000 0?ooo`3oool08P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo00<00000 0?ooo`3oool07`3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo0240oooo00<00000 0?ooo`3oool00P3oool6000001P0oooo000J0?ooo`800000:@3oool00`000000oooo0?ooo`0W0?oo o`040000003oool0oooo000002L0oooo1000000W0?ooo`@000009@3oool00`000000oooo0?ooo`02 0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool07`3oool00`000000oooo0?ooo`05 0?ooo`030000003oool0oooo0200oooo00<000000?ooo`3oool00`3oool010000000oooo0?ooo`00 000I0?ooo`006P3oool3000002T0oooo00<000000?ooo`3oool09P3oool010000000oooo0?ooo`00 000W0?ooo`030000003oool0oooo02L0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?oo o`0R0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3oool00`000000oooo0?oo o`0O0?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool07`3oool00`000000oooo0?oo o`030?ooo`040000003oool0oooo000001T0oooo000J0?ooo`8000009P3oool01@000000oooo0?oo o`3oool0000002T0oooo00<000000?ooo`000000:03oool00`000000oooo0?ooo`0V0?ooo`030000 003oool0oooo0080oooo00<000000?ooo`3oool0803oool3000000@0oooo00<000000?ooo`3oool0 0P3oool00`000000oooo0?ooo`0M0?ooo`<00000103oool01@000000oooo0?ooo`3oool0000001l0 oooo0`0000060?ooo`030000003oool0000001T0oooo000J0?ooo`8000009`3oool3000002/0oooo 0P00000Y0?ooo`<000009P3oool4000002D0oooo00<000000?ooo`3oool00`3oool400000280oooo 00<000000?ooo`3oool00`3oool300000280oooo00<000000?ooo`3oool01@3oool2000001T0oooo 000J0?ooo`800000o`3ooom=0?ooo`006P3oool00`000000oooo0?ooo`3o0?oood`0oooo000J0?oo o`030000003oool0oooo0?l0ooooC03oool001X0oooo00<000000?ooo`3oool0o`3ooom<0?ooo`00 6P3oool00`000000oooo0?ooo`3o0?oood`0oooo000J0?ooo`030000003oool0oooo0?l0ooooC03o ool001X0oooo00<000000?ooo`3oool0o`3ooom<0?ooo`004P3ooooo000005L00000000J0?ooo`03 0000003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`080?ooo`03 0000003oool0oooo00L0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`080?ooo`03 0000003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`070?ooo`03 0000003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`080?ooo`03 0000003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`070?ooo`03 0000003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`080?ooo`03 0000003oool0oooo00P0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`080?ooo`03 0000003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`080?ooo`03 0000003oool0oooo00L0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`080?ooo`03 0000003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`070?ooo`03 0000003oool0oooo00L0oooo000J0?ooo`030000003oool0oooo02P0oooo00<000000?ooo`3oool0 :@3oool00`000000oooo0?ooo`0X0?ooo`030000003oool0oooo02P0oooo00<000000?ooo`3oool0 :03oool00`000000oooo0?ooo`0Y0?ooo`030000003oool0oooo02P0oooo00<000000?ooo`3oool0 703oool001X0oooo00<000000?ooo`3oool0o`3ooom<0?ooo`006P3oool00`000000oooo0?ooo`3o 0?oood`0oooo000J0?ooo`030000003oool0oooo0?l0ooooC03oool00?l0ooooJ@3oool00?l0oooo J@3oool00?l0ooooJ@3oool00?l0ooooJ@3oool00?l0ooooJ@3oool00001\ \>"], ImageRangeCache->{{{0, 359}, {221.375, 0}} -> {-1.23816, 0.990274, \ 0.0578455, 0.00598597}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ \[CapitalUDoubleDot]laltoodud protseduuris Evaluate[u[t]/.funkt[[1]][[1]]] \ ongi k\[ADoubleDot]sklus, mille kohaselt programm v\[OTilde]tab funktsiooni \ u[t] v\[ADoubleDot]\[ADoubleDot]rtuse nii nagu diferensiaalv\[OTilde]rrandi \ lahendamisel leitud.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Evaluate[u[3] /. \(funkt[\([1]\)]\)[\([1]\)]\ ]\)], "Input"], Cell[BoxData[ \(1.5524819569378314`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(2*Sin[4]*Evaluate[u[4] /. \(funkt[\([1]\)]\)[\([1]\)]\ ]\)], "Input"], Cell[BoxData[ \(\(-1.883023830775053`\)\)], "Output"] }, Open ]], Cell["\<\ V\[OTilde]ime lahendada ka mitmest diferentsiaalv\[OTilde]rrandist koosneva s\ \[UDoubleDot]steemi.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(sol = NDSolve[{\(x'\)[t] \[Equal] 2 \((x[t])\)\^2 - 0.1 \((y[t])\)\^2, \[IndentingNewLine]\(y'\)[ t] \[Equal] \(-x[t]\) + y[t], x[0] \[Equal] \(-2\), y[0] \[Equal] 1}, {x, y}, {t, 0, 10}]\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 10.`}}, "<>"]\), False, Editable->False]}], ",", RowBox[{"y", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 10.`}}, "<>"]\), False, Editable->False]}]}], "}"}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(sol[\([1]\)]\)[\([1]\)]\)], "Input"], Cell[BoxData[ RowBox[{"x", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 10.`}}, "<>"]\), False, Editable->False]}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[ Evaluate[x[t] /. \(sol[\([1]\)]\)[\([1]\)]\ ], {t, 0, 10}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0.603319 0.000110423 [ [.21429 .59082 -3 -9 ] [.21429 .59082 3 0 ] [.40476 .59082 -3 -9 ] [.40476 .59082 3 0 ] [.59524 .59082 -3 -9 ] [.59524 .59082 3 0 ] [.78571 .59082 -3 -9 ] [.78571 .59082 3 0 ] [.97619 .59082 -6 -9 ] [.97619 .59082 6 0 ] [.01131 .05121 -30 -4.5 ] [.01131 .05121 0 4.5 ] [.01131 .16163 -30 -4.5 ] [.01131 .16163 0 4.5 ] [.01131 .27205 -30 -4.5 ] [.01131 .27205 0 4.5 ] [.01131 .38247 -30 -4.5 ] [.01131 .38247 0 4.5 ] [.01131 .4929 -30 -4.5 ] [.01131 .4929 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .60332 m .21429 .60957 L s [(2)] .21429 .59082 0 1 Mshowa .40476 .60332 m .40476 .60957 L s [(4)] .40476 .59082 0 1 Mshowa .59524 .60332 m .59524 .60957 L s [(6)] .59524 .59082 0 1 Mshowa .78571 .60332 m .78571 .60957 L s [(8)] .78571 .59082 0 1 Mshowa .97619 .60332 m .97619 .60957 L s [(10)] .97619 .59082 0 1 Mshowa .125 Mabswid .07143 .60332 m .07143 .60707 L s .11905 .60332 m .11905 .60707 L s .16667 .60332 m .16667 .60707 L s .2619 .60332 m .2619 .60707 L s .30952 .60332 m .30952 .60707 L s .35714 .60332 m .35714 .60707 L s .45238 .60332 m .45238 .60707 L s .5 .60332 m .5 .60707 L s .54762 .60332 m .54762 .60707 L s .64286 .60332 m .64286 .60707 L s .69048 .60332 m .69048 .60707 L s .7381 .60332 m .7381 .60707 L s .83333 .60332 m .83333 .60707 L s .88095 .60332 m .88095 .60707 L s .92857 .60332 m .92857 .60707 L s .25 Mabswid 0 .60332 m 1 .60332 L s .02381 .05121 m .03006 .05121 L s [(-5000)] .01131 .05121 1 0 Mshowa .02381 .16163 m .03006 .16163 L s [(-4000)] .01131 .16163 1 0 Mshowa .02381 .27205 m .03006 .27205 L s [(-3000)] .01131 .27205 1 0 Mshowa .02381 .38247 m .03006 .38247 L s [(-2000)] .01131 .38247 1 0 Mshowa .02381 .4929 m .03006 .4929 L s [(-1000)] .01131 .4929 1 0 Mshowa .125 Mabswid .02381 .07329 m .02756 .07329 L s .02381 .09537 m .02756 .09537 L s .02381 .11746 m .02756 .11746 L s .02381 .13954 m .02756 .13954 L s .02381 .18371 m .02756 .18371 L s .02381 .2058 m .02756 .2058 L s .02381 .22788 m .02756 .22788 L s .02381 .24997 m .02756 .24997 L s .02381 .29414 m .02756 .29414 L s .02381 .31622 m .02756 .31622 L s .02381 .3383 m .02756 .3383 L s .02381 .36039 m .02756 .36039 L s .02381 .40456 m .02756 .40456 L s .02381 .42664 m .02756 .42664 L s .02381 .44873 m .02756 .44873 L s .02381 .47081 m .02756 .47081 L s .02381 .51498 m .02756 .51498 L s .02381 .53707 m .02756 .53707 L s .02381 .55915 m .02756 .55915 L s .02381 .58123 m .02756 .58123 L s .02381 .02912 m .02756 .02912 L s .02381 .00704 m .02756 .00704 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .6031 m .02846 .60313 L .03279 .60316 L .03754 .60318 L .04262 .60319 L .04795 .60321 L .053 .60322 L .05749 .60322 L .06244 .60323 L .06754 .60323 L .07295 .60324 L .07536 .60324 L .07796 .60324 L .08039 .60324 L .08265 .60324 L .08412 .60324 L .08546 .60324 L .08694 .60324 L .08775 .60324 L .08852 .60324 L .0892 .60324 L .08992 .60324 L .0912 .60324 L .09192 .60324 L .09258 .60324 L .09332 .60324 L .0941 .60324 L .09545 .60324 L .09692 .60324 L .09958 .60324 L .10218 .60324 L .10458 .60324 L .10921 .60324 L .11421 .60323 L .12324 .60323 L .13399 .60321 L .14385 .6032 L .16277 .60316 L .18347 .60311 L .20308 .60304 L .22403 .60295 L .24538 .60282 L .26553 .60266 L .28554 .60246 L .304 .60223 L .32276 .60192 L .3434 .60149 L .36285 .60096 L .38374 .60023 L .40491 .59925 L Mistroke .42501 .59805 L .44486 .59651 L .46326 .59468 L .48382 .59206 L .50244 .58901 L .52173 .58498 L .54256 .57935 L .56254 .57232 L .58362 .56267 L .60329 .55098 L .62164 .53706 L .64203 .5172 L .6606 .49399 L .67972 .46353 L .7005 .42076 L .72031 .36783 L .74133 .2948 L .76084 .2069 L .77914 .10187 L Mfstroke .77914 .10187 m .79298 0 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgl0oooo00<000000?ooo`3oool0BP3oool002T0oooo00<000000?ooo`3oool0 k`3oool00`000000oooo0?ooo`1:0?ooo`00:@3oool200000>l0oooo00<000000?ooo`3oool0B`3o ool002T0oooo00<000000?ooo`3oool0kP3oool00`000000oooo0?ooo`1;0?ooo`00:@3oool00`00 0000oooo0?ooo`3^0?ooo`030000003oool0oooo04/0oooo000Y0?ooo`030000003oool0oooo0>h0 oooo00<000000?ooo`3oool0B`3oool002T0oooo00<000000?ooo`3oool0kP3oool00`000000oooo 0?ooo`1;0?ooo`00:@3oool00`000000oooo0?ooo`3^0?ooo`030000003oool0oooo04/0oooo000Y 0?ooo`030000003oool0oooo0>d0oooo00<000000?ooo`3oool0C03oool002T0oooo0P00003^0?oo o`030000003oool0oooo04`0oooo000Y0?ooo`030000003oool0oooo0>d0oooo00<000000?ooo`3o ool0C03oool002T0oooo00<000000?ooo`3oool0k@3oool00`000000oooo0?ooo`1<0?ooo`00:@3o ool00`000000oooo0?ooo`3/0?ooo`030000003oool0oooo04d0oooo000Y0?ooo`030000003oool0 oooo0>`0oooo00<000000?ooo`3oool0C@3oool002T0oooo00<000000?ooo`3oool0k03oool00`00 0000oooo0?ooo`1=0?ooo`00:@3oool00`000000oooo0?ooo`3/0?ooo`030000003oool0oooo04d0 oooo000Y0?ooo`800000k03oool00`000000oooo0?ooo`1>0?ooo`00:@3oool00`000000oooo0?oo o`3[0?ooo`030000003oool0oooo04h0oooo000Y0?ooo`030000003oool0oooo0>/0oooo00<00000 0?ooo`3oool0CP3oool002T0oooo00<000000?ooo`3oool0j`3oool00`000000oooo0?ooo`1>0?oo o`00:@3oool00`000000oooo0?ooo`3Z0?ooo`030000003oool0oooo04l0oooo000Y0?ooo`030000 003oool0oooo0>X0oooo00<000000?ooo`3oool0C`3oool002T0oooo00<000000?ooo`3oool0jP3o ool00`000000oooo0?ooo`1?0?ooo`00:@3oool00`000000oooo0?ooo`3Z0?ooo`030000003oool0 oooo04l0oooo000Y0?ooo`800000jP3oool00`000000oooo0?ooo`1@0?ooo`00:@3oool00`000000 oooo0?ooo`3Y0?ooo`030000003oool0oooo0500oooo000Y0?ooo`030000003oool0oooo0>T0oooo 00<000000?ooo`3oool0D03oool002T0oooo00<000000?ooo`3oool0j@3oool00`000000oooo0?oo o`1@0?ooo`001`3oool3000000D0oooo100000040?ooo`@00000103oool4000000H0oooo00<00000 0?ooo`3oool0j03oool00`000000oooo0?ooo`1A0?ooo`001P3oool01@000000oooo0?ooo`3oool0 000000<0oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`0000040?ooo`040000003o ool0oooo000000@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`3X0?ooo`030000 003oool0oooo0540oooo000:0?ooo`050000003oool0oooo0?ooo`000000103oool010000000oooo 0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool00`3oool00`00 0000oooo0?ooo`3X0?ooo`030000003oool0oooo0540oooo0004000000H0oooo00D000000?ooo`3o ool0oooo000000040?ooo`040000003oool0oooo000000@0oooo00@000000?ooo`3oool00000103o ool00`000000oooo0?ooo`030?ooo`<00000j03oool00`000000oooo0?ooo`1A0?ooo`00203oool2 000000@0oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`0000040?ooo`040000003o ool0oooo000000@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`3W0?ooo`030000 003oool0oooo0580oooo000:0?ooo`050000003oool0oooo0?ooo`000000103oool010000000oooo 0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool00`3oool00`00 0000oooo0?ooo`3W0?ooo`030000003oool0oooo0580oooo00060?ooo`050000003oool0oooo0?oo o`0000000`3oool00`000000oooo0?ooo`020?ooo`040000003oool0oooo000000@0oooo00@00000 0?ooo`3oool00000103oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0>L0oooo00<0 00000?ooo`3oool0DP3oool000L0oooo0`0000050?ooo`@00000103oool4000000@0oooo10000006 0?ooo`030000003oool0oooo0>L0oooo00<000000?ooo`3oool0DP3oool002T0oooo00<000000?oo o`3oool0iP3oool00`000000oooo0?ooo`1C0?ooo`00:@3oool00`000000oooo0?ooo`3V0?ooo`03 0000003oool0oooo05<0oooo000Y0?ooo`800000i`3oool00`000000oooo0?ooo`1C0?ooo`00:@3o ool00`000000oooo0?ooo`3V0?ooo`030000003oool0oooo05<0oooo000Y0?ooo`030000003oool0 oooo0>D0oooo00<000000?ooo`3oool0E03oool002T0oooo00<000000?ooo`3oool0i@3oool00`00 0000oooo0?ooo`1D0?ooo`00:@3oool00`000000oooo0?ooo`3U0?ooo`030000003oool0oooo05@0 oooo000Y0?ooo`030000003oool0oooo0>D0oooo00<000000?ooo`3oool0E03oool002T0oooo00<0 00000?ooo`3oool0i03oool00`000000oooo0?ooo`1E0?ooo`00:@3oool200000>D0oooo00<00000 0?ooo`3oool0E@3oool002T0oooo00<000000?ooo`3oool0i03oool00`000000oooo0?ooo`1E0?oo o`00:@3oool00`000000oooo0?ooo`3T0?ooo`030000003oool0oooo05D0oooo000Y0?ooo`030000 003oool0oooo0><0oooo00<000000?ooo`3oool0EP3oool002T0oooo00<000000?ooo`3oool0h`3o ool00`000000oooo0?ooo`1F0?ooo`00:@3oool00`000000oooo0?ooo`3S0?ooo`030000003oool0 oooo05H0oooo000Y0?ooo`030000003oool0oooo0><0oooo00<000000?ooo`3oool0EP3oool002T0 oooo0P00003S0?ooo`030000003oool0oooo05L0oooo000Y0?ooo`030000003oool0oooo0>80oooo 00<000000?ooo`3oool0E`3oool002T0oooo00<000000?ooo`3oool0hP3oool00`000000oooo0?oo o`1G0?ooo`00:@3oool00`000000oooo0?ooo`3R0?ooo`030000003oool0oooo05L0oooo000Y0?oo o`030000003oool0oooo0>40oooo00<000000?ooo`3oool0F03oool002T0oooo00<000000?ooo`3o ool0h@3oool00`000000oooo0?ooo`1H0?ooo`00:@3oool00`000000oooo0?ooo`3Q0?ooo`030000 003oool0oooo05P0oooo000Y0?ooo`030000003oool0oooo0>40oooo00<000000?ooo`3oool0F03o ool002T0oooo0P00003Q0?ooo`030000003oool0oooo05T0oooo000Y0?ooo`030000003oool0oooo 0>00oooo00<000000?ooo`3oool0F@3oool002T0oooo00<000000?ooo`3oool0h03oool00`000000 oooo0?ooo`1I0?ooo`00:@3oool00`000000oooo0?ooo`3P0?ooo`030000003oool0oooo05T0oooo 00060?ooo`D00000103oool4000000@0oooo100000040?ooo`@000001P3oool00`000000oooo0?oo o`3O0?ooo`030000003oool0oooo05X0oooo00060?ooo`050000003oool0oooo0?ooo`0000000`3o ool00`000000oooo0?ooo`020?ooo`040000003oool0oooo000000@0oooo00@000000?ooo`3oool0 0000103oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0=l0oooo00<000000?ooo`3o ool0FP3oool000L0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`020?ooo`040000 003oool0oooo000000@0oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`030?oo o`030000003oool0oooo0=h0oooo00<000000?ooo`3oool0F`3oool000@00000103oool00`000000 oooo0?ooo`030?ooo`030000003oool0oooo0080oooo00@000000?ooo`3oool00000103oool01000 0000oooo0?ooo`0000040?ooo`030000003oool0oooo00<0oooo0`00003N0?ooo`030000003oool0 oooo05/0oooo00090?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3oool01000 0000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool00`3o ool00`000000oooo0?ooo`3N0?ooo`030000003oool0oooo05/0oooo000:0?ooo`050000003oool0 oooo0?ooo`000000103oool010000000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0 oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`3M0?ooo`030000003oool0oooo05`0 oooo00060?ooo`050000003oool0oooo0?ooo`0000000`3oool00`000000oooo0?ooo`020?ooo`04 0000003oool0oooo000000@0oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`03 0?ooo`030000003oool0oooo0=d0oooo00<000000?ooo`3oool0G03oool000L0oooo0`0000050?oo o`@00000103oool4000000@0oooo100000060?ooo`030000003oool0oooo0=`0oooo00<000000?oo o`3oool0G@3oool002T0oooo00<000000?ooo`3oool0g03oool00`000000oooo0?ooo`1M0?ooo`00 :@3oool00`000000oooo0?ooo`3K0?ooo`030000003oool0oooo05h0oooo000Y0?ooo`800000g03o ool00`000000oooo0?ooo`1N0?ooo`00:@3oool00`000000oooo0?ooo`3K0?ooo`030000003oool0 oooo05h0oooo000Y0?ooo`030000003oool0oooo0=X0oooo00<000000?ooo`3oool0G`3oool002T0 oooo00<000000?ooo`3oool0fP3oool00`000000oooo0?ooo`1O0?ooo`00:@3oool00`000000oooo 0?ooo`3I0?ooo`030000003oool0oooo0600oooo000Y0?ooo`030000003oool0oooo0=T0oooo00<0 00000?ooo`3oool0H03oool002T0oooo00<000000?ooo`3oool0f03oool00`000000oooo0?ooo`1Q 0?ooo`00:@3oool200000=T0oooo00<000000?ooo`3oool0H@3oool002T0oooo00<000000?ooo`3o ool0e`3oool00`000000oooo0?ooo`1R0?ooo`00:@3oool00`000000oooo0?ooo`3G0?ooo`030000 003oool0oooo0680oooo000Y0?ooo`030000003oool0oooo0=H0oooo00<000000?ooo`3oool0H`3o ool002T0oooo00<000000?ooo`3oool0eP3oool00`000000oooo0?ooo`1S0?ooo`00:@3oool00`00 0000oooo0?ooo`3E0?ooo`030000003oool0oooo06@0oooo000Y0?ooo`030000003oool0oooo0=D0 oooo00<000000?ooo`3oool0I03oool002T0oooo0P00003E0?ooo`030000003oool0oooo06D0oooo 000Y0?ooo`030000003oool0oooo0=@0oooo00<000000?ooo`3oool0I@3oool002T0oooo00<00000 0?ooo`3oool0d`3oool00`000000oooo0?ooo`1V0?ooo`00:@3oool00`000000oooo0?ooo`3C0?oo o`030000003oool0oooo06H0oooo000Y0?ooo`030000003oool0oooo0=80oooo00<000000?ooo`3o ool0I`3oool002T0oooo00<000000?ooo`3oool0dP3oool00`000000oooo0?ooo`1W0?ooo`00:@3o ool00`000000oooo0?ooo`3A0?ooo`030000003oool0oooo06P0oooo000Y0?ooo`800000dP3oool0 0`000000oooo0?ooo`1X0?ooo`00:@3oool00`000000oooo0?ooo`3@0?ooo`030000003oool0oooo 06T0oooo000Y0?ooo`030000003oool0oooo0=00oooo00<000000?ooo`3oool0J@3oool002T0oooo 00<000000?ooo`3oool0c`3oool00`000000oooo0?ooo`1Z0?ooo`00:@3oool00`000000oooo0?oo o`3>0?ooo`030000003oool0oooo06/0oooo00070?ooo`D000000`3oool4000000@0oooo10000004 0?ooo`@000001P3oool00`000000oooo0?ooo`3>0?ooo`030000003oool0oooo06/0oooo00090?oo o`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`000004 0?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?oo o`3=0?ooo`030000003oool0oooo06`0oooo00090?ooo`030000003oool0oooo0080oooo00<00000 0?ooo`3oool00P3oool010000000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo 00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`3=0?ooo`030000003oool0oooo06`0oooo 0004000000D0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`020?ooo`040000003o ool0oooo000000@0oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`030?ooo`<0 0000c03oool00`000000oooo0?ooo`1]0?ooo`002@3oool00`000000oooo0?ooo`020?ooo`030000 003oool0oooo0080oooo00@000000?ooo`3oool00000103oool010000000oooo0?ooo`0000040?oo o`030000003oool0oooo00<0oooo00<000000?ooo`3oool0b`3oool00`000000oooo0?ooo`1^0?oo o`002@3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo00@000000?ooo`3o ool00000103oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo00<0oooo00<00000 0?ooo`3oool0bP3oool00`000000oooo0?ooo`1_0?ooo`001`3oool3000000@0oooo00<000000?oo o`3oool00P3oool010000000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00<0 00000?ooo`3oool00`3oool00`000000oooo0?ooo`3:0?ooo`030000003oool0oooo06l0oooo0009 0?ooo`030000003oool0oooo00<0oooo100000040?ooo`@00000103oool4000000H0oooo00<00000 0?ooo`3oool0b@3oool00`000000oooo0?ooo`1`0?ooo`00:@3oool00`000000oooo0?ooo`380?oo o`030000003oool0oooo0740oooo000Y0?ooo`030000003oool0oooo003oool50000 03`0oooo0`00000j0?ooo`<00000>P3oool4000003H0oooo1@0000030?ooo`@000000`3oool002T0 oooo0P00000i0?ooo`050000003oool0oooo0?ooo`000000?@3oool00`000000oooo0?ooo`0g0?oo o`8000000`3oool00`000000oooo0?ooo`0f0?ooo`030000003oool0oooo0080oooo00<000000?oo o`3oool0=@3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo0@0000010?oo o`40oooo000Y0?ooo`030000003oool0oooo03T0oooo00<000000?ooo`3oool0?P3oool00`000000 oooo0?ooo`0e0?ooo`80000000<0oooo0000003oool00P3oool00`000000oooo0?ooo`0f0?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`3oool0=@3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo0080oooo0@0000010?ooo`40oooo000Y0?ooo`030000003oool0oooo03X0oooo 00<000000?ooo`3oool0>@3oool6000003@0oooo0P0000030?ooo`050000003oool0oooo0?ooo`00 0000>03oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo03D0oooo00<000000?ooo`3o ool00P3oool00`000000oooo0?ooo`020?ooo`4000000@3oool10?ooo`00:@3oool00`000000oooo 0?ooo`0k0?ooo`030000003oool0oooo03T0oooo00@000000?ooo`3oool00000<`3oool2000000D0 oooo1000000j0?ooo`@00000>03oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080 oooo0@0000010?ooo`40oooo000Y0?ooo`030000003oool0oooo03`0oooo00<000000?ooo`3oool0 >03oool010000000oooo0?ooo`00000a0?ooo`8000001`3oool00`000000oooo0?ooo`0j0?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`3oool0=@3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo0080oooo0@0000010?ooo`40oooo000Y0?ooo`030000003oool0oooo03P0oooo 00D000000?ooo`3oool0oooo0000000k0?ooo`030000003oool0000002l0oooo0P00000:0?ooo`03 0000003oool0oooo03T0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`0c0?ooo`<0 0000103oool00`000000oooo0?ooo`020?ooo`4000000@3oool10?ooo`00:@3oool00`000000oooo 0?ooo`0i0?ooo`<00000?@3oool2000002d0oooo0P00000=0?ooo`<00000>@3oool4000003P0oooo 00<000000?ooo`3oool00`3oool4000000<0oooo000Y0?ooo`800000YP3oool3000009@0oooo000Y 0?ooo`030000003oool0oooo0:40oooo1000002G0?ooo`00:@3oool00`000000oooo0?ooo`2M0?oo o`@00000V`3oool002T0oooo00<000000?ooo`3oool0U`3oool6000009l0oooo000Y0?ooo`030000 003oool0oooo0900oooo1`00002U0?ooo`00:@3oool00`000000oooo0?ooo`240?ooo``00000[03o ool002T0oooo00<000000?ooo`3oool0MP3oool>00000;P0oooo000Y0?ooogT00000aP3oool00240 ooooo`00001800000000:@3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0oooo00`0oooo 00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0oooo00`0oooo 00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0oooo00d0oooo 00<000000?ooo`3oool0303oool00`000000oooo0?ooo`0=0?ooo`030000003oool0oooo00`0oooo 00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0oooo00d0oooo 00<000000?ooo`3oool0303oool00`000000oooo0?ooo`0=0?ooo`030000003oool0oooo00`0oooo 00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0oooo00d0oooo 00<000000?ooo`3oool01P3oool002T0oooo00<000000?ooo`3oool0>`3oool00`000000oooo0?oo o`0k0?ooo`030000003oool0oooo03/0oooo00<000000?ooo`3oool0>`3oool00`000000oooo0?oo o`0k0?ooo`030000003oool0oooo00H0oooo000Y0?ooo`030000003oool0oooo0?l0oooo?@3oool0 02T0oooo00<000000?ooo`3oool0o`3ooolm0?ooo`00o`3ooomY0?ooo`00o`3ooomY0?ooo`00o`3o oomY0?ooo`00o`3ooomY0?ooo`00o`3ooomY0?ooo`00o`3ooomY0?ooo`00o`3ooomY0?ooo`00o`3o oomY0?ooo`00o`3ooomY0?ooo`00o`3ooomY0?ooo`00\ \>"], ImageRangeCache->{{{0, 359}, {221.375, 0}} -> {-1.34218, -5747.88, \ 0.0403629, 34.8124}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[ Evaluate[y[t] /. \(sol[\([1]\)]\)[\([2]\)]\ ], {t, 0, 10}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0.0147151 6.91595e-006 [ [.21429 .00222 -3 -9 ] [.21429 .00222 3 0 ] [.40476 .00222 -3 -9 ] [.40476 .00222 3 0 ] [.59524 .00222 -3 -9 ] [.59524 .00222 3 0 ] [.78571 .00222 -3 -9 ] [.78571 .00222 3 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.01131 .15303 -30 -4.5 ] [.01131 .15303 0 4.5 ] [.01131 .29135 -30 -4.5 ] [.01131 .29135 0 4.5 ] [.01131 .42967 -30 -4.5 ] [.01131 .42967 0 4.5 ] [.01131 .56799 -30 -4.5 ] [.01131 .56799 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01472 m .21429 .02097 L s [(2)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(4)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(6)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(8)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(10)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .15303 m .03006 .15303 L s [(20000)] .01131 .15303 1 0 Mshowa .02381 .29135 m .03006 .29135 L s [(40000)] .01131 .29135 1 0 Mshowa .02381 .42967 m .03006 .42967 L s [(60000)] .01131 .42967 1 0 Mshowa .02381 .56799 m .03006 .56799 L s [(80000)] .01131 .56799 1 0 Mshowa .125 Mabswid .02381 .04929 m .02756 .04929 L s .02381 .08387 m .02756 .08387 L s .02381 .11845 m .02756 .11845 L s .02381 .18761 m .02756 .18761 L s .02381 .22219 m .02756 .22219 L s .02381 .25677 m .02756 .25677 L s .02381 .32593 m .02756 .32593 L s .02381 .36051 m .02756 .36051 L s .02381 .39509 m .02756 .39509 L s .02381 .46425 m .02756 .46425 L s .02381 .49883 m .02756 .49883 L s .02381 .53341 m .02756 .53341 L s .02381 .60257 m .02756 .60257 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .06244 .01473 L .08255 .01473 L .10458 .01474 L .12507 .01475 L .14415 .01476 L .16457 .01477 L .18314 .01478 L .20229 .0148 L .22307 .01483 L .24291 .01486 L .26394 .0149 L .28348 .01496 L .30178 .01502 L .32202 .01511 L .34055 .01522 L .35953 .01536 L .38026 .01555 L .39993 .01579 L .4209 .01613 L .44231 .01657 L .46248 .01712 L .48256 .01783 L .50104 .01866 L .51986 .01974 L .54052 .02127 L .56003 .02313 L .58095 .02572 L .60219 .02918 L .62231 .03344 L .64222 .0389 L .66064 .04536 L .6793 .05367 L .6999 .06547 L .71925 .07979 L .74011 .09979 L .76015 .12477 L .78125 .15904 L .80099 .20071 L .81936 .25021 L .83981 .321 L .8584 .40362 L .87759 .51232 L s .87759 .51232 m .89201 .61803 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgP3oool4000003H0oooo1@0000030?ooo`@000000`3oool0 06@0oooo00D000000?ooo`3oool0oooo0000000m0?ooo`030000003oool0oooo03P0oooo00D00000 0?ooo`3oool0oooo0000000h0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0=@3o ool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080oooo0@0000010?ooo`40oooo001U 0?ooo`030000003oool0oooo03h0oooo00<000000?ooo`3oool0>03oool01@000000oooo0?ooo`3o ool0000003P0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`0e0?ooo`030000003o ool0oooo0080oooo00<000000?ooo`3oool00P3oool100000040oooo0@3oool006H0oooo00<00000 0?ooo`3oool0>@3oool6000003T0oooo00D000000?ooo`3oool0oooo0000000h0?ooo`030000003o ool0oooo0080oooo00<000000?ooo`3oool0=@3oool00`000000oooo0?ooo`020?ooo`030000003o ool0oooo0080oooo0@0000010?ooo`40oooo001W0?ooo`030000003oool0oooo03T0oooo00@00000 0?ooo`3oool00000>P3oool4000003X0oooo1000000h0?ooo`030000003oool0oooo0080oooo00<0 00000?ooo`3oool00P3oool100000040oooo0@3oool006P0oooo00<000000?ooo`3oool0>03oool0 10000000oooo0?ooo`00000j0?ooo`030000003oool0oooo03X0oooo00<000000?ooo`3oool00P3o ool00`000000oooo0?ooo`0e0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool00P3o ool100000040oooo0@3oool006@0oooo00D000000?ooo`3oool0oooo0000000k0?ooo`030000003o ool0000003/0oooo00<000000?ooo`3oool0>@3oool00`000000oooo0?ooo`020?ooo`030000003o ool0oooo03<0oooo0`0000040?ooo`030000003oool0oooo0080oooo0@0000010?ooo`40oooo001U 0?ooo`<00000?@3oool2000003`0oooo0`00000i0?ooo`@00000>03oool00`000000oooo0?ooo`03 0?ooo`@000000`3oool00?l0ooooJ@3oool00?l0ooooJ@3oool00?l0ooooJ@3oool002T0oooo00<0 00000?ooo`3oool0o`3ooolm0?ooo`00:@3oool00`000000oooo0?ooo`3o0?ooocd0oooo000Y0?oo o`030000003oool0oooo0?l0oooo?@3oool002T0oooo00<000000?ooo`3oool0o`3ooolm0?ooo`00 8@3ooooo000004P00000000Y0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0303o ool00`000000oooo0?ooo`0=0?ooo`030000003oool0oooo00`0oooo00<000000?ooo`3oool0303o ool00`000000oooo0?ooo`0=0?oooc/000000`3oool00`000000oooo0?ooo`0<0?ooo`030000003o ool0oooo00d0oooo00<000000?ooo`3oool0303oool00`000000oooo0?ooo`0=0?ooo`030000003o ool0oooo00`0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0<0?ooo`030000003o ool0oooo00d0oooo00<000000?ooo`3oool0303oool00`000000oooo0?ooo`0=0?ooo`030000003o ool0oooo00H0oooo000Y0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0303oool0 0`000000oooo0?ooo`0=0?ooo`030000003oool0oooo00`0oooo00<000000?ooo`3oool0303oool0 0`000000oooo0?ooo`0=0?ooo`030000003oool0oooo00`0oooo00<000000?ooo`3oool03@3oool0 0`000000oooo0?ooo`0<0?ooo`030000003oool0oooo00X0oooo3@0000050?ooo`030000003oool0 oooo00d0oooo00<000000?ooo`3oool0303oool00`000000oooo0?ooo`0=0?ooo`030000003oool0 oooo00`0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0 oooo00d0oooo00<000000?ooo`3oool0303oool00`000000oooo0?ooo`0=0?ooo`030000003oool0 oooo00H0oooo000Y0?ooo`030000003oool0oooo0:80oooo3@00002=0?ooo`00:@3oool00`000000 oooo0?ooo`2_0?ooo`L00000QP3oool002T0oooo00<000000?ooo`3oool0]P3oool7000007l0oooo 000Y0?ooo`030000003oool0oooo0;d0oooo1@00001j0?ooo`00:@3oool00`000000oooo0?ooo`32 0?ooo`<00000M`3oool002T0oooo00<000000?ooo`3oool0a@3oool3000007@0oooo000Y0?ooo`03 0000003oool0oooo080oooo 0P00001H0?ooo`00:@3oool00`000000oooo0?ooo`3T0?ooo`030000003oool0oooo05D0oooo000Y 0?ooo`030000003oool0oooo0>D0oooo00<000000?ooo`3oool0E03oool002T0oooo00<000000?oo o`3oool0iP3oool00`000000oooo0?ooo`1C0?ooo`00:@3oool00`000000oooo0?ooo`3W0?ooo`03 0000003oool0oooo0580oooo000Y0?ooo`030000003oool0oooo0>P0oooo00<000000?ooo`3oool0 D@3oool002T0oooo00<000000?ooo`3oool0j@3oool00`000000oooo0?ooo`1@0?ooo`00:@3oool0 0`000000oooo0?ooo`3Y0?ooo`030000003oool0oooo0500oooo000Y0?ooo`030000003oool0oooo 0>X0oooo00<000000?ooo`3oool0C`3oool002T0oooo0P00003/0?ooo`030000003oool0oooo04h0 oooo000Y0?ooo`030000003oool0oooo0>`0oooo00<000000?ooo`3oool0C@3oool002T0oooo00<0 00000?ooo`3oool0k@3oool00`000000oooo0?ooo`1<0?ooo`00:@3oool00`000000oooo0?ooo`3^ 0?ooo`030000003oool0oooo04/0oooo000Y0?ooo`030000003oool0oooo0>h0oooo00<000000?oo o`3oool0B`3oool002T0oooo00<000000?ooo`3oool0k`3oool00`000000oooo0?ooo`1:0?ooo`00 :@3oool00`000000oooo0?ooo`3_0?ooo`030000003oool0oooo04X0oooo000Y0?ooo`030000003o ool0oooo0?00oooo00<000000?ooo`3oool0B@3oool000<00000103oool4000000@0oooo10000004 0?ooo`@00000103oool4000000H0oooo00<000000?ooo`3oool0l03oool00`000000oooo0?ooo`19 0?ooo`000P3oool01@000000oooo0?ooo`3oool0000000@0oooo00@000000?ooo`3oool00000103o ool010000000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3o ool00`3oool00`000000oooo0?ooo`3a0?ooo`030000003oool0oooo04P0oooo00060?ooo`030000 003oool0oooo0080oooo00@000000?ooo`3oool00000103oool010000000oooo0?ooo`0000040?oo o`040000003oool0oooo000000@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`3a 0?ooo`030000003oool0oooo04P0oooo00000`000000oooo0?ooo`030?ooo`030000003oool0oooo 0080oooo00@000000?ooo`3oool00000103oool010000000oooo0?ooo`0000040?ooo`040000003o ool0oooo000000@0oooo00<000000?ooo`3oool00`3oool300000?80oooo00<000000?ooo`3oool0 A`3oool000030?ooo`000000oooo00<0oooo00<000000?ooo`3oool00P3oool010000000oooo0?oo o`0000040?ooo`040000003oool0oooo000000@0oooo00@000000?ooo`3oool00000103oool00`00 0000oooo0?ooo`030?ooo`030000003oool0oooo0?80oooo00<000000?ooo`3oool0A`3oool00080 oooo00D000000?ooo`3oool0oooo000000040?ooo`040000003oool0oooo000000@0oooo00@00000 0?ooo`3oool00000103oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo00<0oooo 00<000000?ooo`3oool0l`3oool00`000000oooo0?ooo`160?ooo`000P3oool01@000000oooo0?oo o`3oool0000000@0oooo00@000000?ooo`3oool00000103oool010000000oooo0?ooo`0000040?oo o`040000003oool0oooo000000@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`3c 0?ooo`030000003oool0oooo04H0oooo0002000000D0oooo100000040?ooo`@00000103oool40000 00@0oooo100000060?ooo`030000003oool0oooo0?@0oooo00<000000?ooo`3oool0A@3oool002T0 oooo00<000000?ooo`3oool0m03oool00`000000oooo0?ooo`150?ooo`00:@3oool00`000000oooo 0?ooo`3e0?ooo`030000003oool0oooo04@0oooo000Y0?ooo`030000003oool0oooo0?D0oooo00<0 00000?ooo`3oool0A03oool002T0oooo00<000000?ooo`3oool0mP3oool00`000000oooo0?ooo`13 0?ooo`00:@3oool00`000000oooo0?ooo`3f0?ooo`030000003oool0oooo04<0oooo000Y0?ooo`03 0000003oool0oooo0?L0oooo00<000000?ooo`3oool0@P3oool002T0oooo00<000000?ooo`3oool0 m`3oool00`000000oooo0?ooo`120?ooo`00:@3oool200000?T0oooo00<000000?ooo`3oool0@@3o ool002T0oooo00<000000?ooo`3oool0n03oool00`000000oooo0?ooo`110?ooo`00:@3oool00`00 0000oooo0?ooo`3i0?ooo`030000003oool0oooo0400oooo000Y0?ooo`030000003oool0oooo0?T0 oooo00<000000?ooo`3oool0@03oool002T0oooo00<000000?ooo`3oool0nP3oool00`000000oooo 0?ooo`0o0?ooo`00:@3oool00`000000oooo0?ooo`3j0?ooo`030000003oool0oooo03l0oooo000Y 0?ooo`030000003oool0oooo0?/0oooo00<000000?ooo`3oool0?P3oool002T0oooo00<000000?oo o`3oool0n`3oool00`000000oooo0?ooo`0n0?ooo`00:@3oool00`000000oooo0?ooo`3k0?ooo`03 0000003oool0oooo03h0oooo000Y0?ooo`030000003oool0oooo0?`0oooo00<000000?ooo`3oool0 ?@3oool002T0oooo00<000000?ooo`3oool0o03oool00`000000oooo0?ooo`0m0?ooo`00:@3oool2 00000?h0oooo00<000000?ooo`3oool0?03oool002T0oooo00<000000?ooo`3oool0o@3oool00`00 0000oooo0?ooo`0l0?ooo`00:@3oool00`000000oooo0?ooo`3m0?ooo`030000003oool0oooo03`0 oooo000Y0?ooo`030000003oool0oooo0?h0oooo00<000000?ooo`3oool0>`3oool002T0oooo00<0 00000?ooo`3oool0oP3oool00`000000oooo0?ooo`0k0?ooo`00:@3oool00`000000oooo0?ooo`3n 0?ooo`030000003oool0oooo03/0oooo000Y0?ooo`030000003oool0oooo0?l0oooo00<000000?oo o`3oool0>P3oool002T0oooo00<000000?ooo`3oool0o`3oool00`000000oooo0?ooo`0j0?ooo`00 :@3oool00`000000oooo0?ooo`3o0?ooo`40oooo00<000000?ooo`3oool0>@3oool002T0oooo00<0 00000?ooo`3oool0o`3oool10?ooo`030000003oool0oooo03T0oooo000Y0?ooo`030000003oool0 oooo0?l0oooo0@3oool00`000000oooo0?ooo`0i0?ooo`00:@3oool200000?l0oooo0`3oool00`00 0000oooo0?ooo`0h0?ooo`00:@3oool00`000000oooo0?ooo`3o0?ooo`80oooo00<000000?ooo`3o ool0>03oool002T0oooo00<000000?ooo`3oool0o`3oool20?ooo`030000003oool0oooo03P0oooo 000Y0?ooo`030000003oool0oooo0?l0oooo0P3oool00`000000oooo0?ooo`0h0?ooo`00:@3oool0 0`000000oooo0?ooo`3o0?ooo`<0oooo00<000000?ooo`3oool0=`3oool002T0oooo00<000000?oo o`3oool0o`3oool30?ooo`030000003oool0oooo03L0oooo000Y0?ooo`030000003oool0oooo0?l0 oooo0`3oool00`000000oooo0?ooo`0g0?ooo`00:@3oool00`000000oooo0?ooo`3o0?ooo`<0oooo 00<000000?ooo`3oool0=`3oool000040?ooo`0000000000000000<0oooo100000040?ooo`@00000 103oool4000000@0oooo100000060?ooo`030000003oool0oooo0?l0oooo103oool00`000000oooo 0?ooo`0f0?ooo`000P3oool01@000000oooo0?ooo`3oool0000000@0oooo00@000000?ooo`3oool0 0000103oool010000000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00<00000 0?ooo`3oool00`3oool00`000000oooo0?ooo`3o0?ooo`@0oooo00<000000?ooo`3oool0=P3oool0 0080oooo00D000000?ooo`3oool0oooo000000040?ooo`040000003oool0oooo000000@0oooo00@0 00000?ooo`3oool00000103oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo00<0 oooo00<000000?ooo`3oool0o`3oool40?ooo`030000003oool0oooo03H0oooo000400000080oooo 00<000000?ooo`3oool00P3oool010000000oooo0?ooo`0000040?ooo`040000003oool0oooo0000 00@0oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`030?ooo`<00000o`3oool4 0?ooo`030000003oool0oooo03H0oooo00020?ooo`050000003oool0oooo0?ooo`000000103oool0 10000000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00@000000?ooo`3oool0 0000103oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0?l0oooo1@3oool00`000000 oooo0?ooo`0e0?ooo`000P3oool01@000000oooo0?ooo`3oool0000000@0oooo00@000000?ooo`3o ool00000103oool010000000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00<0 00000?ooo`3oool00`3oool00`000000oooo0?ooo`3o0?ooo`D0oooo00<000000?ooo`3oool0=@3o ool000030000003oool0000000<0oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`00 00040?ooo`040000003oool0oooo000000@0oooo00@000000?ooo`3oool00000103oool00`000000 oooo0?ooo`030?ooo`030000003oool0oooo0?l0oooo1@3oool00`000000oooo0?ooo`0e0?ooo`00 00<0oooo000000000000103oool4000000@0oooo100000040?ooo`@00000103oool4000000H0oooo 00<000000?ooo`3oool0o`3oool50?ooo`030000003oool0oooo03D0oooo000Y0?ooo`030000003o ool0oooo0?l0oooo1P3oool00`000000oooo0?ooo`0d0?ooo`00:@3oool00`000000oooo0?ooo`3o 0?ooo`H0oooo00<000000?ooo`3oool0=03oool002T0oooo00<000000?ooo`3oool0o`3oool60?oo o`030000003oool0oooo03@0oooo000Y0?ooo`030000003oool0oooo0?l0oooo1P3oool00`000000 oooo0?ooo`0d0?ooo`00:@3oool00`000000oooo0?ooo`3o0?ooo`L0oooo00<000000?ooo`3oool0 <`3oool002T0oooo00<000000?ooo`3oool0o`3oool70?ooo`030000003oool0oooo03<0oooo000Y 0?ooo`030000003oool0oooo0?l0oooo1`3oool00`000000oooo0?ooo`0c0?ooo`00:@3oool20000 0?l0oooo203oool00`000000oooo0?ooo`0c0?ooo`00:@3oool00`000000oooo0?ooo`3o0?ooo`P0 oooo00<000000?ooo`3oool00?ooo`030000003oool0oooo02`0oooo000Y0?ooo`030000003oool0oooo0?l0oooo3P3oool0 0`000000oooo0?ooo`0/0?ooo`000`0000040?ooo`@00000103oool4000000@0oooo100000040?oo o`@000001P3oool00`000000oooo0?ooo`3o0?ooo`h0oooo00<000000?ooo`3oool0;03oool000<0 oooo00@000000?ooo`3oool00000103oool010000000oooo0?ooo`0000040?ooo`040000003oool0 oooo000000@0oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`030?ooo`030000 003oool0oooo0?l0oooo3P3oool00`000000oooo0?ooo`0/0?ooo`000`3oool010000000oooo0?oo o`0000040?ooo`040000003oool0oooo000000@0oooo00@000000?ooo`3oool00000103oool01000 0000oooo0?ooo`0000040?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0o`3oool> 0?ooo`030000003oool0oooo02`0oooo00030?ooo`040000003oool0oooo000000@0oooo00@00000 0?ooo`3oool00000103oool010000000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0 oooo00<000000?ooo`3oool00`3oool300000?l0oooo3`3oool00`000000oooo0?ooo`0[0?ooo`00 0`0000030?ooo`030000003oool0oooo0080oooo00@000000?ooo`3oool00000103oool010000000 oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`3o0?ooo`l0oooo00<000000?ooo`3oool0:`3oool000H0oooo00<000000?oo o`3oool00P3oool010000000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00@0 00000?ooo`3oool00000103oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0?l0oooo 3`3oool00`000000oooo0?ooo`0[0?ooo`0000<000000?ooo`3oool00`3oool00`000000oooo0?oo o`020?ooo`040000003oool0oooo000000@0oooo00@000000?ooo`3oool00000103oool010000000 oooo0?ooo`0000040?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0o`3oool?0?oo o`030000003oool0oooo02/0oooo0000103oool000000000000000030?ooo`@00000103oool40000 00@0oooo100000040?ooo`@000001P3oool00`000000oooo0?ooo`3o0?ooo`l0oooo00<000000?oo o`3oool0:`3oool002T0oooo00<000000?ooo`3oool0o`3oool@0?ooo`030000003oool0oooo02X0 oooo000Y0?ooo`030000003oool0oooo0?l0oooo403oool00`000000oooo0?ooo`0Z0?ooo`00:@3o ool00`000000oooo0?ooo`3o0?oooa00oooo00<000000?ooo`3oool0:P3oool002T0oooo00<00000 0?ooo`3oool0o`3oool@0?ooo`030000003oool0oooo02X0oooo000Y0?ooo`030000003oool0oooo 0?l0oooo403oool00`000000oooo0?ooo`0Z0?ooo`00:@3oool00`000000oooo0?ooo`3o0?oooa40 oooo00<000000?ooo`3oool0:@3oool002T0oooo00<000000?ooo`3oool0o`3ooolA0?ooo`030000 003oool0oooo02T0oooo000Y0?ooo`800000o`3ooolB0?ooo`030000003oool0oooo02T0oooo000Y 0?ooo`030000003oool0oooo0?l0oooo4@3oool00`000000oooo0?ooo`0Y0?ooo`00:@3oool00`00 0000oooo0?ooo`3o0?oooa40oooo00<000000?ooo`3oool0:@3oool002T0oooo00<000000?ooo`3o ool0o`3ooolB0?ooo`030000003oool0oooo02P0oooo000Y0?ooo`030000003oool0oooo0?l0oooo 4P3oool00`000000oooo0?ooo`0X0?ooo`00:@3oool00`000000oooo0?ooo`3o0?oooa80oooo00<0 00000?ooo`3oool0:03oool002T0oooo00<000000?ooo`3oool0o`3ooolB0?ooo`030000003oool0 oooo02P0oooo000Y0?ooo`030000003oool0oooo0?l0oooo4P3oool00`000000oooo0?ooo`0X0?oo o`00:@3oool00`000000oooo0?ooo`3o0?oooa<0oooo00<000000?ooo`3oool09`3oool002T0oooo 00<000000?ooo`3oool0o`3ooolC0?ooo`030000003oool0oooo02L0oooo000Y0?ooo`030000003o ool0oooo0?l0oooo4`3oool00`000000oooo0?ooo`0W0?ooo`00:@3oool200000?l0oooo503oool0 0`000000oooo0?ooo`0W0?ooo`00:@3oool00`000000oooo0?ooo`3o0?oooa<0oooo00<000000?oo o`3oool09`3oool002T0oooo00<000000?ooo`3oool0o`3ooolD0?ooo`030000003oool0oooo02H0 oooo000Y0?ooo`030000003oool0oooo0?l0oooo503oool00`000000oooo0?ooo`0V0?ooo`00:@3o ool00`000000oooo0?ooo`3o0?oooa@0oooo00<000000?ooo`3oool09P3oool002T0oooo00<00000 0?ooo`3oool0o`3ooolD0?ooo`030000003oool0oooo02H0oooo000Y0?ooo`030000003oool0oooo 0?l0oooo503oool00`000000oooo0?ooo`0V0?ooo`00:@3oool00`000000oooo0?ooo`3o0?oooa@0 oooo00<000000?ooo`3oool09P3oool002T0oooo00<000000?ooo`3oool0o`3ooolD0?ooo`030000 003oool0oooo02H0oooo000Y0?ooo`030000003oool0oooo0?l0oooo5@3oool00`000000oooo0?oo o`0U0?ooo`00:@3oool00`000000oooo0?ooo`3o0?oooaD0oooo00<000000?ooo`3oool09@3oool0 02T0oooo0P00003o0?oooaH0oooo00<000000?ooo`3oool09@3oool002T0oooo00<000000?ooo`3o ool0o`3ooolE0?ooo`030000003oool0oooo02D0oooo000Y0?ooo`030000003oool0oooo0?l0oooo 5@3oool00`000000oooo0?ooo`0U0?ooo`00:@3oool00`000000oooo0?ooo`3o0?oooaD0oooo00<0 00000?ooo`3oool09@3oool002T0oooo00<000000?ooo`3oool0o`3ooolE0?ooo`030000003oool0 oooo02D0oooo000Y0?ooo`030000003oool0oooo0?l0oooo5@3oool00`000000oooo0?ooo`0U0?oo o`00:@3oool00`000000oooo0?ooo`3o0?oooaD0oooo00<000000?ooo`3oool09@3oool002T0oooo 00<000000?ooo`3oool0o`3ooolF0?ooo`030000003oool0oooo02@0oooo0003000000@0oooo1000 00040?ooo`@00000103oool4000000@0oooo100000060?ooo`030000003oool0oooo0?l0oooo5P3o ool00`000000oooo0?ooo`0T0?ooo`000`3oool010000000oooo0?ooo`0000040?ooo`040000003o ool0oooo000000@0oooo00@000000?ooo`3oool00000103oool010000000oooo0?ooo`0000040?oo o`030000003oool0oooo00<0oooo00<000000?ooo`3oool0o`3ooolF0?ooo`030000003oool0oooo 02@0oooo00030?ooo`040000003oool0oooo000000@0oooo00@000000?ooo`3oool00000103oool0 10000000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool0 0`3oool00`000000oooo0?ooo`3o0?oooaH0oooo00<000000?ooo`3oool0903oool000<0oooo00@0 00000?ooo`3oool00000103oool010000000oooo0?ooo`0000040?ooo`040000003oool0oooo0000 00@0oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`030?ooo`<00000o`3ooolF 0?ooo`030000003oool0oooo02@0oooo0003000000<0oooo00<000000?ooo`3oool00P3oool01000 0000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0oooo00@000000?ooo`3oool00000 103oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0?l0oooo5P3oool00`000000oooo 0?ooo`0T0?ooo`000`3oool010000000oooo0?ooo`0000040?ooo`040000003oool0oooo000000@0 oooo00@000000?ooo`3oool00000103oool010000000oooo0?ooo`0000040?ooo`030000003oool0 oooo00<0oooo00<000000?ooo`3oool0o`3ooolF0?ooo`030000003oool0oooo02@0oooo00030?oo o`040000003oool0oooo000000@0oooo00@000000?ooo`3oool00000103oool010000000oooo0?oo o`0000040?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`3o0?oooaH0oooo00<000000?ooo`3oool0903oool000<00000103oool4000000@0oooo 100000040?ooo`@00000103oool4000000H0oooo00<000000?ooo`3oool0o`3ooolG0?ooo`030000 003oool0oooo02<0oooo000Y0?ooo`030000003oool0oooo0?l0oooo5`3oool00`000000oooo0?oo o`0S0?ooo`00:@3oool00`000000oooo0?ooo`3o0?oooaL0oooo00<000000?ooo`3oool08`3oool0 02T0oooo00<000000?ooo`3oool0o`3ooolG0?ooo`030000003oool0oooo02<0oooo000Y0?ooo`03 0000003oool0oooo0?l0oooo5`3oool00`000000oooo0?ooo`0S0?ooo`00:@3oool00`000000oooo 0?ooo`3o0?oooaL0oooo00<000000?ooo`3oool08`3oool002T0oooo00<000000?ooo`3oool0o`3o oolG0?ooo`030000003oool0oooo02<0oooo000Y0?ooo`030000003oool0oooo0?l0oooo5`3oool0 0`000000oooo0?ooo`0S0?ooo`00:@3oool200000?l0oooo603oool00`000000oooo0?ooo`0S0?oo o`00:@3oool00`000000oooo0?ooo`3o0?oooaP0oooo00<000000?ooo`3oool08P3oool002T0oooo 00<000000?ooo`3oool0o`3ooolH0?ooo`030000003oool0oooo0280oooo000Y0?ooo`030000003o ool0oooo0?l0oooo603oool00`000000oooo0?ooo`0R0?ooo`00:@3oool00`000000oooo0?ooo`3o 0?oooaP0oooo00<000000?ooo`3oool08P3oool002T0oooo00<000000?ooo`3oool0o`3ooolH0?oo o`030000003oool0oooo0280oooo003o0?ooofT0oooo003o0?ooofT0oooo003o0?ooofT0oooo003o 0?ooofT0oooo0000\ \>"], ImageRangeCache->{{{0, 359}, {221.375, 0}} -> {-1.34218, -9005.65, \ 0.0403629, 555.83}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ M\[OTilde]ned n\[ADoubleDot]ited integraali numbrilise arvutuse kohta. Esmalt \ - kuidas oleks tulemus tavakujul ja NIntegrate abil.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\_1\%3 E\^\(x\^2\)/x\^3 \[DifferentialD]x\)], "Input"], Cell[BoxData[ \(1\/2\ \((\[ExponentialE] - ExpIntegralEi[1])\) + 1\/18\ \((\(-\[ExponentialE]\^9\) + 9\ ExpIntegralEi[9])\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[%33]\)], "Input"], Cell[BoxData[ \(69.17939805485317`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(NIntegrate[E\^\(x\^2\)/x\^3, {x, 1, 3}]\)], "Input"], Cell[BoxData[ \(69.17939805485295`\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["6. Vektorid, maatriksid, listid.", "Subtitle"], Cell["6.1. Tehteid listidega", "Subsubtitle"], Cell[BoxData[ \(\($Line = 0;\)\)], "Input"], Cell["\<\ Listiks v\[OTilde]iks nimetada igasugust t\[UDoubleDot]\[UDoubleDot]pi \ avaldis, mis avaldatakse loogeliste sulgude vahel ning avaldise liikmed on \ omavahel eraldatud komadega. M\[OTilde]ned n\[ADoubleDot]ited:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(v = {2, 3, 4}\)], "Input"], Cell[BoxData[ \({2, 3, 4}\)], "Output"] }, Open ]], Cell["\<\ Toodud \[UDoubleDot]herealist listi v\[OTilde]ime nimetada ka vektoriks. \ Allpool vataleme ka pikemalt, kuidas vektoritega tehteid teha. M\[OTilde]ned \ lihtsamad aga siin.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Sqrt[v]\)], "Input"], Cell[BoxData[ \({\@2, \@3, 2}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[%]\)], "Input"], Cell[BoxData[ \({1.4142135623730951`, 1.7320508075688772`, 2.`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(v + 2\)], "Input"], Cell[BoxData[ \({4, 5, 6}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(v*a\)], "Input"], Cell[BoxData[ \({2\ a, 3\ a, 4\ a}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(x\^v\)], "Input"], Cell[BoxData[ \({x\^2, x\^3, x\^4}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(D[\(\(x\)\(\ \)\)\^v, x]\)], "Input"], Cell[BoxData[ \({2\ x, 3\ x\^2, 4\ x\^3}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\_0\%3\( x\^v\) \[DifferentialD]x\)], "Input"], Cell[BoxData[ \({9, 81\/4, 243\/5}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\_0\%3\( v\^x\) \[DifferentialD]x\)], "Input"], Cell[BoxData[ \({7\/Log[2], 26\/Log[3], 63\/Log[4]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[%]\)], "Input"], Cell[BoxData[ \({10.098865286222743`, 23.66621989229777`, 45.44489378800235`}\)], "Output"] }, Open ]], Cell["\<\ Seega v\[OTilde]ib antud juhul vaadata listi kui mingit andmetekogumit. \ Kasutades listi mingites algebralistes operatsioonides, rakendatakse neid \ operatsioone k\[OTilde]igile listi liikmetele. Mingi algoritmi \ j\[ADoubleDot]rgi saab listi genereerida kasutades k\[ADoubleDot]sku Table.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(li = Table[i\^2, {i, 5}]\)], "Input"], Cell[BoxData[ \({1, 4, 9, 16, 25}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(li2 = Table[i - 3, {i, 5}]\)], "Input"], Cell[BoxData[ \({\(-2\), \(-1\), 0, 1, 2}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(li + li2\)], "Input"], Cell[BoxData[ \({\(-1\), 3, 9, 17, 27}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Table[Sin[n/5], {n, \(-2\), 4}]\)], "Input"], Cell[BoxData[ \({\(-Sin[2\/5]\), \(-Sin[1\/5]\), 0, Sin[1\/5], Sin[2\/5], Sin[3\/5], Sin[4\/5]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(maat = Table[x\^i + y\^j, {i, 3}, {j, 2}]\)], "Input"], Cell[BoxData[ \({{x + y, x + y\^2}, {x\^2 + y, x\^2 + y\^2}, {x\^3 + y, x\^3 + y\^2}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[%]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {\(x + y\), \(x + y\^2\)}, {\(x\^2 + y\), \(x\^2 + y\^2\)}, {\(x\^3 + y\), \(x\^3 + y\^2\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Table[Random[], \ {4}]\)], "Input"], Cell[BoxData[ \({0.3026483497899472`, 0.1158109292600887`, 0.14333745059971142`, 0.0509787892338992`}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["Table[f, {", Background->GrayLevel[0.900008]], StyleBox["imax", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["}]\t\t\tgenereeritakse list, milles on imax liiget, antakse \ funktsiooni f abil\nTable{f,{", Background->GrayLevel[0.900008]], StyleBox["i, imax", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["}]\t\t\tgenereeritakse list, mille liikmed antakse f abil 1-st \ kuni imax-ni\nTable[f, {", Background->GrayLevel[0.900008]], StyleBox["i, imin, imax", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["}]\t\tgenereeritakse list, mille liikmed antakse f abil imin-st \ kuni imax-ni\nTable{f, {", Background->GrayLevel[0.900008]], StyleBox["i, imin, imax, di", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["}]\t\tgenereeritakse list, mille liikmed antakse f abil 1-st kuni \ imax-ni sammuga di\nTable[f, {", Background->GrayLevel[0.900008]], StyleBox["i,imin,imax", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["},{", Background->GrayLevel[0.900008]], StyleBox["j,jmin,jmax", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["}] \tgenereeritakse tabel (v\[OTilde]i maatriks) funktsiooni f \ abil\nTableForm[", Background->GrayLevel[0.900008]], StyleBox["list", FontSlant->"Italic", Background->GrayLevel[0.900008]], StyleBox["]\t\t\tlist kuvatakse tabeli kujul", Background->GrayLevel[0.900008]] }], "Text", Background->GrayLevel[0.900008]], Cell["\<\ Listidest ja maatriksitest saab v\[ADoubleDot]lja eraldada m\[OTilde]ningaid \ liikmeid, teha tehteid nendega ning koostada neist uusi liste.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(maks = maat[\([3]\)]\)], "Input"], Cell[BoxData[ \({x\^3 + y, x\^3 + y\^2}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(li3 = li2[\([2]\)]\)], "Input"], Cell[BoxData[ \(\(-1\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(li2[\([{3, 4, 5}]\)]\)], "Input"], Cell[BoxData[ \({0, 1, 2}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(li3*maks\)], "Input"], Cell[BoxData[ \({\(-x\^3\) - y, \(-x\^3\) - y\^2}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["t[[i]] ", FontColor->GrayLevel[0], Background->GrayLevel[0.900008]], StyleBox["v\[OTilde]i", FontSlant->"Italic", FontColor->GrayLevel[0], Background->GrayLevel[0.900008]], StyleBox[" Part[t,i]\t\t\tannab listi t alamlisti i (vt maks) v\[OTilde]i \ \[UDoubleDot]he elemendi (vt li3)\n\t\t\t\t\talamlistiks v\[OTilde]ib olla ka \ vaid \[UDoubleDot]ks listi liige\n", FontColor->GrayLevel[0], Background->GrayLevel[0.900008]], Cell[BoxData[ FormBox[ RowBox[{ StyleBox[\(t[\([{i\_1, \ i\_2, \ ... , \ i\_n}]\)]\), FontColor->GrayLevel[0]], StyleBox[ RowBox[{ StyleBox[" ", FontColor->GrayLevel[0]], " "}]]}], TraditionalForm]], FontColor->RGBColor[1, 0, 0]], "\t\t\t", StyleBox["genereeritakse uus n liikmeline list vanast listist t\n\ t[[i,j,...]] ehk Part[t,i,j,...]\t\tantakse listi t osa i-nda osa j-s osa ", FontColor->GrayLevel[0]] }], "Text", FontColor->GrayLevel[0.900008], Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[ \(t = {{2, 3}, {a + z, g}, {d, \@\(3 + 5\)}}\)], "Input"], Cell[BoxData[ \({{2, 3}, {a + z, g}, {d, 2\ \@2}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t[\([2]\)]\)], "Input"], Cell[BoxData[ \({a + z, g}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t[\([2, 1]\)]\)], "Input"], Cell[BoxData[ \(a + z\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(t[\([2]\)]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \(a + z\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(t[\([2]\)]\)[\([1]\)]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \(a\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t[\([2, 1, 1]\)]\)], "Input"], Cell[BoxData[ \(a\)], "Output"] }, Open ]], Cell["\<\ Nagu \[UDoubleDot]laltoodud n\[ADoubleDot]idetest n\[ADoubleDot]ha \ v\[OTilde]ib sel moel tuua ka pikast avaldisest v\[ADoubleDot]lja erinevaid \ osi, antud juhul listi \[UDoubleDot]he osa \[UDoubleDot]ht liidetavatest. M\ \[OTilde]ned sarnased n\[ADoubleDot]ited veel, kus saab mingist pikemast \ avaldisest osa liikmeid v\[ADoubleDot]lja tuua.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(vorrandilahend = Solve[{x + 2 y - 3.0 z \[Equal] 2, y - z \[Equal] 0.5, x + 2 y - 6 z \[Equal] 4}, {x, y, z}]\)], "Input"], Cell[BoxData[ \({{x \[Rule] 0.3333333333333333`, y \[Rule] \(-0.16666666666666666`\), z \[Rule] \(-0.6666666666666666`\)}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(iks = \(vorrandilahend[\([1]\)]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \(x \[Rule] 0.3333333333333333`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ks = \(\(vorrandilahend[\([1]\)]\)[\([1]\)]\)[\([2]\)]\)], "Input"], Cell[BoxData[ \(0.3333333333333333`\)], "Output"] }, Open ]], Cell["\<\ Siin kasutasime asjaolu, et v\[OTilde]rrandi lahend antakse listina - see on \ antud loogeliste sulgude vahel. Sel listil on omakorda 3 liiget (x->0.333333, \ y->0.166667, z->0.666667), mis koosnevad kahest liikmest. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(ig = \(\(vorrandilahend[\([1]\)]\)[\([2]\)]\)[\([2]\)]\)], "Input"], Cell[BoxData[ \(\(-0.16666666666666666`\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ze = \(\(vorrandilahend[\([1]\)]\)[\([3]\)]\)[\([2]\)]\)], "Input"], Cell[BoxData[ \(\(-0.6666666666666666`\)\)], "Output"] }, Open ]], Cell[BoxData[ \(Clear[x, t]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(difvor = DSolve[{2.0 \( x''\)[t] + 0.5 \( x'\)[t] + 5 x[t] \[Equal] 2.5\ Sin[5 t], \(x'\)[0] \[Equal] 2, x[0] \[Equal] \(-1\)}, x[t], t]\)], "Input"], Cell[BoxData[ \(Less::"nord" \(\(:\)\(\ \)\) "Invalid comparison with \!\(\(\(0.` \[InvisibleSpace]\)\) - \ \(\(3.152380053229623`\\ \[ImaginaryI]\)\)\) attempted."\)], "Message"], Cell[BoxData[ \({{x[ t] \[Rule] \((\(-0.49846153846153846`\) - 0.6827564113351899`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\((\ \(-0.125`\) - 1.5761900266148114`\ \[ImaginaryI])\)\ t\)\ \ \((\((\(-0.3046267164378083`\) - 0.9524718177627719`\ \[ImaginaryI])\) + \((\(\(1.`\)\(\ \[InvisibleSpace]\)\) + 1.0842021724855044`*^-19\ \[ImaginaryI])\)\ \ \[ExponentialE]\^\(3.152380053229623`\ \[ImaginaryI]\ t\) + \ \((\(\(0.002146213838154912`\)\(\[InvisibleSpace]\)\) - 0.0029397278326011474`\ \[ImaginaryI])\)\ \ \[ExponentialE]\^\(\((\(\(0.125`\)\(\[InvisibleSpace]\)\) + \ 1.5761900266148114`\ \[ImaginaryI])\)\ t\)\ Cos[ 5.`\ t] + \ \((\(\(0.03863184908678842`\)\(\[InvisibleSpace]\)\) - 0.05291510098682066`\ \[ImaginaryI])\)\ \[ExponentialE]\ \^\(\((\(\(0.125`\)\(\[InvisibleSpace]\)\) + 1.5761900266148114`\ \ \[ImaginaryI])\)\ t\)\ Sin[5.`\ t])\)}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Chop[%]\)], "Input"], Cell[BoxData[ \({{x[ t] \[Rule] \((\(-0.49846153846153846`\) - 0.6827564113351899`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\((\ \(-0.125`\) - 1.5761900266148114`\ \[ImaginaryI])\)\ t\)\ \ \((\((\(-0.3046267164378083`\) - 0.9524718177627719`\ \[ImaginaryI])\) + 1.`\ \[ExponentialE]\^\(3.152380053229623`\ \[ImaginaryI]\ \ t\) + \((\(\(0.002146213838154912`\)\(\[InvisibleSpace]\)\) - 0.0029397278326011474`\ \[ImaginaryI])\)\ \ \[ExponentialE]\^\(\((\(\(0.125`\)\(\[InvisibleSpace]\)\) + \ 1.5761900266148114`\ \[ImaginaryI])\)\ t\)\ Cos[ 5.`\ t] + \ \((\(\(0.03863184908678842`\)\(\[InvisibleSpace]\)\) - 0.05291510098682066`\ \[ImaginaryI])\)\ \[ExponentialE]\ \^\(\((\(\(0.125`\)\(\[InvisibleSpace]\)\) + 1.5761900266148114`\ \ \[ImaginaryI])\)\ t\)\ Sin[5.`\ t])\)}}\)], "Output"] }, Open ]], Cell["Allpool defineerime suuruse fun listi abil. ", "Text"], Cell[BoxData[ \(fun := \(\(difvor[\([1]\)]\)[\([1]\)]\)[\([2]\)]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[fun, {t, 0, 50}, PlotRange \[Rule] All]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0190476 0.2687 0.237864 [ [.21429 .2562 -6 -9 ] [.21429 .2562 6 0 ] [.40476 .2562 -6 -9 ] [.40476 .2562 6 0 ] [.59524 .2562 -6 -9 ] [.59524 .2562 6 0 ] [.78571 .2562 -6 -9 ] [.78571 .2562 6 0 ] [.97619 .2562 -6 -9 ] [.97619 .2562 6 0 ] [.01131 .03084 -12 -4.5 ] [.01131 .03084 0 4.5 ] [.01131 .14977 -24 -4.5 ] [.01131 .14977 0 4.5 ] [.01131 .38763 -18 -4.5 ] [.01131 .38763 0 4.5 ] [.01131 .50656 -6 -4.5 ] [.01131 .50656 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .2687 m .21429 .27495 L s [(10)] .21429 .2562 0 1 Mshowa .40476 .2687 m .40476 .27495 L s [(20)] .40476 .2562 0 1 Mshowa .59524 .2687 m .59524 .27495 L s [(30)] .59524 .2562 0 1 Mshowa .78571 .2687 m .78571 .27495 L s [(40)] .78571 .2562 0 1 Mshowa .97619 .2687 m .97619 .27495 L s [(50)] .97619 .2562 0 1 Mshowa .125 Mabswid .0619 .2687 m .0619 .27245 L s .1 .2687 m .1 .27245 L s .1381 .2687 m .1381 .27245 L s .17619 .2687 m .17619 .27245 L s .25238 .2687 m .25238 .27245 L s .29048 .2687 m .29048 .27245 L s .32857 .2687 m .32857 .27245 L s .36667 .2687 m .36667 .27245 L s .44286 .2687 m .44286 .27245 L s .48095 .2687 m .48095 .27245 L s .51905 .2687 m .51905 .27245 L s .55714 .2687 m .55714 .27245 L s .63333 .2687 m .63333 .27245 L s .67143 .2687 m .67143 .27245 L s .70952 .2687 m .70952 .27245 L s .74762 .2687 m .74762 .27245 L s .82381 .2687 m .82381 .27245 L s .8619 .2687 m .8619 .27245 L s .9 .2687 m .9 .27245 L s .9381 .2687 m .9381 .27245 L s .25 Mabswid 0 .2687 m 1 .2687 L s .02381 .03084 m .03006 .03084 L s [(-1)] .01131 .03084 1 0 Mshowa .02381 .14977 m .03006 .14977 L s [(-0.5)] .01131 .14977 1 0 Mshowa .02381 .38763 m .03006 .38763 L s [(0.5)] .01131 .38763 1 0 Mshowa .02381 .50656 m .03006 .50656 L s [(1)] .01131 .50656 1 0 Mshowa .125 Mabswid .02381 .05462 m .02756 .05462 L s .02381 .07841 m .02756 .07841 L s .02381 .1022 m .02756 .1022 L s .02381 .12598 m .02756 .12598 L s .02381 .17355 m .02756 .17355 L s .02381 .19734 m .02756 .19734 L s .02381 .22113 m .02756 .22113 L s .02381 .24491 m .02756 .24491 L s .02381 .29249 m .02756 .29249 L s .02381 .31627 m .02756 .31627 L s .02381 .34006 m .02756 .34006 L s .02381 .36385 m .02756 .36385 L s .02381 .41142 m .02756 .41142 L s .02381 .4352 m .02756 .4352 L s .02381 .45899 m .02756 .45899 L s .02381 .48278 m .02756 .48278 L s .02381 .00705 m .02756 .00705 L s .02381 .53035 m .02756 .53035 L s .02381 .55414 m .02756 .55414 L s .02381 .57792 m .02756 .57792 L s .02381 .60171 m .02756 .60171 L s .25 Mabswid .02381 0 m .02381 .61803 L s .5 Mabswid .02381 .03084 m .03279 .30233 L .03543 .38938 L .03793 .46426 L .04037 .52442 L .04262 .56541 L .04377 .58055 L .045 .59223 L .04622 .59965 L .04692 .60205 L .04758 .6032 L .04826 .60332 L .04891 .60248 L .05013 .59865 L .05145 .59163 L .05288 .58108 L .05528 .55781 L .05784 .52591 L .06244 .44768 L .06791 .3162 L .07382 .15728 L .07654 .09733 L .07802 .07117 L .07941 .05145 L .08059 .03825 L .08186 .02767 L .08258 .02318 L .08326 .01988 L .08454 .01599 L .08569 .01472 L .08696 .01535 L .0876 .01636 L .08828 .01791 L .08953 .0218 L .0907 .02666 L .09193 .03301 L .09414 .0478 L .09672 .07211 L .09913 .10325 L .10176 .14784 L .10458 .20589 L .10955 .31723 L .11228 .37041 L .11482 .40907 L .11615 .42437 L .11757 .4372 L .11838 .44297 L .11915 .44751 L .11985 .45093 L .1206 .45389 L Mistroke .12192 .45769 L .12315 .45987 L .1239 .46069 L .12461 .46115 L .12593 .46131 L .1271 .46069 L .12838 .45912 L .12903 .45791 L .12972 .45625 L .13097 .45215 L .13222 .44635 L .1334 .43901 L .13561 .41964 L .13688 .40503 L .13822 .38679 L .14063 .34795 L .14608 .24863 L .14847 .21015 L .15098 .17806 L .15313 .15816 L .15434 .14968 L .15547 .1433 L .15804 .13279 L .16037 .12607 L .16166 .12296 L .16305 .12001 L .16437 .11778 L .16559 .11645 L .16664 .11609 L .16778 .11681 L .16885 .11879 L .16982 .12189 L .17097 .12727 L .17221 .13545 L .17339 .14543 L .17448 .15657 L .18388 .28802 L .18613 .31376 L .1885 .33421 L .18975 .34237 L .1911 .34969 L .19349 .3598 L .19822 .37694 L .20028 .38437 L .20137 .38792 L .20252 .39108 L .20318 .39249 L .2039 .39362 L .20517 .39429 L .20646 .39292 L Mistroke .20768 .38948 L .20839 .38643 L .20906 .3828 L .21033 .37414 L .21319 .34688 L .21839 .28493 L .22085 .25919 L .22311 .24069 L .22549 .22668 L .22806 .21596 L .23271 .19892 L .23759 .17704 L .23892 .17161 L .23966 .16907 L .24035 .16708 L .241 .16565 L .2417 .16462 L .24294 .1643 L .24401 .16573 L .24519 .16924 L .24642 .17506 L .24758 .1824 L .25188 .22039 L .25425 .24321 L .25678 .26437 L .258 .27272 L .25916 .27936 L .26133 .28886 L .26358 .296 L .26603 .303 L .2687 .3125 L .27117 .32396 L .27377 .33755 L .2762 .34873 L .27742 .35272 L .27874 .35521 L .27948 .35567 L .28019 .35541 L .28083 .35459 L .28153 .35305 L .28278 .34861 L .28397 .34265 L .28618 .32794 L .28876 .30786 L .29113 .29028 L .29322 .2777 L .29541 .26821 L .29655 .26469 L .29762 .26208 L .30003 .25736 L Mistroke .30248 .25204 L .30371 .24838 L .30506 .24334 L .3079 .22956 L .31052 .21505 L .31179 .2086 L .31299 .2034 L .31365 .20106 L .31438 .19903 L .31564 .19693 L .31685 .19682 L .31813 .19877 L .31934 .20247 L .32044 .2072 L .33902 .27283 L .34389 .2923 L .34655 .30721 L .34785 .31412 L .34903 .3196 L .35012 .32362 L .35115 .32631 L .35224 .32782 L .35343 .32782 L .35464 .32607 L .35593 .32244 L .35704 .31814 L .35825 .31246 L .36077 .29947 L .36342 .28736 L .36481 .28274 L .36559 .28077 L .36632 .27934 L .36761 .27774 L .36833 .27726 L .36899 .27704 L .3702 .27697 L .37148 .27702 L .37214 .27696 L .37288 .27672 L .37417 .27566 L .37539 .27368 L .3767 .27028 L .37794 .26585 L .37907 .26084 L .38385 .2352 L .38522 .2288 L .38652 .22416 L .38768 .22142 L .38893 .22017 L .39004 .22058 L Mistroke .39125 .22255 L .39252 .22608 L .3937 .23042 L .3958 .2394 L .39808 .2488 L .39948 .25335 L .40078 .25636 L .40201 .25807 L .40332 .25869 L .40449 .25841 L .40559 .25766 L .40679 .25663 L .4081 .25567 L .40941 .25535 L .41012 .25559 L .41079 .25614 L .41198 .25801 L .41326 .26133 L .41398 .2638 L .41476 .26691 L .41617 .27355 L .41882 .28764 L .42118 .29912 L .42186 .30178 L .42251 .30392 L .42372 .30683 L .42486 .30814 L .42591 .30808 L .42707 .3067 L .4283 .30391 L .43872 .27762 L .43996 .27849 L .44128 .28018 L .4425 .28206 L .44365 .28374 L .44495 .2851 L .44613 .28551 L .44744 .28473 L .44817 .28365 L .44885 .28222 L .45017 .27833 L .45161 .2725 L .45455 .25788 L .45595 .25088 L .45728 .24504 L .45847 .24088 L .45978 .23785 L .46099 .23658 L .46228 .23692 L .46351 .23868 L Mistroke .46461 .24129 L .46711 .24924 L .46843 .25362 L .46981 .25767 L .47102 .26032 L .47233 .26204 L .47353 .26244 L .47465 .26184 L .47581 .26039 L .47686 .25853 L .47921 .25366 L .48035 .25166 L .48155 .25024 L .48258 .24983 L .48371 .2504 L .48492 .25229 L .48623 .25581 L .48746 .26036 L .4886 .26534 L .49099 .27698 L .49217 .28247 L .49325 .28693 L .49422 .29023 L .49528 .29292 L .49635 .29453 L .49748 .29499 L .49866 .29415 L .49993 .29193 L .50113 .28888 L .50222 .28559 L .50465 .27815 L .50531 .2764 L .50602 .27479 L .50729 .27272 L .50856 .27187 L .50975 .27222 L .51082 .27344 L .51197 .27554 L .51427 .28111 L .51539 .28386 L .51641 .28601 L .51762 .28783 L .51892 .28857 L .51959 .28838 L .52033 .28769 L .52102 .28658 L .52166 .28517 L .52294 .28132 L .52435 .27579 L .5272 .26274 L Mistroke .52846 .25729 L .52967 .25289 L .53033 .25092 L .53105 .24919 L .53232 .24735 L .53352 .24703 L .5348 .24817 L .53602 .25044 L .53711 .25323 L .53963 .26071 L .54086 .26405 L .54198 .26647 L .54316 .26812 L .54443 .26868 L .5451 .26845 L .54582 .26781 L .54713 .26568 L .55151 .25401 L .55271 .25124 L .554 .24924 L .55522 .24858 L .55634 .24918 L .55756 .25116 L .55825 .25286 L .55889 .25479 L .56158 .26539 L .56308 .27201 L .5645 .2778 L .56577 .28209 L .56649 .28398 L .56715 .28534 L .56827 .28671 L .5695 .28685 L .57078 .28556 L .57199 .28322 L .57467 .27576 L .57597 .272 L .57716 .26911 L .5784 .26693 L .57956 .26592 L .5808 .26607 L .58149 .26671 L .58213 .26762 L .58339 .27024 L .58477 .27405 L .58622 .27856 L .58755 .28251 L .58882 .28565 L .59002 .28768 L .59128 .28855 L Mistroke .592 .28838 L .59266 .28781 L .59376 .28595 L .59497 .28273 L .59742 .27354 L .59967 .26424 L .60089 .25979 L .60203 .25647 L .60326 .25404 L .60392 .25331 L .60461 .25296 L .60586 .25346 L .60699 .25502 L .60814 .25752 L .6092 .26039 L .6116 .26742 L .61269 .27021 L .61372 .27226 L .61478 .27362 L .61596 .27407 L .61721 .27326 L .61791 .27225 L .61854 .27102 L .61978 .2679 L .62094 .26434 L .62232 .25982 L .62378 .25532 L .62502 .25221 L .62572 .2509 L .62638 .25003 L .62758 .24943 L .62867 .25005 L .62994 .25213 L .63113 .2553 L .63362 .26443 L .63626 .27464 L .63732 .27797 L .63846 .28067 L .63971 .28236 L .64089 .28266 L .64203 .28177 L .64312 .27997 L .64409 .27771 L .64516 .27476 L .64758 .26761 L .64822 .26592 L .64891 .26432 L .65016 .26219 L .65143 .26125 L .6526 .2616 L Mistroke .65367 .26295 L .65481 .26532 L .65714 .27236 L .65837 .27656 L .65967 .28075 L .66081 .28379 L .66207 .28615 L .66321 .28716 L .66428 .287 L .66493 .28639 L .66562 .28532 L .66684 .28247 L .66816 .27829 L .6696 .27291 L .6709 .26788 L .67213 .26347 L .67334 .2599 L .67444 .25751 L .67551 .25617 L .67664 .25588 L .67778 .25673 L .67903 .25885 L .68025 .26186 L .68157 .26572 L .6827 .26918 L .68394 .27268 L .68517 .27549 L .68631 .27719 L .6874 .27785 L .68856 .27742 L .6897 .27588 L .69077 .27352 L .69277 .2674 L .69503 .25963 L .69627 .25588 L .69744 .25314 L .69811 .25204 L .69883 .25128 L .70009 .25109 L .70138 .25241 L .70256 .25488 L .70747 .27182 L .70882 .27603 L .70953 .27781 L .71027 .27927 L .71092 .28018 L .71164 .28075 L .71289 .28063 L .71407 .27928 L .71514 .27715 L Mistroke .71637 .27389 L .71754 .27036 L .71964 .26403 L .72069 .26141 L .72186 .25933 L .72309 .25828 L .72424 .25848 L .72529 .25968 L .72643 .26197 L .72775 .2657 L .72901 .26993 L .73137 .27808 L .73251 .28137 L .73373 .284 L .73489 .28537 L .73595 .28556 L .73713 .28456 L .73841 .2821 L .73906 .28039 L .73976 .2783 L .74101 .27401 L .74233 .26918 L .74377 .26424 L .74443 .26225 L .74512 .26042 L .74637 .25802 L .74757 .25696 L .7487 .25713 L .74993 .25857 L .75062 .2599 L .75125 .26138 L .75344 .2678 L .75577 .27487 L .75646 .2766 L .75711 .27796 L .75832 .27969 L .75946 .28019 L .76069 .27943 L .76178 .2777 L .76297 .27479 L .76537 .26687 L .7676 .25925 L .76858 .2565 L .76967 .2542 L .77088 .25276 L .77218 .2527 L .77286 .25329 L .77359 .25437 L .77428 .25579 L .77491 .25738 L Mistroke .77728 .2651 L .77854 .26958 L .77988 .27398 L .78111 .27725 L .78223 .2793 L .78335 .2803 L .78441 .2802 L .78561 .27893 L .7867 .27678 L .78791 .27358 L .78919 .26962 L .79167 .26193 L .79238 .26012 L .79306 .25868 L .79433 .25691 L .79553 .25649 L .79664 .25724 L .79785 .25927 L .79915 .26261 L .80211 .27273 L .80357 .27757 L .8042 .27941 L .8049 .28114 L .80612 .2833 L .8074 .2842 L .80808 .28406 L .8088 .28345 L .8101 .28124 L .81506 .26542 L .81626 .26181 L .81756 .25888 L .8183 .25778 L .81898 .25718 L .81966 .257 L .82031 .25721 L .821 .25784 L .82174 .25895 L .82244 .26036 L .82307 .26192 L .82607 .27129 L .82739 .27535 L .82808 .27721 L .82881 .27887 L .82946 .28002 L .83016 .28091 L .8314 .28145 L .83204 .28118 L .83275 .28047 L .83402 .27812 L .83527 .27475 L Mistroke .83642 .27096 L .83898 .26201 L .84034 .25799 L .84111 .25622 L .84181 .25499 L .84299 .25386 L .84424 .25405 L .84533 .25536 L .84652 .25788 L .84778 .26148 L .84912 .26599 L .85153 .27407 L .85276 .27733 L .85346 .27873 L .85412 .2797 L .85544 .28052 L .85618 .2803 L .85686 .27967 L .85806 .27764 L .85938 .27431 L .86177 .26663 L .8632 .26209 L .86456 .2586 L .8653 .25717 L .86611 .25611 L .86685 .25564 L .86753 .25563 L .86876 .25669 L .86947 .25787 L .87012 .25931 L .87287 .26787 L .87412 .27231 L .87548 .27678 L .87677 .28017 L .87796 .28226 L .87903 .28311 L .88021 .28284 L .88144 .28124 L .88259 .27867 L .885 .27111 L .88757 .26264 L .88833 .2606 L .88905 .25901 L .8897 .25792 L .89039 .25712 L .89106 .25675 L .89176 .25679 L .89301 .25795 L .89418 .26018 L .89544 .26354 L Mistroke .89771 .27095 L .89909 .27537 L .9004 .27883 L .90158 .28097 L .90286 .28201 L .9041 .28162 L .90481 .28078 L .90547 .27962 L .9068 .27633 L .90824 .27172 L .91062 .26342 L .91188 .25958 L .91257 .25783 L .91322 .2565 L .9145 .25489 L .91566 .25468 L .91674 .25559 L .91792 .25769 L .91917 .26096 L .9205 .26521 L .92288 .27323 L .92392 .27627 L .92505 .27881 L .92612 .28033 L .92709 .28086 L .92823 .28041 L .92947 .27864 L .93065 .27592 L .93174 .27272 L .93421 .26448 L .93555 .2604 L .93681 .25744 L .93747 .25635 L .93818 .25558 L .93896 .25523 L .93967 .2554 L .94032 .25594 L .94103 .25695 L .94231 .25976 L .94713 .27566 L .94831 .27889 L .94957 .28133 L .95029 .28214 L .95096 .28247 L .95226 .28195 L .95343 .28025 L .95451 .27774 L .95697 .26997 L .95831 .26543 L .95957 .26159 L Mistroke .9607 .25886 L .96193 .25696 L .96302 .25635 L .96418 .25687 L .96516 .25822 L .96625 .26057 L .96864 .26789 L .97087 .27529 L .97155 .27725 L .9723 .27909 L .973 .28049 L .97365 .28144 L .97488 .28224 L .97619 .28158 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{355.938, 220}, ImageMargins->{{35, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["6.2. Vektorid ja maatriksid.", "Subsubtitle"], Cell["\<\ Vektor on samasugustest elementidest koosnev \[UDoubleDot]herealine list (\ \[UDoubleDot]herealine maatriks). Maatriksil v\[OTilde]ib \ m\[OTilde]\[OTilde]tmeid olla tunduvalt rohkem, kuigi enamkasutatav on kahem\ \[OTilde]\[OTilde]tmeline maatriks.\ \>", "Text"], Cell[TextData[{ "{a, b, c}\t\t\t\t\tvektor (a,b,c) ehk \ \[UDoubleDot]hem\[OTilde]\[OTilde]tmeline 1x3 maatriks\n{{a,b},{c,d}}\t\t\t\t\ \tkahem\[OTilde]\[OTilde]tmeline 2x2 maatriks ", Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"a", "b"}, {"c", "d"} }], ")"}], TraditionalForm]]], " \n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ FormBox[\({{{a\_1, \ a\_2, \ a\_3}, {\), "TraditionalForm"], \(b\_1\)}], ",", " ", \(b\_2\), ",", " ", \(b\_3\)}], "}"}], "}"}], ",", " ", \({{c\_1, \ c\_2\)}], TraditionalForm]]], ", ", Cell[BoxData[ \(TraditionalForm\`\(\(\(\(\(c\_3\)\(}\)\), \ {d\_1, \ d\_2, \ d\_3}\)\(}\)\)\(}\)\)\)]], " \n\t\t\t\t\t\tkolmem\[OTilde]\[OTilde]tmeline 2x2x3-maatriks\nc v\t\t\t\t\ \t\tvektori korrutamine skalaariga\na.b\t\t\t\t\t\tvektorite skalaarkorrutis\n\ Cross[a,b]\t\t\t\t\tvektorite vektorkorrutis" }], "Text", Background->GrayLevel[0.900008]], Cell[BoxData[{ \(\(a = {3, 1, 2};\)\), "\[IndentingNewLine]", \(\(b = {3, \(-2\), 0};\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(a . b\)], "Input"], Cell[BoxData[ \(7\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Cross[a, b]\)], "Input"], Cell[BoxData[ \({4, 6, \(-9\)}\)], "Output"] }, Open ]], Cell["\<\ Juhul, kui nii a kui ka b on m\[OTilde]lemad samade \ m\[OTilde]\[OTilde]tmetega vektorid, t\[ADoubleDot]hendab a b uut vektorit, \ mille komponentideks on vastavate komponentide korrutised. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(a\ b\)], "Input"], Cell[BoxData[ \({9, \(-2\), 0}\)], "Output"] }, Open ]], Cell[BoxData[ \(Clear[a, b, c, v]\)], "Input"], Cell[BoxData[{ \(\(a = {{2, 3, 4}, {\(-1\), 0, 3}};\)\), "\[IndentingNewLine]", \(\(b = {{0, \(-2\)}, {3, 2}, {\(-1\), \(-2\)}};\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[a]\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"2", "3", "4"}, {\(-1\), "0", "3"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[b]\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", \(-2\)}, {"3", "2"}, {\(-1\), \(-2\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(a . b\)], "Input"], Cell[BoxData[ \({{5, \(-6\)}, {\(-3\), \(-4\)}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(b . a\)], "Input"], Cell[BoxData[ \({{2, 0, \(-6\)}, {4, 9, 18}, {0, \(-3\), \(-10\)}}\)], "Output"] }, Open ]], Cell[TextData[StyleBox["Tehted vektoritega:", FontColor->RGBColor[0, 0, 1]]], "Text", FontWeight->"Bold"], Cell[TextData[{ "Table[f, {i,n}]\t\t\t\tn-m\[OTilde]\[OTilde]tmelise vektori loomine \ funktsiooni f abil, i=1,2,...,n\nArray[a,n]\t\t\t\t\ n-m\[OTilde]\[OTilde]tmelise vektori loomine kujul {a[1], a[2], ..., a[n]}\n\ Range[n]\t\t\t\tlisti {1,2,...,n} loomine\n", Cell[BoxData[ \(TraditionalForm\`Range[\(n\_\(\(1\)\(,\)\)\) n\_2]\)]], "\t\t\t\tlisti ", Cell[BoxData[ \(TraditionalForm\`\(\({\(n\_\(\(1\)\(,\)\(\ \)\)\) n\_1 + 1, \ ... , \ n\_2 - 1, \ n\_2}\)\(\ \)\)\)]], "loomine\n", Cell[BoxData[ \(TraditionalForm\`Range[n\_1, \ n\_2, \ dn]\)]], "\t\t\tlisti ", Cell[BoxData[ \(TraditionalForm\`\(\({n\_1, \ n\_1 + dn, \ ... , \ n\_2 - dn, \ n\_2}\)\(\ \)\)\)]], " loomine\nlist[[i]] ehk Part[list, i]\t\t\tannab listi ", StyleBox["i", FontSlant->"Italic"], "-nda elemendi\nLength[list]\t\t\t\tannab listis olevate elementide arvu\n\ ColumnForm[list]\t\t\tn\[ADoubleDot]itab vektorit ekraanil \[UDoubleDot]hes \ veerus" }], "Text", Background->GrayLevel[0.900008]], Cell[TextData[StyleBox["Tehted maatriksitega:", FontWeight->"Bold"]], "Text", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "Table[f, {i,n},{j,n}]\t\t\tm \[Times] n maatriksi loomine funktsiooni f \ abil\nArray[a,{m,n}]\t\t\tm \[Times] n maatriksi loomine, kus maatriksi i-nda \ rea j-nda veeru element\n\t\t\t\t\tantakse kujul a[i,j]\nIdentityMatrix[n]\t\t\ \tn \[Times] n \[UDoubleDot]hikmaatriksi loomine\nDiagonalMatrix[list]\t\t\t\ luuakse ruutmaatriks, mille diagonaalil on listi elemendid\nlist[[i]]\tehk \ Part[list,i]\t\t\tantakse maatriksi ", StyleBox["list", FontSlant->"Italic"], " i-rida\nlist[[i,j]] ehk Part[list,i,j]\t\tantakse listi ", StyleBox["i", FontSlant->"Italic"], "-nda rea ", StyleBox["j-", FontSlant->"Italic"], "nda veeru element\nDimensions[list]\t\t\tannab listi dimensioonid\n\ MatrixForm[list]\t\t\tmaatriks kuvatakse ekraanile maatriksina\nc m\t\t\t\t\t\ maatriksi m korrutamine skalaariga c \na.b \t\t\t\t\tmaatriksite korrutamine\n\ Inverse[m]\t\t\t\tp\[ODoubleDot]\[ODoubleDot]rdmaatriksi leidmine\n\ MatrixPower[m,n]\t\t\tmaatriksi m ", StyleBox["n-s", FontSlant->"Italic"], " aste\nDet[m]\t\t\t\t\tdeterminant\nTr[m]\t\t\t\t\tmaatriksi \ j\[ADoubleDot]lg\nTranspose[m]\t\t\t\ttransponeeritud maatriksi leidmine\n\ Eigenvalues[m]\t\t\tmaatriksi omav\[ADoubleDot]\[ADoubleDot]rtuste leidmine\n\ Eigenvectors[\t\t\t\tomavektorite leidmine\nEigenvalues[N[m]], \ Eigenvectors[N[m]]\tnumbrilised omav\[ADoubleDot]\[ADoubleDot]rtused ja \ omavektorid" }], "Text", Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[ \(mx = Table[s\^\(i - j\), {i, 3}, {j, 4}]\)], "Input"], Cell[BoxData[ \({{1, 1\/s, 1\/s\^2, 1\/s\^3}, {s, 1, 1\/s, 1\/s\^2}, {s\^2, s, 1, 1\/s}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[mx]\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", \(1\/s\), \(1\/s\^2\), \(1\/s\^3\)}, {"s", "1", \(1\/s\), \(1\/s\^2\)}, {\(s\^2\), "s", "1", \(1\/s\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(sx = Table[i - j, {i, 4}, {j, 3}]\)], "Input"], Cell[BoxData[ \({{0, \(-1\), \(-2\)}, {1, 0, \(-1\)}, {2, 1, 0}, {3, 2, 1}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[sx]\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", \(-1\), \(-2\)}, {"1", "0", \(-1\)}, {"2", "1", "0"}, {"3", "2", "1"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(mx . sx\)], "Input"], Cell[BoxData[ \({{3\/s\^3 + 2\/s\^2 + 1\/s, \(-1\) + 2\/s\^3 + 1\/s\^2, \(-2\) + 1\/s\^3 - 1\/s}, {1 + 3\/s\^2 + 2\/s, 2\/s\^2 + 1\/s - s, \(-1\) + 1\/s\^2 - 2\ s}, {2 + 3\/s + s, 1 + 2\/s - s\^2, 1\/s - s - 2\ s\^2}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[%]\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(3\/s\^3 + 2\/s\^2 + 1\/s\), \(\(-1\) + 2\/s\^3 + 1\/s\^2\), \(\(-2\) + 1\/s\^3 - 1\/s\)}, {\(1 + 3\/s\^2 + 2\/s\), \(2\/s\^2 + 1\/s - s\), \(\(-1\) + 1\/s\^2 - 2\ s\)}, {\(2 + 3\/s + s\), \(1 + 2\/s - s\^2\), \(1\/s - s - 2\ s\^2\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[2\ sx]\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", \(-2\), \(-4\)}, {"2", "0", \(-2\)}, {"4", "2", "0"}, {"6", "4", "2"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Det[mx . sx]\)], "Input"], Cell[BoxData[ \(0\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Tr[mx . sx]\)], "Input"], Cell[BoxData[ \(3\/s\^3 + 4\/s\^2 + 3\/s - 2\ s - 2\ s\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Eigenvectors[mx . sx]\)], "Input"], Cell[BoxData[ \({{\(-\(\(1 - s\^2 - 2\ s\^3\)\/\(3 + 2\ s + s\^2\)\)\), 0, 1}, {\(-\(\(2 + s - s\^3\)\/\(3 + 2\ s + s\^2\)\)\), 1, 0}, {1\/s\^2, 1\/s, 1}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Eigenvalues[mx . sx]\)], "Input"], Cell[BoxData[ \({0, 0, \(3 + 4\ s + 3\ s\^2 - 2\ s\^4 - 2\ s\^5\)\/s\^3}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ahaa = {{2, 3}, {1, 7}}\)], "Input"], Cell[BoxData[ \({{2, 3}, {1, 7}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Eigenvalues[N[ahaa]]\)], "Input"], Cell[BoxData[ \({7.54138126514911`, 1.4586187348508903`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Eigenvectors[N[ahaa]]\)], "Input"], Cell[BoxData[ \({{\(-0.47608908969149805`\), \(-0.8793970540527872`\)}, \ {\(-0.9841042271508811`\), 0.17759186384451034`}}\)], "Output"] }, Open ]], Cell[TextData[{ "Seega saame maatriksi ahaa avaldada omav\[ADoubleDot]\[ADoubleDot]rtuste \ ja omavektorite abil j\[ADoubleDot]rgmiselt:\n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"(", GridBox[{ {"2", "3"}, {"1", "7"} }], ")"}], RowBox[{"(", GridBox[{ {\(-0.4761\)}, {\(-0.8794\)} }], ")"}]}], "=", RowBox[{"7.54138", RowBox[{"(", GridBox[{ {\(-0.4761\)}, {\(-0.8794\)} }], ")"}], " "}]}], TraditionalForm]]], " ning\n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"(", GridBox[{ {"2", "3"}, {"1", "7"} }], ")"}], RowBox[{"(", GridBox[{ {\(-0.9841\)}, {\(-0.1776\)} }], ")"}]}], "=", RowBox[{"1.45862", RowBox[{"(", GridBox[{ {\(-0.9841\)}, {\(-0.1776\)} }], ")"}]}]}], TraditionalForm]]] }], "Text"], Cell["\<\ \[CapitalUDoubleDot]lal on toodud kaks erinevat v\[OTilde]imalust maatriksite \ defineerimiseks - Array ning Table abil. Table abil on mugavam luua maatriksit mingi algoritmi j\[ADoubleDot]rgi. \ Array-ga loodud maatriksis on maatriksi elementide muutmine m\[OTilde]neti \ lihtsam (sarnane erinevates programmeerimiskeeltega). Seet\[OTilde]ttu on ka \ Array kasutamine programmeerimisel \[UDoubleDot]sna loomulik.\ \>", "Text"], Cell[BoxData[ \(Clear[s, v, a, b]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(s = Table[i*j, {i, 3}, {j, 3}]\)], "Input"], Cell[BoxData[ \({{1, 2, 3}, {2, 4, 6}, {3, 6, 9}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s[\([2]\)]\)], "Input"], Cell[BoxData[ \({2, 4, 6}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(s[\([2]\)]\)[\([3]\)]\)], "Input"], Cell[BoxData[ \(6\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(s[\([2]\)]\)[\([3]\)] = 2\)], "Input"], Cell[BoxData[ \(Set::"setps" \(\(:\)\(\ \)\) "\!\(s \[LeftDoubleBracket] 2 \[RightDoubleBracket]\) in assignment of \ part is not a symbol."\)], "Message"], Cell[BoxData[ \(2\)], "Output"] }, Open ]], Cell["Nagu n\[ADoubleDot]ha, keelatakse selline omistamine \[ADoubleDot]ra. \ ", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(a = Array[v, {3, 3}]\)], "Input"], Cell[BoxData[ \({{v[1, 1], v[1, 2], v[1, 3]}, {v[2, 1], v[2, 2], v[2, 3]}, {v[3, 1], v[3, 2], v[3, 3]}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(v[1, 1] = 2\)], "Input"], Cell[BoxData[ \(2\)], "Output"] }, Open ]], Cell[BoxData[ \(For[i = 1, i \[LessEqual] 3, i = i + 1, \[IndentingNewLine]For[j = 1, j \[LessEqual] 3, j = j + 1, \[IndentingNewLine]v[i, j] = i*j\[IndentingNewLine]]\[IndentingNewLine]]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(a\)], "Input"], Cell[BoxData[ \({{1, 2, 3}, {2, 4, 6}, {3, 6, 9}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(a[\([2]\)]\)], "Input"], Cell[BoxData[ \({2, 4, 6}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(v[2, 3]\)], "Input"], Cell[BoxData[ \(6\)], "Output"] }, Open ]], Cell["\<\ Selliselt oli ka k\[ADoubleDot]su Array korral maatriksile a v\[OTilde]imalik \ omistada samasuguseid v\[ADoubleDot]\[ADoubleDot]rtusi nagu maatriksis s. \ Erinevalt Table-k\[ADoubleDot]su kasutamisest, saab maatriksi elementide v\ \[ADoubleDot]\[ADoubleDot]rtusi p\[ADoubleDot]rast maatriksi loomist muuta.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ 6.3. Protseduure (ja tehteid) maatriksite ja listide osadega.\ \>", "Subsubtitle"], Cell[TextData[{ "First[list]\t\t\t\tlisti esimene liige\nLast[list]\t\t\t \tlisti viimane \ liige\nPart[list,n] ehk list[[n]]\t\tlisti ", StyleBox["n-s ", FontSlant->"Italic"], "liige\nPart[list,-n] ehk list[[-n]]\t\tlisti tagantpoolt lugedes ", StyleBox["n", FontSlant->"Italic"], "-s liige\n", Cell[BoxData[ \(TraditionalForm\`Part[list, {n\_1, \ n\_2, \ ... }]\)]], "\t\tuus list, mille elementideks on vana listi elemendid\n\t\t\t\t\t\ positsioonidel ", Cell[BoxData[ \(TraditionalForm\`n\_1, \ n\_\(\(2\)\(,\)\) ... \)]], "\nTake[list,n]\t\t\t\tlisti n esimest liiget\nTake[list,-n]\t\t\t\tlisti n \ viimast liiget\nTake[list,{m,n}]\t\t\tlisti liikmed alates ", StyleBox["m", FontSlant->"Italic"], "-ndast kuni ", StyleBox["n", FontSlant->"Italic"], "-ndani (kaasa arvatud)\nTake[list,{m,n,step}]\t\t\tlisti liikmed alates ", StyleBox["m", FontSlant->"Italic"], "-nast kuni ", StyleBox["n-", FontSlant->"Italic"], "ndani sammuga s\nRest[list]\t\t\t\tlist ilma esimese liikmeta\n\ Drop[list,n]\t\t\t\tlist ilma esimese n liikmeta\nDrop[list,-n]\t\t\t\tlist \ ilma viimase n liikmeta\nDrop[list,{m,n}]\t\t\tlist, millest elemendid ", StyleBox["m-", FontSlant->"Italic"], "ndast kuni ", StyleBox["n", FontSlant->"Italic"], "-ndani on \[ADoubleDot]ra j\[ADoubleDot]etud\nDrop[list,{m,n,s}]\t\t\t\ list, millest on v\[ADoubleDot]lja j\[ADoubleDot]etud elemendid ", StyleBox["m", FontSlant->"Italic"], "-ndast kuni ", StyleBox["n", FontSlant->"Italic"], "-ndani\n\t\t\t\t\tsammuga s" }], "Text", Background->GrayLevel[0.900008]], Cell[BoxData[ \(\($Line = 0;\)\)], "Input"], Cell[BoxData[ \(Clear[a, b, c, d, e, f, g, h, t]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(t = {a, b, c, d, e, f, g}\)], "Input"], Cell[BoxData[ \({a, b, c, d, e, f, g}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Last[t]\)], "Input"], Cell[BoxData[ \(g\)], "Output"] }, Open ]], Cell["Leiame listi t 3.nda elemendi", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(t[\([3]\)]\)], "Input"], Cell[BoxData[ \(c\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t[\([{2, 5}]\)]\)], "Input"], Cell[BoxData[ \({b, e}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Take[t, \(-2\)]\)], "Input"], Cell[BoxData[ \({f, g}\)], "Output"] }, Open ]], Cell["\<\ Teeme uue listi, milles on k\[OTilde]ik listi t liikmed, v\[ADoubleDot]lja \ arvatud 4.s\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Drop[t, {4, 4}]\)], "Input"], Cell[BoxData[ \({a, b, c, e, f, g}\)], "Output"] }, Open ]], Cell[TextData[{ "Part[list,i,j,...] ehk list[[i]][[j]][[...]] ehk list[[i,j,...]]\t\n\t\t\t\ listi ", StyleBox["i", FontSlant->"Italic"], "-nda liikme ", StyleBox["j-", FontSlant->"Italic"], "nda alamlisti ... (jne)\n", Cell[BoxData[ \(TraditionalForm\`\(\(Part[ list, {i\_1, \ i\_2, \ ... }, {j\_1, j\_2, \ ... }, ... ]\)\(\ \ \)\)\)]], "v\[OTilde]i ", Cell[BoxData[ \(TraditionalForm\`list[\([{i\_1, i\_2, \ ... }, {j\_1, j\_2, ... }, ... ]\)]\)]], " \n\t\t\tuus list vana listi elemendidest\nPart[list,...,All,...] ehk \ list[[...,All,...]]\n\t\t\tlist elementidest, milles on k\[OTilde]ik antud \ tasandi elemendid sees\nPart[list,All,i] ehk\tlist[[All,i]]\n\t\t\tlisti ", StyleBox["i-", FontSlant->"Italic"], "s veerg" }], "Text", Background->GrayLevel[0.900008]], Cell[BoxData[ \(Clear[t]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(t = {{a, b, c}, {d, e, f}}\)], "Input"], Cell[BoxData[ \({{a, b, c}, {d, e, f}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t[\([2]\)]\)], "Input"], Cell[BoxData[ \({d, e, f}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t[\([2, 3]\)]\)], "Input"], Cell[BoxData[ \(f\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(t[\([2]\)]\)[\([3]\)]\)], "Input"], Cell[BoxData[ \(f\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t[\([{2, 2, 1, 1}]\)]\)], "Input"], Cell[BoxData[ \({{d, e, f}, {d, e, f}, {a, b, c}, {a, b, c}}\)], "Output"] }, Open ]], Cell["\<\ See andis uue listi, milles on kaks korda esitatud vana listi teine rida, \ kaks korda esimene rida.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(t[\([{2, 2, 1, 1}, {2, 3}]\)]\)], "Input"], Cell[BoxData[ \({{e, f}, {e, f}, {b, c}, {b, c}}\)], "Output"] }, Open ]], Cell["\<\ Eelnevast n\[ADoubleDot]itest v\[OTilde]eti k\[OTilde]igist ridadest vaid 2. \ ja 3. element.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(t[\([All, 1]\)]\)], "Input"], Cell[BoxData[ \({a, d}\)], "Output"] }, Open ]], Cell["Leidsime listi (maatriksi) esimese veeru.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(t[\([1]\)]\)], "Input"], Cell[BoxData[ \({a, b, c}\)], "Output"] }, Open ]], Cell["Selliselt leidi maatriksi esimene rida.", "Text"], Cell[BoxData[{ \(\(si\_1 = {{a\_1, a\_2}, {a\_3, a\_4}};\)\), "\[IndentingNewLine]", \(\(si\_2 = {{b\_1, b\_2}, {b\_3, b\_4}};\)\), "\[IndentingNewLine]", \(\(si\_3 = {{c\_1, c\_2}, {c\_3, c\_4}};\)\), "\[IndentingNewLine]", \(\(si\_4 = {{d\_1, d\_2}, {d\_3, d\_4}};\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(s = {{si\_1, si\_2}, {si\_3, si\_4}}\)], "Input"], Cell[BoxData[ \({{{{a\_1, a\_2}, {a\_3, a\_4}}, {{b\_1, b\_2}, {b\_3, b\_4}}}, {{{c\_1, c\_2}, {c\_3, c\_4}}, {{d\_1, d\_2}, {d\_3, d\_4}}}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[s]\)], "Input"], Cell[BoxData[ InterpretationBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", GridBox[{ {\(a\_1\), \(a\_2\)}, {\(a\_3\), \(a\_4\)} }], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {\(b\_1\), \(b\_2\)}, {\(b\_3\), \(b\_4\)} }], "\[NoBreak]", ")"}]}, { RowBox[{"(", "\[NoBreak]", GridBox[{ {\(c\_1\), \(c\_2\)}, {\(c\_3\), \(c\_4\)} }], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {\(d\_1\), \(d\_2\)}, {\(d\_3\), \(d\_4\)} }], "\[NoBreak]", ")"}]} }], "\[NoBreak]", ")"}], MatrixForm[ {{{{ Subscript[ a, 1], Subscript[ a, 2]}, { Subscript[ a, 3], Subscript[ a, 4]}}, {{ Subscript[ b, 1], Subscript[ b, 2]}, { Subscript[ b, 3], Subscript[ b, 4]}}}, {{{ Subscript[ c, 1], Subscript[ c, 2]}, { Subscript[ c, 3], Subscript[ c, 4]}}, {{ Subscript[ d, 1], Subscript[ d, 2]}, { Subscript[ d, 3], Subscript[ d, 4]}}}}]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Part[s, 2]\)], "Input"], Cell[BoxData[ \({{{c\_1, c\_2}, {c\_3, c\_4}}, {{d\_1, d\_2}, {d\_3, d\_4}}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[%]\)], "Input"], Cell[BoxData[ InterpretationBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", GridBox[{ {\(c\_1\)}, {\(c\_2\)} }], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {\(c\_3\)}, {\(c\_4\)} }], "\[NoBreak]", ")"}]}, { RowBox[{"(", "\[NoBreak]", GridBox[{ {\(d\_1\)}, {\(d\_2\)} }], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {\(d\_3\)}, {\(d\_4\)} }], "\[NoBreak]", ")"}]} }], "\[NoBreak]", ")"}], MatrixForm[ {{{ Subscript[ c, 1], Subscript[ c, 2]}, { Subscript[ c, 3], Subscript[ c, 4]}}, {{ Subscript[ d, 1], Subscript[ d, 2]}, { Subscript[ d, 3], Subscript[ d, 4]}}}]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Part[s, 2, 1]\)], "Input"], Cell[BoxData[ \({{c\_1, c\_2}, {c\_3, c\_4}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Part[s, 2, 1, 1]\)], "Input"], Cell[BoxData[ \({c\_1, c\_2}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Part[s, 2, 2, 1, 1]\)], "Input"], Cell[BoxData[ \(d\_1\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Part[s, 2, All, 2]\)], "Input"], Cell[BoxData[ \({{c\_3, c\_4}, {d\_3, d\_4}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Part[s, All, 2]\)], "Input"], Cell[BoxData[ \({{{b\_1, b\_2}, {b\_3, b\_4}}, {{d\_1, d\_2}, {d\_3, d\_4}}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[%]\)], "Input"], Cell[BoxData[ InterpretationBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", GridBox[{ {\(b\_1\)}, {\(b\_2\)} }], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {\(b\_3\)}, {\(b\_4\)} }], "\[NoBreak]", ")"}]}, { RowBox[{"(", "\[NoBreak]", GridBox[{ {\(d\_1\)}, {\(d\_2\)} }], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {\(d\_3\)}, {\(d\_4\)} }], "\[NoBreak]", ")"}]} }], "\[NoBreak]", ")"}], MatrixForm[ {{{ Subscript[ b, 1], Subscript[ b, 2]}, { Subscript[ b, 3], Subscript[ b, 4]}}, {{ Subscript[ d, 1], Subscript[ d, 2]}, { Subscript[ d, 3], Subscript[ d, 4]}}}]]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ 6.4. Listi ja maatriksi elementide otsimine, testimine, asendamine, kustutamine. \ \>", "Subsubtitle"], Cell["\<\ Position[list, form]\t\t\tpositsioonid, milles form listis esineb Count[list,form]\t\t\tmitu korda form listis esineb MemberQ[list,form]\t\t\ttesti, kas form on \[UDoubleDot]ks listi elementidest FreeQ[list,form]\t\t\ttesti, kas form ei ole \[UDoubleDot]ks listi \ elementidest (ei leidu mitte kusagil)\ \>", "Text", Background->GrayLevel[0.900008]], Cell[TextData[{ "Nagu kusagil \[UDoubleDot]leval juba mainitud, kehtivad paljud listide \ kohta k\[ADoubleDot]ivad protseduurid ka algebraliste avaldiste kohta v\ \[OTilde]i muude ", StyleBox["Mathematica", FontSlant->"Italic"], " konstruktsioonide kohta." }], "Text"], Cell[BoxData[ \(\($Line = 0;\)\)], "Input"], Cell[BoxData[ \(Clear[s, t]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(t = {a, b, c, d, a, d, f, e, e, a}\)], "Input"], Cell[BoxData[ \({a, b, c, d, a, d, f, e, e, a}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Count[t, a]\)], "Input"], Cell[BoxData[ \(3\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Position[t, a]\)], "Input"], Cell[BoxData[ \({{1}, {5}, {10}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MemberQ[t, f]\)], "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(FreeQ[t, 0]\)], "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(u = 2 + b + v + m + j*2\/w\)], "Input"], Cell[BoxData[ \(2 + b + m + v + 8\/w\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MemberQ[u, v]\)], "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Take[u, {2, 3}]\)], "Input"], Cell[BoxData[ \(b + m\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Take[u, {3, 5}]\)], "Input"], Cell[BoxData[ \(m + v + 8\/w\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(u[\([5]\)]\)], "Input"], Cell[BoxData[ \(8\/w\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(u[\([5, 1]\)]\)], "Input"], Cell[BoxData[ \(8\)], "Output"] }, Open ]], Cell[TextData[{ "\[CapitalUDoubleDot]laltoodud n\[ADoubleDot]ited algebralistest \ avaldistest m\[OTilde]nede liikmete eraldamise kohta on \[UDoubleDot]snagi \ lihtsad. Kui avaldis (n\[ADoubleDot]iteks m\[OTilde]ne arvutuse tulemus) on \ mitmeid lehek\[UDoubleDot]lgi pikk, ei v\[OTilde]i v\[ADoubleDot]ga kindel \ olla, et programm eraldab sealt t\[OTilde]esti just sellise osa, mida \ eeldaks. Peale selle - \[UDoubleDot]laltoodud u avaldises paistab ka v\ \[ADoubleDot]lja, et kusagil on ", StyleBox["j", FontSlant->"Italic"], "-le omistatud v\[ADoubleDot]\[ADoubleDot]rtus (For-lauses vist) - veel \ \[UDoubleDot]ks probleem, mis v\[OTilde]ib tekkida pika ", StyleBox["Mathematica", FontSlant->"Italic"], " dokumendi loomisel, arvutuste tegemisel." }], "Text"], Cell[TextData[{ "Prepend[list,element]\t\t\tlisab elemendi listi algusesse\n\ Append[list,element]\t\t\tlisab elemendi listi l\[OTilde]ppu\nInsert[list, \ element, i]\t\t\tlisab elemendi listi ", StyleBox["i", FontSlant->"Italic"], "-ndale positsioonile\nInsert[list, element, -i]\t\t\tlisab elemendi listi \ l\[OTilde]pust lugedes ", StyleBox["i", FontSlant->"Italic"], "-ndale positsioonile\nInsert[list,element,{i,j,...}]\t\tlisab elemendi \ listi mitmetesse kohtadesse\nDelete[list,i]\t\t\t\tkustutab listi ", StyleBox["i", FontSlant->"Italic"], "-nda elemendi\n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{ FormBox[\(\(Delete\)\([\)\(list, {{i\_1\)\), "TraditionalForm"], ",", \(j\_1\)}], "}"}], ",", \({i\_2, j\_2}\)}], TraditionalForm]]], ",...}]\tkustutab mitmeid listi elemente\nReplacePart[list,uus,i]\t\t\t\ asendab listis ", StyleBox["i", FontSlant->"Italic"], "-ndal kohal oleva elemendi ", StyleBox["uue-", FontSlant->"Italic"], "ga\nReplacePart[list,uus,-i]\t\tasendab listis tagantpoolt ", StyleBox["i", FontSlant->"Italic"], "-ndal kohal oleva elemendi ", StyleBox["uue", FontSlant->"Italic"], "-ga\nReplacePart[list,uus,{i,j,...}]\t\tasendab listis ", StyleBox["i-", FontSlant->"Italic"], "ndal, ", StyleBox["j", FontSlant->"Italic"], "-ndal ... kohal olevad elemendid ", StyleBox["uue-", FontSlant->"Italic"], "ga" }], "Text", Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[ \(Prepend[{a, b, c}, x]\)], "Input"], Cell[BoxData[ \({x, a, b, c}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Append[%, y]\)], "Input"], Cell[BoxData[ \({x, a, b, c, y}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Insert[%, h, 3]\)], "Input"], Cell[BoxData[ \({x, a, h, b, c, y}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Insert[%, hg, \(-3\)]\)], "Input"], Cell[BoxData[ \({x, a, h, b, hg, c, y}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Delete[%30, {{3}, {2}}]\)], "Input"], Cell[BoxData[ \(Delete::"partw" \(\(:\)\(\ \)\) "Part \!\({3}\) of \!\({\(\({\(\({b\_1, b\_2}\)\), \(\({b\_3, \ b\_4}\)\)}\)\), \(\({\(\({d\_1, d\_2}\)\), \(\({d\_3, d\_4}\)\)}\)\)}\) does \ not exist."\)], "Message"], Cell[BoxData[ \(Delete[{{{b\_1, b\_2}, {b\_3, b\_4}}, {{d\_1, d\_2}, {d\_3, d\_4}}}, {{3}, {2}}]\)], "Output"] }, Open ]], Cell[BoxData[ \(\(uus = {x, a, h, b, hg, c, y};\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(ReplacePart[uus, 2 x, {{2}, {4}}]\)], "Input"], Cell[BoxData[ \({x, 2\ x, h, 2\ x, hg, c, y}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(m = {{1, 0, 0}, {0, 0, 2}, {3, 2, 1}}\)], "Input"], Cell[BoxData[ \({{1, 0, 0}, {0, 0, 2}, {3, 2, 1}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(m = ReplacePart[m, {r, q}, {2, 2}]\)], "Input"], Cell[BoxData[ \({{1, 0, 0}, {0, {r, q}, 2}, {3, 2, 1}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[m]\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "0", "0"}, {"0", \({r, q}\), "2"}, {"3", "2", "1"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`Join[list\_1, \ list\_2, \ ... ]\)]], "\t\t\tlistide \[UDoubleDot]heks liitmine\n", Cell[BoxData[ \(TraditionalForm\`Union[list\_1, \ list\_2, \ ... ]\)]], "\t\t\tlistide liitmine, kusjuures korduvad elemendid eemaldatakse \n\t\t\t\ \t\tja j\[ADoubleDot]rgi j\[ADoubleDot]\[ADoubleDot]nud eemaldatakse\n\ Sort[list]\t\t\t\tlisti elementide sorteerimine kasvavas \ j\[ADoubleDot]rjekorras\nReverse[list]\t\t\t\tlisti elementide \ j\[ADoubleDot]rjekorra p\[ODoubleDot]\[ODoubleDot]ramine\nRotateLeft[list]\t\t\ \tlisti liikmete asukoha nihutamine \[UDoubleDot]he koha v\[OTilde]rra \ vasakule\nRotateLeft[list,n]\t\t\tlisti liikmete asukoha nihutamine n kohta \ vasakule\nRotateRight[list]\t\t\tlisti liikmete asukoha nihutamine \ \[UDoubleDot]he koha v\[OTilde]rra paremale\nRotateRight[list,n]\t\t\tlisti \ liikmete asukoha nihutamine n kohta paremale\nPartition[list,n]\t\t\t\tlisti \ l\[OTilde]hkumine n-elemendilisteks t\[UDoubleDot]kkideks\nPartition[list, n, \ d]\t\t\tlisti l\[OTilde]hkumine n-elemendilisteks t\[UDoubleDot]kkideks \ sammuga d\nApply[Plus, list]\t\t\tlisti k\[OTilde]igi liikmete summa\n\ Apply[Times, list]\t\t\tlisti k\[OTilde]igi liikmete korrutamine\n\ Flatten[list]\t\t\t\tlisti silumine \[UDoubleDot]heks 'vektoriks'\n\ Flatten[list,n]\t\t\t\t\[UDoubleDot]lemisel n astmel olevate listi liikmete \ silumine \[UDoubleDot]heks\nFlattenAt[list,i]\t\t\t\tlisti ", StyleBox["i", FontSlant->"Italic"], "-ndal positsioonil oleva alamlisti silumine \[UDoubleDot]heks" }], "Text", Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[ \(Join[m, uus]\)], "Input"], Cell[BoxData[ \({{1, 0, 0}, {0, {r, q}, 2}, {3, 2, 1}, x, a, h, b, hg, c, y}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Flatten[%]\)], "Input"], Cell[BoxData[ \({1, 0, 0, 0, r, q, 2, 3, 2, 1, x, a, h, b, hg, c, y}\)], "Output"] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"4.2 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 715}}, WindowToolbars->"EditBar", WindowSize->{851, 597}, WindowMargins->{{2, Automatic}, {Automatic, 5}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, Magnification->1.25, StyleDefinitions -> "Classic.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{ "Info3284449932-5100889"->{ Cell[156108, 6046, 405, 10, 82, "Print", CellTags->"Info3284449932-5100889"], Cell[156516, 6058, 1805, 34, 278, "Print", CellTags->"Info3284449932-5100889"]} } *) (*CellTagsIndex CellTagsIndex->{ {"Info3284449932-5100889", 620730, 21179} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1776, 53, 96, 4, 98, "Title"], Cell[1875, 59, 35, 0, 77, "Subtitle"], Cell[1913, 61, 2405, 66, 177, "Text"], Cell[CellGroupData[{ Cell[4343, 131, 38, 1, 45, "Input"], Cell[4384, 134, 35, 1, 40, "Output"] }, Open ]], Cell[4434, 138, 1380, 23, 268, "Text"], Cell[CellGroupData[{ Cell[5839, 165, 44, 0, 77, "Subtitle"], Cell[5886, 167, 84, 1, 72, "Subsubtitle"], Cell[5973, 170, 57, 0, 38, "Text"], Cell[6033, 172, 11423, 308, 126, "Text"], Cell[17459, 482, 176, 4, 61, "Text"], Cell[CellGroupData[{ Cell[17660, 490, 44, 1, 45, "Input"], Cell[17707, 493, 39, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17783, 499, 40, 1, 45, "Input"], Cell[17826, 502, 36, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17899, 508, 40, 1, 46, "Input"], Cell[17942, 511, 57, 1, 40, "Output"] }, Open ]], Cell[18014, 515, 281, 6, 61, "Text"], Cell[CellGroupData[{ Cell[18320, 525, 44, 1, 46, "Input"], Cell[18367, 528, 42, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[18446, 534, 43, 1, 45, "Input"], Cell[18492, 537, 42, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[18571, 543, 40, 1, 45, "Input"], Cell[18614, 546, 42, 1, 40, "Output"] }, Open ]], Cell[18671, 550, 348, 6, 61, "Text"], Cell[CellGroupData[{ Cell[19044, 560, 38, 1, 46, "Input"], Cell[19085, 563, 50, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19172, 569, 45, 1, 46, "Input"], Cell[19220, 572, 56, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19313, 578, 41, 1, 46, "Input"], Cell[19357, 581, 56, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19450, 587, 41, 1, 46, "Input"], Cell[19494, 590, 53, 1, 40, "Output"] }, Open ]], Cell[19562, 594, 318, 5, 61, "Text"], Cell[CellGroupData[{ Cell[19905, 603, 42, 1, 45, "Input"], Cell[19950, 606, 40, 1, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[20027, 612, 39, 1, 45, "Input"], Cell[20069, 615, 41, 1, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[20147, 621, 41, 1, 45, "Input"], Cell[20191, 624, 52, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[20280, 630, 45, 1, 45, "Input"], Cell[20328, 633, 51, 1, 40, "Output"] }, Open ]], Cell[20394, 637, 130, 3, 38, "Text"], Cell[20527, 642, 103, 2, 39, "Text"], Cell[20633, 646, 2084, 63, 417, "Text"], Cell[22720, 711, 467, 11, 85, "Text"], Cell[23190, 724, 115, 3, 39, "Text"], Cell[23308, 729, 754, 22, 138, "Text"], Cell[24065, 753, 249, 5, 61, "Text"], Cell[CellGroupData[{ Cell[24339, 762, 40, 1, 45, "Input"], Cell[24382, 765, 42, 1, 51, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24461, 771, 39, 1, 45, "Input"], Cell[24503, 774, 53, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24593, 780, 60, 1, 45, "Input"], Cell[24656, 783, 53, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24746, 789, 54, 1, 46, "Input"], Cell[24803, 792, 55, 1, 40, "Output"] }, Open ]], Cell[24873, 796, 215, 6, 39, "Text"], Cell[25091, 804, 95, 2, 39, "Text"], Cell[25189, 808, 672, 19, 160, "Text"], Cell[25864, 829, 35, 0, 38, "Text"], Cell[CellGroupData[{ Cell[25924, 833, 59, 1, 45, "Input"], Cell[25986, 836, 56, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[26079, 842, 61, 1, 59, "Input"], Cell[26143, 845, 91, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[26271, 851, 48, 1, 45, "Input"], Cell[26322, 854, 124, 2, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[26483, 861, 52, 0, 72, "Subsubtitle"], Cell[26538, 863, 4056, 119, 189, "Text"], Cell[30597, 984, 2204, 63, 390, "Text"], Cell[32804, 1049, 47, 1, 45, "Input"], Cell[32854, 1052, 35, 0, 38, "Text"], Cell[CellGroupData[{ Cell[32914, 1056, 105, 2, 65, "Input"], Cell[33022, 1060, 110, 2, 60, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[33169, 1067, 42, 1, 45, "Input"], Cell[33214, 1070, 176, 3, 60, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[33427, 1078, 49, 1, 45, "Input"], Cell[33479, 1081, 148, 2, 58, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[33664, 1088, 44, 1, 45, "Input"], Cell[33711, 1091, 84, 1, 58, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[33832, 1097, 41, 1, 45, "Input"], Cell[33876, 1100, 121, 2, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[34034, 1107, 42, 1, 45, "Input"], Cell[34079, 1110, 110, 2, 60, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[34226, 1117, 44, 1, 45, "Input"], Cell[34273, 1120, 110, 2, 60, "Output"] }, Open ]], Cell[34398, 1125, 117, 1, 38, "Text"], Cell[CellGroupData[{ Cell[34540, 1130, 76, 1, 46, "Input"], Cell[34619, 1133, 70, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[34726, 1139, 42, 1, 45, "Input"], Cell[34771, 1142, 150, 2, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[34958, 1149, 46, 1, 45, "Input"], Cell[35007, 1152, 154, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[35198, 1160, 50, 1, 45, "Input"], Cell[35251, 1163, 91, 1, 40, "Output"] }, Open ]], Cell[35357, 1167, 1034, 29, 206, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[36428, 1201, 142, 3, 94, "Subsubtitle"], Cell[36573, 1206, 1274, 34, 183, "Text"], Cell[37850, 1242, 63, 0, 38, "Text"], Cell[CellGroupData[{ Cell[37938, 1246, 54, 1, 46, "Input"], Cell[37995, 1249, 52, 1, 40, "Output"] }, Open ]], Cell[38062, 1253, 192, 4, 38, "Text"], Cell[CellGroupData[{ Cell[38279, 1261, 51, 1, 45, "Input"], Cell[38333, 1264, 71, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[38441, 1270, 63, 1, 45, "Input"], Cell[38507, 1273, 53, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[38597, 1279, 66, 1, 45, "Input"], Cell[38666, 1282, 57, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[38760, 1288, 70, 1, 46, "Input"], Cell[38833, 1291, 58, 1, 40, "Output"] }, Open ]], Cell[38906, 1295, 686, 13, 107, "Text"], Cell[CellGroupData[{ Cell[39617, 1312, 60, 1, 46, "Input"], Cell[39680, 1315, 84, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[39801, 1321, 42, 1, 45, "Input"], Cell[39846, 1324, 85, 1, 40, "Output"] }, Open ]], Cell[39946, 1328, 374, 8, 61, "Text"], Cell[CellGroupData[{ Cell[40345, 1340, 195, 4, 120, "Input"], Cell[40543, 1346, 90, 1, 40, "Output"] }, Open ]], Cell[40648, 1350, 1264, 22, 199, "Text"], Cell[CellGroupData[{ Cell[41937, 1376, 111, 2, 67, "Input"], Cell[42051, 1380, 58, 1, 40, "Output"], Cell[42112, 1383, 54, 1, 40, "Output"] }, Open ]], Cell[42181, 1387, 557, 8, 84, "Text"], Cell[CellGroupData[{ Cell[42763, 1399, 91, 1, 67, "Input"], Cell[42857, 1402, 61, 1, 40, "Output"] }, Open ]], Cell[42933, 1406, 215, 5, 61, "Text"], Cell[43151, 1413, 289, 6, 114, "Text"], Cell[43443, 1421, 304, 5, 61, "Text"], Cell[CellGroupData[{ Cell[43772, 1430, 39, 1, 46, "Input"], Cell[43814, 1433, 53, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[43904, 1439, 51, 1, 46, "Input"], Cell[43958, 1442, 89, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[44084, 1448, 50, 1, 45, "Input"], Cell[44137, 1451, 130, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[44304, 1459, 42, 1, 45, "Input"], Cell[44349, 1462, 88, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[44474, 1468, 44, 1, 45, "Input"], Cell[44521, 1471, 234, 4, 40, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[44804, 1481, 298, 9, 88, "Subsubtitle"], Cell[45105, 1492, 108, 3, 38, "Text"], Cell[45216, 1497, 105, 2, 66, "Input"], Cell[CellGroupData[{ Cell[45346, 1503, 49, 1, 50, "Input"], Cell[45398, 1506, 40, 1, 43, "Output"] }, Open ]], Cell[45453, 1510, 238, 6, 61, "Text"], Cell[CellGroupData[{ Cell[45716, 1520, 56, 1, 50, "Input"], Cell[45775, 1523, 35, 1, 40, "Output"] }, Open ]], Cell[45825, 1527, 575, 14, 84, "Text"], Cell[CellGroupData[{ Cell[46425, 1545, 85, 1, 45, "Input"], Cell[46513, 1548, 40, 1, 40, "Output"] }, Open ]], Cell[46568, 1552, 1087, 35, 229, "Text"], Cell[47658, 1589, 279, 5, 61, "Text"], Cell[47940, 1596, 849, 33, 137, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[48838, 1635, 96, 3, 114, "Subtitle"], Cell[48937, 1640, 115, 3, 94, "Subsubtitle"], Cell[49055, 1645, 53, 1, 45, "Input"], Cell[49111, 1648, 3381, 100, 426, "Text"], Cell[52495, 1750, 64, 1, 38, "Text"], Cell[CellGroupData[{ Cell[52584, 1755, 53, 1, 46, "Input"], Cell[52640, 1758, 41, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[52718, 1764, 43, 1, 45, "Input"], Cell[52764, 1767, 54, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[52855, 1773, 43, 1, 45, "Input"], Cell[52901, 1776, 46, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[52984, 1782, 65, 1, 46, "Input"], Cell[53052, 1785, 50, 1, 40, "Output"] }, Open ]], Cell[53117, 1789, 885, 22, 84, "Text"], Cell[CellGroupData[{ Cell[54027, 1815, 76, 1, 46, "Input"], Cell[54106, 1818, 45, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[54188, 1824, 72, 1, 46, "Input"], Cell[54263, 1827, 35, 1, 40, "Output"] }, Open ]], Cell[54313, 1831, 481, 8, 84, "Text"], Cell[CellGroupData[{ Cell[54819, 1843, 76, 1, 46, "Input"], Cell[54898, 1846, 41, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[54976, 1852, 60, 1, 46, "Input"], Cell[55039, 1855, 41, 1, 40, "Output"] }, Open ]], Cell[55095, 1859, 169, 3, 38, "Text"], Cell[CellGroupData[{ Cell[55289, 1866, 62, 1, 45, "Input"], Cell[55354, 1869, 157, 4, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[55548, 1878, 54, 1, 45, "Input"], Cell[55605, 1881, 228, 5, 40, "Output"] }, Open ]], Cell[55848, 1889, 162, 3, 38, "Text"], Cell[CellGroupData[{ Cell[56035, 1896, 49, 1, 45, "Input"], Cell[56087, 1899, 62, 1, 40, "Output"] }, Open ]], Cell[56164, 1903, 822, 25, 38, "Text"], Cell[56989, 1930, 53, 1, 38, "Text"], Cell[CellGroupData[{ Cell[57067, 1935, 91, 1, 62, "Input"], Cell[57161, 1938, 49, 1, 54, "Output"] }, Open ]], Cell[57225, 1942, 304, 5, 61, "Text"], Cell[CellGroupData[{ Cell[57554, 1951, 80, 1, 64, "Input"], Cell[57637, 1954, 40, 1, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[57714, 1960, 75, 1, 62, "Input"], Cell[57792, 1963, 86, 1, 54, "Output"] }, Open ]], Cell[57893, 1967, 1426, 41, 63, "Text"], Cell[59322, 2010, 19848, 248, 282, 19756, 245, "GraphicsData", "Metafile", \ "Graphics"], Cell[CellGroupData[{ Cell[79195, 2262, 153, 2, 69, "Input"], Cell[79351, 2266, 39, 1, 54, "Output"] }, Open ]], Cell[79405, 2270, 93, 1, 38, "Text"], Cell[CellGroupData[{ Cell[79523, 2275, 87, 1, 59, "Input"], Cell[79613, 2278, 39, 1, 54, "Output"] }, Open ]], Cell[79667, 2282, 245, 4, 61, "Text"], Cell[79915, 2288, 90, 1, 38, "Text"], Cell[80008, 2291, 818, 22, 137, "Text"], Cell[CellGroupData[{ Cell[80851, 2317, 86, 1, 45, "Input"], Cell[80940, 2320, 385, 10, 57, "Output"] }, Open ]], Cell[81340, 2333, 264, 7, 61, "Text"], Cell[CellGroupData[{ Cell[81629, 2344, 42, 1, 45, "Input"], Cell[81674, 2347, 101, 2, 57, "Output"] }, Open ]], Cell[81790, 2352, 383, 8, 61, "Text"], Cell[CellGroupData[{ Cell[82198, 2364, 46, 1, 59, "Input"], Cell[82247, 2367, 43, 1, 55, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[82327, 2373, 54, 1, 45, "Input"], Cell[82384, 2376, 35, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[82456, 2382, 49, 1, 45, "Input"], Cell[82508, 2385, 117, 2, 54, "Message"], Cell[82628, 2389, 216, 3, 40, "Message"], Cell[82847, 2394, 47, 1, 40, "Output"] }, Open ]], Cell[82909, 2398, 212, 4, 61, "Text"], Cell[CellGroupData[{ Cell[83146, 2406, 79, 1, 65, "Input"], Cell[83228, 2409, 80, 1, 58, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[83345, 2415, 54, 1, 45, "Input"], Cell[83402, 2418, 42, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[83481, 2424, 49, 1, 45, "Input"], Cell[83533, 2427, 117, 2, 54, "Message"], Cell[83653, 2431, 216, 3, 40, "Message"], Cell[83872, 2436, 47, 1, 40, "Output"] }, Open ]], Cell[83934, 2440, 54, 0, 38, "Text"], Cell[CellGroupData[{ Cell[84013, 2444, 90, 1, 45, "Input"], Cell[84106, 2447, 40, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[84183, 2453, 66, 1, 56, "Input"], Cell[84252, 2456, 94, 2, 40, "Output"] }, Open ]], Cell[84361, 2461, 59, 1, 38, "Text"], Cell[CellGroupData[{ Cell[84445, 2466, 66, 1, 85, "Input"], Cell[84514, 2469, 41, 1, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[84592, 2475, 37, 1, 45, "Input"], Cell[84632, 2478, 52, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[84721, 2484, 71, 1, 73, "Input"], Cell[84795, 2487, 45, 1, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[84877, 2493, 97, 2, 73, "Input"], Cell[84977, 2497, 98, 2, 67, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[85112, 2504, 37, 1, 45, "Input"], Cell[85152, 2507, 54, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[85243, 2513, 91, 1, 77, "Input"], Cell[85337, 2516, 104, 2, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[85478, 2523, 58, 1, 45, "Input"], Cell[85539, 2526, 108, 2, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[85684, 2533, 56, 0, 72, "Subsubtitle"], Cell[85743, 2535, 99, 2, 66, "Input"], Cell[85845, 2539, 230, 6, 61, "Text"], Cell[86078, 2547, 60, 1, 46, "Input"], Cell[86141, 2550, 196, 4, 61, "Text"], Cell[CellGroupData[{ Cell[86362, 2558, 37, 1, 45, "Input"], Cell[86402, 2561, 52, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[86491, 2567, 39, 1, 45, "Input"], Cell[86533, 2570, 40, 1, 40, "Output"] }, Open ]], Cell[86588, 2574, 83, 1, 38, "Text"], Cell[86674, 2577, 59, 1, 46, "Input"], Cell[CellGroupData[{ Cell[86758, 2582, 37, 1, 45, "Input"], Cell[86798, 2585, 38, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[86873, 2591, 37, 1, 45, "Input"], Cell[86913, 2594, 38, 1, 40, "Output"] }, Open ]], Cell[86966, 2598, 277, 5, 61, "Text"], Cell[CellGroupData[{ Cell[87268, 2607, 52, 1, 45, "Input"], Cell[87323, 2610, 52, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[87412, 2616, 52, 1, 45, "Input"], Cell[87467, 2619, 36, 1, 40, "Output"] }, Open ]], Cell[87518, 2623, 296, 5, 61, "Text"], Cell[87817, 2630, 41, 1, 45, "Input"], Cell[87861, 2633, 56, 1, 46, "Input"], Cell[CellGroupData[{ Cell[87942, 2638, 49, 1, 45, "Input"], Cell[87994, 2641, 36, 1, 40, "Output"] }, Open ]], Cell[88045, 2645, 468, 9, 84, "Text"], Cell[88516, 2656, 41, 1, 45, "Input"], Cell[88560, 2659, 73, 1, 59, "Input"], Cell[CellGroupData[{ Cell[88658, 2664, 45, 1, 45, "Input"], Cell[88706, 2667, 38, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[88781, 2673, 45, 1, 45, "Input"], Cell[88829, 2676, 37, 1, 40, "Output"] }, Open ]], Cell[88881, 2680, 102, 3, 38, "Text"], Cell[88986, 2685, 89, 1, 73, "Input"], Cell[CellGroupData[{ Cell[89100, 2690, 41, 1, 45, "Input"], Cell[89144, 2693, 73, 1, 40, "Output"] }, Open ]], Cell[89232, 2697, 210, 6, 61, "Text"], Cell[89445, 2705, 101, 2, 73, "Input"], Cell[CellGroupData[{ Cell[89571, 2711, 42, 1, 45, "Input"], Cell[89616, 2714, 38, 1, 40, "Output"] }, Open ]], Cell[89669, 2718, 114, 3, 38, "Text"], Cell[89786, 2723, 768, 16, 229, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[90591, 2744, 46, 0, 72, "Subsubtitle"], Cell[90640, 2746, 1491, 46, 130, "Text"], Cell[CellGroupData[{ Cell[92156, 2796, 38, 1, 45, "Input"], Cell[92197, 2799, 35, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[92269, 2805, 45, 1, 45, "Input"], Cell[92317, 2808, 38, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[92392, 2814, 49, 1, 45, "Input"], Cell[92444, 2817, 38, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[92519, 2823, 48, 1, 45, "Input"], Cell[92570, 2826, 39, 1, 40, "Output"] }, Open ]], Cell[92624, 2830, 38, 1, 45, "Input"], Cell[92665, 2833, 164, 5, 38, "Text"], Cell[CellGroupData[{ Cell[92854, 2842, 45, 1, 45, "Input"], Cell[92902, 2845, 40, 1, 40, "Output"] }, Open ]], Cell[92957, 2849, 654, 15, 84, "Text"], Cell[CellGroupData[{ Cell[93636, 2868, 64, 1, 46, "Input"], Cell[93703, 2871, 59, 1, 40, "Output"] }, Open ]], Cell[93777, 2875, 2898, 88, 252, "Text"], Cell[96678, 2965, 299, 7, 61, "Text"], Cell[96980, 2974, 112, 2, 39, "Text"], Cell[97095, 2978, 496, 12, 114, "Text"], Cell[97594, 2992, 238, 4, 61, "Text"], Cell[CellGroupData[{ Cell[97857, 3000, 45, 1, 45, "Input"], Cell[97905, 3003, 78, 1, 44, "Output"] }, Open ]], Cell[97998, 3007, 344, 6, 61, "Text"], Cell[CellGroupData[{ Cell[98367, 3017, 37, 1, 45, "Input"], Cell[98407, 3020, 113, 2, 40, "Output"] }, Open ]], Cell[98535, 3025, 116, 3, 38, "Text"], Cell[CellGroupData[{ Cell[98676, 3032, 56, 1, 45, "Input"], Cell[98735, 3035, 78, 1, 40, "Output"] }, Open ]], Cell[98828, 3039, 290, 9, 38, "Text"], Cell[CellGroupData[{ Cell[99143, 3052, 57, 1, 45, "Input"], Cell[99203, 3055, 58, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[99298, 3061, 57, 1, 45, "Input"], Cell[99358, 3064, 50, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[99445, 3070, 47, 1, 48, "Input"], Cell[99495, 3073, 133, 2, 40, "Output"] }, Open ]], Cell[99643, 3078, 425, 9, 84, "Text"], Cell[CellGroupData[{ Cell[100093, 3091, 72, 1, 46, "Input"], Cell[100168, 3094, 303, 5, 82, "Output"] }, Open ]], Cell[100486, 3102, 158, 3, 38, "Text"], Cell[CellGroupData[{ Cell[100669, 3109, 74, 1, 46, "Input"], Cell[100746, 3112, 318, 5, 61, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[101101, 3122, 60, 1, 45, "Input"], Cell[101164, 3125, 160, 3, 61, "Message"], Cell[101327, 3130, 57, 1, 40, "Output"] }, Open ]], Cell[101399, 3134, 444, 9, 61, "Text"], Cell[CellGroupData[{ Cell[101868, 3147, 60, 1, 45, "Input"], Cell[101931, 3150, 175, 3, 61, "Message"], Cell[102109, 3155, 55, 1, 40, "Output"] }, Open ]], Cell[102179, 3159, 444, 6, 84, "Text"], Cell[102626, 3167, 1635, 45, 229, "Text"], Cell[CellGroupData[{ Cell[104286, 3216, 142, 2, 45, "Input"], Cell[104431, 3220, 118, 2, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[104586, 3227, 143, 2, 45, "Input"], Cell[104732, 3231, 156, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[104925, 3239, 110, 2, 45, "Input"], Cell[105038, 3243, 55, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[105130, 3249, 114, 2, 45, "Input"], Cell[105247, 3253, 102, 2, 54, "Output"] }, Open ]], Cell[105364, 3258, 948, 13, 176, "Text"], Cell[106315, 3273, 49, 1, 45, "Input"], Cell[106367, 3276, 67, 1, 46, "Input"], Cell[CellGroupData[{ Cell[106459, 3281, 59, 1, 45, "Input"], Cell[106521, 3284, 3973, 276, 243, 3850, 272, "GraphicsData", "PostScript", \ "Graphics", ImageCacheValid->False], Cell[110497, 3562, 130, 3, 40, "Output"] }, Open ]], Cell[110642, 3568, 166, 3, 38, "Text"], Cell[CellGroupData[{ Cell[110833, 3575, 66, 1, 45, "Input"], Cell[110902, 3578, 49, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[110988, 3584, 68, 1, 45, "Input"], Cell[111059, 3587, 65, 1, 40, "Output"] }, Open ]], Cell[111139, 3591, 147, 5, 38, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[111335, 3602, 31, 0, 77, "Subtitle"], Cell[111369, 3604, 45, 0, 72, "Subsubtitle"], Cell[111417, 3606, 550, 15, 114, "Text"], Cell[111970, 3623, 47, 1, 45, "Input"], Cell[CellGroupData[{ Cell[112042, 3628, 82, 1, 46, "Input"], Cell[112127, 3631, 5318, 368, 243, 5195, 364, "GraphicsData", "PostScript", \ "Graphics", ImageCacheValid->False], Cell[117448, 4001, 130, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[117615, 4009, 110, 2, 46, "Input"], Cell[117728, 4013, 6430, 386, 243, 6307, 382, "GraphicsData", "PostScript", \ "Graphics", ImageCacheValid->False], Cell[124161, 4401, 130, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[124328, 4409, 45, 1, 45, "Input"], Cell[124376, 4412, 5262, 351, 243, 5139, 347, "GraphicsData", "PostScript", \ "Graphics", ImageCacheValid->False], Cell[129641, 4765, 130, 3, 40, "Output"] }, Open ]], Cell[129786, 4771, 374, 8, 61, "Text"], Cell[130163, 4781, 97, 1, 38, "Text"], Cell[CellGroupData[{ Cell[130285, 4786, 302, 5, 108, "Input"], Cell[130590, 4793, 154, 3, 40, "Message"], Cell[130747, 4798, 162, 3, 40, "Message"], Cell[130912, 4803, 161, 3, 40, "Message"], Cell[131076, 4808, 162, 3, 61, "Message"], Cell[131241, 4813, 7252, 460, 380, 7125, 456, "GraphicsData", "PostScript", \ "Graphics", ImageCacheValid->False], Cell[138496, 5275, 130, 3, 40, "Output"] }, Open ]], Cell[138641, 5281, 391, 6, 84, "Text"], Cell[139035, 5289, 57, 1, 45, "Input"], Cell[CellGroupData[{ Cell[139117, 5294, 309, 6, 87, "Input"], Cell[139429, 5302, 15467, 712, 243, 15344, 708, "GraphicsData", "PostScript", \ "Graphics", ImageCacheValid->False], Cell[154899, 6016, 130, 3, 40, "Output"] }, Open ]], Cell[155044, 6022, 893, 14, 298, "Text"], Cell[155940, 6038, 100, 1, 38, "Text"], Cell[CellGroupData[{ Cell[156065, 6043, 40, 1, 45, "Input"], Cell[156108, 6046, 405, 10, 82, "Print", CellTags->"Info3284449932-5100889"], Cell[156516, 6058, 1805, 34, 278, "Print", CellTags->"Info3284449932-5100889"] }, Open ]], Cell[158336, 6095, 153, 3, 38, "Text"], Cell[CellGroupData[{ Cell[158514, 6102, 44, 0, 72, "Subsubtitle"], Cell[158561, 6104, 276, 7, 68, "Text"], Cell[CellGroupData[{ Cell[158862, 6115, 87, 1, 46, "Input"], Cell[158952, 6118, 21207, 798, 312, 21084, 794, "GraphicsData", "PostScript", \ "Graphics", ImageCacheValid->False], Cell[180162, 6918, 137, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[180336, 6926, 294, 5, 87, "Input"], Cell[180633, 6933, 60250, 1934, 329, 60127, 1930, "GraphicsData", \ "PostScript", "Graphics", ImageCacheValid->False], Cell[240886, 8869, 137, 3, 40, "Output"] }, Open ]], Cell[241038, 8875, 151, 3, 38, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[241226, 8883, 53, 0, 72, "Subsubtitle"], Cell[241282, 8885, 884, 20, 206, "Text"], Cell[CellGroupData[{ Cell[242191, 8909, 123, 2, 45, "Input"], Cell[242317, 8913, 4918, 346, 380, 4787, 342, "GraphicsData", "PostScript", \ "Graphics", ImageCacheValid->False], Cell[247238, 9261, 130, 3, 40, "Output"] }, Open ]], Cell[247383, 9267, 148, 3, 38, "Text"], Cell[CellGroupData[{ Cell[247556, 9274, 209, 3, 66, "Input"], Cell[247768, 9279, 12154, 801, 243, 12031, 797, "GraphicsData", "PostScript", \ "Graphics", ImageCacheValid->False], Cell[259925, 10082, 130, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[260092, 10090, 87, 1, 45, "Input"], Cell[260182, 10093, 8310, 630, 636, 8184, 626, "GraphicsData", "PostScript", \ "Graphics", ImageCacheValid->False], Cell[268495, 10725, 132, 3, 40, "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[268688, 10735, 147, 4, 151, "Subtitle"], Cell[268838, 10741, 836, 20, 132, "Text"], Cell[269677, 10763, 297, 7, 66, "Text"], Cell[CellGroupData[{ Cell[269999, 10774, 89, 1, 45, "Input"], Cell[270091, 10777, 128, 3, 54, "Output"] }, Open ]], Cell[270234, 10783, 89, 1, 38, "Text"], Cell[CellGroupData[{ Cell[270348, 10788, 79, 1, 45, "Input"], Cell[270430, 10791, 128, 3, 54, "Output"] }, Open ]], Cell[270573, 10797, 244, 5, 61, "Text"], Cell[CellGroupData[{ Cell[270842, 10806, 130, 3, 59, "Input"], Cell[270975, 10811, 158, 3, 55, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[271170, 10819, 74, 1, 45, "Input"], Cell[271247, 10822, 128, 2, 55, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[271412, 10829, 122, 2, 45, "Input"], Cell[271537, 10833, 4136, 288, 243, 4008, 284, "GraphicsData", "PostScript", \ "Graphics", ImageCacheValid->False], Cell[275676, 11123, 130, 3, 40, "Output"] }, Open ]], Cell[275821, 11129, 475, 8, 107, "Text"], Cell[276299, 11139, 136, 2, 60, "Input"], Cell[CellGroupData[{ Cell[276460, 11145, 104, 2, 45, "Input"], Cell[276567, 11149, 24458, 567, 243, 4474, 316, "GraphicsData", "PostScript", \ "Graphics"], Cell[301028, 11718, 130, 3, 40, "Output"] }, Open ]], Cell[301173, 11724, 291, 5, 84, "Text"], Cell[CellGroupData[{ Cell[301489, 11733, 213, 4, 66, "Input"], Cell[301705, 11739, 191, 3, 40, "Message"], Cell[301899, 11744, 2210, 37, 229, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[304146, 11786, 148, 2, 66, "Input"], Cell[304297, 11790, 82977, 2298, 243, 24130, 1567, "GraphicsData", \ "PostScript", "Graphics"], Cell[387277, 14090, 130, 3, 40, "Output"] }, Open ]], Cell[387422, 14096, 339, 6, 84, "Text"], Cell[CellGroupData[{ Cell[387786, 14106, 51, 1, 45, "Input"], Cell[387840, 14109, 1451, 21, 187, "Output"] }, Open ]], Cell[389306, 14133, 315, 8, 68, "Text"], Cell[CellGroupData[{ Cell[389646, 14145, 146, 2, 45, "Input"], Cell[389795, 14149, 82977, 2298, 243, 24130, 1567, "GraphicsData", \ "PostScript", "Graphics"], Cell[472775, 16449, 130, 3, 40, "Output"] }, Open ]], Cell[472920, 16455, 50, 1, 45, "Input"], Cell[472973, 16458, 390, 7, 84, "Text"], Cell[CellGroupData[{ Cell[473388, 16469, 147, 3, 46, "Input"], Cell[473538, 16474, 225, 6, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[473800, 16485, 103, 2, 45, "Input"], Cell[473906, 16489, 36045, 791, 243, 6177, 418, "GraphicsData", "PostScript", \ "Graphics"], Cell[509954, 17282, 130, 3, 40, "Output"] }, Open ]], Cell[510099, 17288, 277, 5, 61, "Text"], Cell[CellGroupData[{ Cell[510401, 17297, 80, 1, 45, "Input"], Cell[510484, 17300, 53, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[510574, 17306, 89, 1, 45, "Input"], Cell[510666, 17309, 57, 1, 40, "Output"] }, Open ]], Cell[510738, 17313, 123, 3, 38, "Text"], Cell[CellGroupData[{ Cell[510886, 17320, 265, 5, 67, "Input"], Cell[511154, 17327, 415, 11, 61, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[511606, 17343, 58, 1, 45, "Input"], Cell[511667, 17346, 157, 4, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[511861, 17355, 103, 2, 45, "Input"], Cell[511967, 17359, 23735, 540, 243, 4254, 295, "GraphicsData", "PostScript", \ "Graphics"], Cell[535705, 17901, 130, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[535872, 17909, 103, 2, 45, "Input"], Cell[535978, 17913, 23682, 490, 243, 3420, 235, "GraphicsData", "PostScript", \ "Graphics"], Cell[559663, 18405, 130, 3, 40, "Output"] }, Open ]], Cell[559808, 18411, 156, 3, 38, "Text"], Cell[CellGroupData[{ Cell[559989, 18418, 85, 1, 64, "Input"], Cell[560077, 18421, 148, 2, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[560262, 18428, 39, 1, 45, "Input"], Cell[560304, 18431, 52, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[560393, 18437, 72, 1, 51, "Input"], Cell[560468, 18440, 52, 1, 40, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[560569, 18447, 52, 0, 77, "Subtitle"], Cell[560624, 18449, 45, 0, 72, "Subsubtitle"], Cell[560672, 18451, 47, 1, 45, "Input"], Cell[560722, 18454, 236, 4, 61, "Text"], Cell[CellGroupData[{ Cell[560983, 18462, 46, 1, 45, "Input"], Cell[561032, 18465, 43, 1, 40, "Output"] }, Open ]], Cell[561090, 18469, 197, 4, 61, "Text"], Cell[CellGroupData[{ Cell[561312, 18477, 40, 1, 45, "Input"], Cell[561355, 18480, 47, 1, 44, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[561439, 18486, 37, 1, 45, "Input"], Cell[561479, 18489, 81, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[561597, 18495, 38, 1, 45, "Input"], Cell[561638, 18498, 43, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[561718, 18504, 36, 1, 45, "Input"], Cell[561757, 18507, 52, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[561846, 18513, 37, 1, 45, "Input"], Cell[561886, 18516, 52, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[561975, 18522, 57, 1, 45, "Input"], Cell[562035, 18525, 58, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[562130, 18531, 77, 1, 64, "Input"], Cell[562210, 18534, 52, 1, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[562299, 18540, 77, 1, 64, "Input"], Cell[562379, 18543, 69, 1, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[562485, 18549, 37, 1, 45, "Input"], Cell[562525, 18552, 102, 2, 40, "Output"] }, Open ]], Cell[562642, 18557, 314, 5, 61, "Text"], Cell[CellGroupData[{ Cell[562981, 18566, 57, 1, 46, "Input"], Cell[563041, 18569, 51, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[563129, 18575, 59, 1, 45, "Input"], Cell[563191, 18578, 59, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[563287, 18584, 41, 1, 45, "Input"], Cell[563331, 18587, 56, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[563424, 18593, 64, 1, 45, "Input"], Cell[563491, 18596, 120, 2, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[563648, 18603, 74, 1, 46, "Input"], Cell[563725, 18606, 112, 2, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[563874, 18613, 45, 1, 45, "Input"], Cell[563922, 18616, 362, 11, 98, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[564321, 18632, 55, 1, 45, "Input"], Cell[564379, 18635, 126, 2, 40, "Output"] }, Open ]], Cell[564520, 18640, 1594, 44, 160, "Text"], Cell[566117, 18686, 165, 3, 38, "Text"], Cell[CellGroupData[{ Cell[566307, 18693, 53, 1, 45, "Input"], Cell[566363, 18696, 57, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[566457, 18702, 51, 1, 45, "Input"], Cell[566511, 18705, 40, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[566588, 18711, 53, 1, 45, "Input"], Cell[566644, 18714, 43, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[566724, 18720, 41, 1, 45, "Input"], Cell[566768, 18723, 67, 1, 40, "Output"] }, Open ]], Cell[566850, 18727, 1079, 29, 114, "Text"], Cell[CellGroupData[{ Cell[567954, 18760, 75, 1, 49, "Input"], Cell[568032, 18763, 67, 1, 44, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[568136, 18769, 43, 1, 45, "Input"], Cell[568182, 18772, 44, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[568263, 18778, 46, 1, 45, "Input"], Cell[568312, 18781, 39, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[568388, 18787, 56, 1, 45, "Input"], Cell[568447, 18790, 39, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[568523, 18796, 69, 1, 45, "Input"], Cell[568595, 18799, 35, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[568667, 18805, 49, 1, 45, "Input"], Cell[568719, 18808, 35, 1, 40, "Output"] }, Open ]], Cell[568769, 18812, 370, 6, 61, "Text"], Cell[CellGroupData[{ Cell[569164, 18822, 164, 3, 45, "Input"], Cell[569331, 18827, 149, 2, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[569517, 18834, 75, 1, 45, "Input"], Cell[569595, 18837, 63, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[569695, 18843, 87, 1, 45, "Input"], Cell[569785, 18846, 53, 1, 40, "Output"] }, Open ]], Cell[569853, 18850, 241, 4, 61, "Text"], Cell[CellGroupData[{ Cell[570119, 18858, 87, 1, 45, "Input"], Cell[570209, 18861, 59, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[570305, 18867, 87, 1, 45, "Input"], Cell[570395, 18870, 58, 1, 40, "Output"] }, Open ]], Cell[570468, 18874, 44, 1, 45, "Input"], Cell[CellGroupData[{ Cell[570537, 18879, 200, 4, 87, "Input"], Cell[570740, 18885, 190, 3, 40, "Message"], Cell[570933, 18890, 1006, 18, 103, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[571976, 18913, 40, 1, 45, "Input"], Cell[572019, 18916, 898, 15, 82, "Output"] }, Open ]], Cell[572932, 18934, 60, 0, 38, "Text"], Cell[572995, 18936, 81, 1, 45, "Input"], Cell[CellGroupData[{ Cell[573101, 18941, 77, 1, 45, "Input"], Cell[573181, 18944, 13807, 909, 295, 13684, 905, "GraphicsData", \ "PostScript", "Graphics", ImageCacheValid->False], Cell[586991, 19855, 130, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[587158, 19863, 51, 0, 72, "Subsubtitle"], Cell[587212, 19865, 273, 5, 100, "Text"], Cell[587488, 19872, 1119, 30, 195, "Text"], Cell[588610, 19904, 110, 2, 66, "Input"], Cell[CellGroupData[{ Cell[588745, 19910, 38, 1, 45, "Input"], Cell[588786, 19913, 35, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[588858, 19919, 44, 1, 45, "Input"], Cell[588905, 19922, 48, 1, 40, "Output"] }, Open ]], Cell[588968, 19926, 215, 4, 61, "Text"], Cell[CellGroupData[{ Cell[589208, 19934, 37, 1, 45, "Input"], Cell[589248, 19937, 48, 1, 40, "Output"] }, Open ]], Cell[589311, 19941, 50, 1, 45, "Input"], Cell[589364, 19944, 153, 2, 66, "Input"], Cell[CellGroupData[{ Cell[589542, 19950, 46, 1, 45, "Input"], Cell[589591, 19953, 240, 7, 72, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[589868, 19965, 46, 1, 45, "Input"], Cell[589917, 19968, 260, 8, 90, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[590214, 19981, 38, 1, 45, "Input"], Cell[590255, 19984, 65, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[590357, 19990, 38, 1, 45, "Input"], Cell[590398, 19993, 84, 1, 40, "Output"] }, Open ]], Cell[590497, 19997, 109, 2, 38, "Text"], Cell[590609, 20001, 1042, 25, 341, "Text"], Cell[591654, 20028, 111, 2, 38, "Text"], Cell[591768, 20032, 1455, 29, 459, "Text"], Cell[CellGroupData[{ Cell[593248, 20065, 73, 1, 46, "Input"], Cell[593324, 20068, 115, 2, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[593476, 20075, 47, 1, 45, "Input"], Cell[593526, 20078, 325, 8, 120, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[593888, 20091, 66, 1, 45, "Input"], Cell[593957, 20094, 93, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[594087, 20100, 47, 1, 45, "Input"], Cell[594137, 20103, 304, 9, 108, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[594478, 20117, 40, 1, 45, "Input"], Cell[594521, 20120, 264, 4, 92, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[594822, 20129, 46, 1, 45, "Input"], Cell[594871, 20132, 486, 10, 120, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[595394, 20147, 50, 1, 45, "Input"], Cell[595447, 20150, 304, 9, 108, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[595788, 20164, 45, 1, 45, "Input"], Cell[595836, 20167, 35, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[595908, 20173, 44, 1, 45, "Input"], Cell[595955, 20176, 75, 1, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[596067, 20182, 54, 1, 45, "Input"], Cell[596124, 20185, 190, 3, 58, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[596351, 20193, 53, 1, 45, "Input"], Cell[596407, 20196, 90, 1, 57, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[596534, 20202, 56, 1, 45, "Input"], Cell[596593, 20205, 50, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[596680, 20211, 53, 1, 45, "Input"], Cell[596736, 20214, 74, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[596847, 20220, 54, 1, 45, "Input"], Cell[596904, 20223, 141, 2, 40, "Output"] }, Open ]], Cell[597060, 20228, 1193, 38, 131, "Text"], Cell[598256, 20268, 438, 7, 107, "Text"], Cell[598697, 20277, 50, 1, 45, "Input"], Cell[CellGroupData[{ Cell[598772, 20282, 63, 1, 45, "Input"], Cell[598838, 20285, 67, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[598942, 20291, 43, 1, 45, "Input"], Cell[598988, 20294, 43, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[599068, 20300, 56, 1, 45, "Input"], Cell[599127, 20303, 35, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[599199, 20309, 60, 1, 45, "Input"], Cell[599262, 20312, 166, 3, 40, "Message"], Cell[599431, 20317, 35, 1, 40, "Output"] }, Open ]], Cell[599481, 20321, 88, 1, 38, "Text"], Cell[CellGroupData[{ Cell[599594, 20326, 53, 1, 45, "Input"], Cell[599650, 20329, 130, 2, 61, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[599817, 20336, 44, 1, 45, "Input"], Cell[599864, 20339, 35, 1, 40, "Output"] }, Open ]], Cell[599914, 20343, 231, 4, 129, "Input"], Cell[CellGroupData[{ Cell[600170, 20351, 34, 1, 45, "Input"], Cell[600207, 20354, 67, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[600311, 20360, 43, 1, 45, "Input"], Cell[600357, 20363, 43, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[600437, 20369, 40, 1, 45, "Input"], Cell[600480, 20372, 35, 1, 40, "Output"] }, Open ]], Cell[600530, 20376, 331, 5, 61, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[600898, 20386, 92, 2, 72, "Subsubtitle"], Cell[600993, 20390, 1632, 45, 390, "Text"], Cell[602628, 20437, 47, 1, 45, "Input"], Cell[602678, 20440, 65, 1, 45, "Input"], Cell[CellGroupData[{ Cell[602768, 20445, 58, 1, 45, "Input"], Cell[602829, 20448, 55, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[602921, 20454, 40, 1, 45, "Input"], Cell[602964, 20457, 35, 1, 40, "Output"] }, Open ]], Cell[603014, 20461, 45, 0, 38, "Text"], Cell[CellGroupData[{ Cell[603084, 20465, 43, 1, 45, "Input"], Cell[603130, 20468, 35, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[603202, 20474, 48, 1, 45, "Input"], Cell[603253, 20477, 40, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[603330, 20483, 48, 1, 45, "Input"], Cell[603381, 20486, 40, 1, 40, "Output"] }, Open ]], Cell[603436, 20490, 112, 3, 38, "Text"], Cell[CellGroupData[{ Cell[603573, 20497, 48, 1, 45, "Input"], Cell[603624, 20500, 52, 1, 40, "Output"] }, Open ]], Cell[603691, 20504, 854, 24, 206, "Text"], Cell[604548, 20530, 41, 1, 45, "Input"], Cell[CellGroupData[{ Cell[604614, 20535, 59, 1, 45, "Input"], Cell[604676, 20538, 56, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[604769, 20544, 43, 1, 45, "Input"], Cell[604815, 20547, 43, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[604895, 20553, 46, 1, 45, "Input"], Cell[604944, 20556, 35, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[605016, 20562, 56, 1, 45, "Input"], Cell[605075, 20565, 35, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[605147, 20571, 54, 1, 45, "Input"], Cell[605204, 20574, 78, 1, 40, "Output"] }, Open ]], Cell[605297, 20578, 124, 3, 38, "Text"], Cell[CellGroupData[{ Cell[605446, 20585, 62, 1, 45, "Input"], Cell[605511, 20588, 66, 1, 40, "Output"] }, Open ]], Cell[605592, 20592, 117, 3, 38, "Text"], Cell[CellGroupData[{ Cell[605734, 20599, 48, 1, 45, "Input"], Cell[605785, 20602, 40, 1, 40, "Output"] }, Open ]], Cell[605840, 20606, 57, 0, 38, "Text"], Cell[CellGroupData[{ Cell[605922, 20610, 43, 1, 45, "Input"], Cell[605968, 20613, 43, 1, 40, "Output"] }, Open ]], Cell[606026, 20617, 55, 0, 38, "Text"], Cell[606084, 20619, 301, 4, 108, "Input"], Cell[CellGroupData[{ Cell[606410, 20627, 69, 1, 45, "Input"], Cell[606482, 20630, 171, 2, 61, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[606690, 20637, 46, 1, 45, "Input"], Cell[606739, 20640, 1356, 38, 108, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[608132, 20683, 43, 1, 45, "Input"], Cell[608178, 20686, 105, 2, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[608320, 20693, 46, 1, 45, "Input"], Cell[608369, 20696, 1044, 30, 108, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[609450, 20731, 46, 1, 45, "Input"], Cell[609499, 20734, 62, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[609598, 20740, 49, 1, 45, "Input"], Cell[609650, 20743, 46, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[609733, 20749, 52, 1, 45, "Input"], Cell[609788, 20752, 38, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[609863, 20758, 51, 1, 45, "Input"], Cell[609917, 20761, 62, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[610016, 20767, 48, 1, 45, "Input"], Cell[610067, 20770, 105, 2, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[610209, 20777, 46, 1, 45, "Input"], Cell[610258, 20780, 1044, 30, 108, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[611351, 20816, 113, 3, 94, "Subsubtitle"], Cell[611467, 20821, 361, 7, 114, "Text"], Cell[611831, 20830, 278, 7, 61, "Text"], Cell[612112, 20839, 47, 1, 45, "Input"], Cell[612162, 20842, 44, 1, 45, "Input"], Cell[CellGroupData[{ Cell[612231, 20847, 67, 1, 45, "Input"], Cell[612301, 20850, 64, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[612402, 20856, 44, 1, 45, "Input"], Cell[612449, 20859, 35, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[612521, 20865, 47, 1, 45, "Input"], Cell[612571, 20868, 50, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[612658, 20874, 46, 1, 45, "Input"], Cell[612707, 20877, 38, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[612782, 20883, 44, 1, 45, "Input"], Cell[612829, 20886, 38, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[612904, 20892, 59, 1, 59, "Input"], Cell[612966, 20895, 54, 1, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[613057, 20901, 46, 1, 45, "Input"], Cell[613106, 20904, 38, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[613181, 20910, 48, 1, 45, "Input"], Cell[613232, 20913, 39, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[613308, 20919, 48, 1, 45, "Input"], Cell[613359, 20922, 46, 1, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[613442, 20928, 43, 1, 45, "Input"], Cell[613488, 20931, 38, 1, 54, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[613563, 20937, 46, 1, 45, "Input"], Cell[613612, 20940, 35, 1, 40, "Output"] }, Open ]], Cell[613662, 20944, 782, 15, 107, "Text"], Cell[614447, 20961, 1550, 47, 252, "Text"], Cell[CellGroupData[{ Cell[616022, 21012, 54, 1, 45, "Input"], Cell[616079, 21015, 46, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[616162, 21021, 45, 1, 45, "Input"], Cell[616210, 21024, 49, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[616296, 21030, 48, 1, 45, "Input"], Cell[616347, 21033, 52, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[616436, 21039, 54, 1, 45, "Input"], Cell[616493, 21042, 56, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[616586, 21048, 56, 1, 45, "Input"], Cell[616645, 21051, 228, 4, 61, "Message"], Cell[616876, 21057, 127, 2, 40, "Output"] }, Open ]], Cell[617018, 21062, 66, 1, 45, "Input"], Cell[CellGroupData[{ Cell[617109, 21067, 67, 1, 45, "Input"], Cell[617179, 21070, 62, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[617278, 21076, 70, 1, 45, "Input"], Cell[617351, 21079, 67, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[617455, 21085, 67, 1, 45, "Input"], Cell[617525, 21088, 72, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[617634, 21094, 46, 1, 45, "Input"], Cell[617683, 21097, 273, 8, 90, "Output"] }, Open ]], Cell[617971, 21108, 1614, 27, 390, "Text"], Cell[CellGroupData[{ Cell[619610, 21139, 45, 1, 45, "Input"], Cell[619658, 21142, 101, 2, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[619796, 21149, 43, 1, 45, "Input"], Cell[619842, 21152, 86, 1, 40, "Output"] }, Open ]] }, Open ]] }, Open ]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)