(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of 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[ 50536, 2115]*) (*NotebookOutlinePosition[ 51590, 2151]*) (* CellTagsIndexPosition[ 51546, 2147]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{Cell[TextData[{ StyleBox[ " (C) Copyright 1994 D.C.M. Burbulla and C.T.J. Dodson\n \ ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"times", FontSize->12, PrivateFontOptions->{"FontPostScriptName"->Automatic}], StyleBox[" Notebook to support the book", Evaluatable->False, AspectRatioFixed->True, FontFamily->"times", FontSize->17, FontSlant->"Italic", PrivateFontOptions->{"FontPostScriptName"->Automatic}], StyleBox["\n Self-Tutor for Computer Calculus", Evaluatable->False, AspectRatioFixed->True, FontFamily->"times", PrivateFontOptions->{"FontPostScriptName"->Automatic}] }], "Title", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Using ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"times", FontSize->23, PrivateFontOptions->{"FontPostScriptName"->Automatic}], StyleBox["Mathematica 2 ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"times", FontSize->23, FontWeight->"Plain", FontSlant->"Italic", PrivateFontOptions->{"FontPostScriptName"->Automatic}] }], "Subtitle", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ " by\n D. C. M. Burbulla and C. T. J. Dodson, University of Toronto\n\ Published by: \n Prentice-Hall Canada (English) ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"times", FontSize->12, PrivateFontOptions->{"FontPostScriptName"->Automatic}], StyleBox[" ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"times", FontSize->11, PrivateFontOptions->{"FontPostScriptName"->Automatic}], StyleBox[" ISBN 0130152803", Evaluatable->False, AspectRatioFixed->True, FontFamily->"courier", FontSize->11, PrivateFontOptions->{"FontPostScriptName"->Automatic}], StyleBox[" and \n Prentice-Hall Japan (Japanese) ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"times", FontSize->12, PrivateFontOptions->{"FontPostScriptName"->Automatic}], StyleBox["ISBN4-8101-8558-3 C3055 P2880E", Evaluatable->False, AspectRatioFixed->True, FontFamily->"courier", FontSize->11, PrivateFontOptions->{"FontPostScriptName"->Automatic}] }], "Subsubtitle", Evaluatable->False, AspectRatioFixed->True, FontFamily->"times"], Cell[CellGroupData[{Cell[TextData["Trigonometric and Hyperbolic Functions"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[StyleBox[ "We make some suggestions for exploring these functions. You should first\n\ plot all these new functions and decide where they are increasing, \ decreasing,\ncritical, undefined. Decide also where they have inverse \ functions defined.\nNote that there is a special package to help with \ trigonometric identities; you\ncan call this in with:", AspectRatioFixed->True, FontFamily->"courier", FontWeight->"Plain", PrivateFontOptions->{"FontPostScriptName"->Automatic}]], "Input", AspectRatioFixed->True], Cell[TextData["<< Algebra/Trigonometry.m"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["?TrigReduce"], "Input", AspectRatioFixed->True], Cell[TextData[ "TrigReduce[expr] writes trigonometric functions of\n multiple angles as \ sums of products of trigonometric\n functions of that angle."], "Print", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["Chap11.m"], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ " in[n_] := n/2 (Sin[2 Pi/n]) (* Inscribed n-gon area *)\n\n ex[n_] := n \ (Tan[Pi/n]) (* Exscribed n-gon area *)"], "Input", AspectRatioFixed->True], Cell[TextData[StyleBox[ "We look at the plots of these functions, which give the areas of the \ inscribed\nand the exscribed polygons of n sides for a unit circle.", AspectRatioFixed->True, FontFamily->"courier", FontWeight->"Plain", PrivateFontOptions->{"FontPostScriptName"->Automatic}]], "Input", AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[ "ListPlot[Table[n/2(Sin[2 Pi/n]) ,{n,4,100}],\n \ AxesLabel->{\"n\",\"\"}];"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.009818 -14.53167 4.820788 [ [(20)] .22018 .41277 0 2 Msboxa [(40)] .41654 .41277 0 2 Msboxa [(60)] .61291 .41277 0 2 Msboxa [(80)] .80928 .41277 0 2 Msboxa [(n)] 1.025 .41277 -1 0 Msboxa [(3.02)] .01131 .02711 1 0 Msboxa [(3.04)] .01131 .12353 1 0 Msboxa [(3.06)] .01131 .21994 1 0 Msboxa [(3.08)] .01131 .31636 1 0 Msboxa [(3.12)] .01131 .50919 1 0 Msboxa [(3.14)] .01131 .6056 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .22018 .41277 m .22018 .41902 L s P [(20)] .22018 .41277 0 2 Mshowa p .002 w .41654 .41277 m .41654 .41902 L s P [(40)] .41654 .41277 0 2 Mshowa p .002 w .61291 .41277 m .61291 .41902 L s P [(60)] .61291 .41277 0 2 Mshowa p .002 w .80928 .41277 m .80928 .41902 L s P [(80)] .80928 .41277 0 2 Mshowa p .001 w .06308 .41277 m .06308 .41652 L s P p .001 w .10236 .41277 m .10236 .41652 L s P p .001 w .14163 .41277 m .14163 .41652 L s P p .001 w .1809 .41277 m .1809 .41652 L s P p .001 w .25945 .41277 m .25945 .41652 L s P p .001 w .29872 .41277 m .29872 .41652 L s P p .001 w .338 .41277 m .338 .41652 L s P p .001 w .37727 .41277 m .37727 .41652 L s P p .001 w .45582 .41277 m .45582 .41652 L s P p .001 w .49509 .41277 m .49509 .41652 L s P p .001 w .53436 .41277 m .53436 .41652 L s P p .001 w .57364 .41277 m .57364 .41652 L s P p .001 w .65218 .41277 m .65218 .41652 L s P p .001 w .69146 .41277 m .69146 .41652 L s P p .001 w .73073 .41277 m .73073 .41652 L s P p .001 w .77 .41277 m .77 .41652 L s P p .001 w .84855 .41277 m .84855 .41652 L s P p .001 w .88783 .41277 m .88783 .41652 L s P p .001 w .9271 .41277 m .9271 .41652 L s P p .001 w .96637 .41277 m .96637 .41652 L s P [(n)] 1.025 .41277 -1 0 Mshowa p .002 w 0 .41277 m 1 .41277 L s P p .002 w .02381 .02711 m .03006 .02711 L s P [(3.02)] .01131 .02711 1 0 Mshowa p .002 w .02381 .12353 m .03006 .12353 L s P [(3.04)] .01131 .12353 1 0 Mshowa p .002 w .02381 .21994 m .03006 .21994 L s P [(3.06)] .01131 .21994 1 0 Mshowa p .002 w .02381 .31636 m .03006 .31636 L s P [(3.08)] .01131 .31636 1 0 Mshowa p .002 w .02381 .50919 m .03006 .50919 L s P [(3.12)] .01131 .50919 1 0 Mshowa p .002 w .02381 .6056 m .03006 .6056 L s P [(3.14)] .01131 .6056 1 0 Mshowa p .001 w .02381 .04639 m .02756 .04639 L s P p .001 w .02381 .06568 m .02756 .06568 L s P p .001 w .02381 .08496 m .02756 .08496 L s P p .001 w .02381 .10424 m .02756 .10424 L s P p .001 w .02381 .14281 m .02756 .14281 L s P p .001 w .02381 .16209 m .02756 .16209 L s P p .001 w .02381 .18137 m .02756 .18137 L s P p .001 w .02381 .20066 m .02756 .20066 L s P p .001 w .02381 .23922 m .02756 .23922 L s P p .001 w .02381 .25851 m .02756 .25851 L s P p .001 w .02381 .27779 m .02756 .27779 L s P p .001 w .02381 .29707 m .02756 .29707 L s P p .001 w .02381 .33564 m .02756 .33564 L s P p .001 w .02381 .35492 m .02756 .35492 L s P p .001 w .02381 .37421 m .02756 .37421 L s P p .001 w .02381 .39349 m .02756 .39349 L s P p .001 w .02381 .43206 m .02756 .43206 L s P p .001 w .02381 .45134 m .02756 .45134 L s P p .001 w .02381 .47062 m .02756 .47062 L s P p .001 w .02381 .48991 m .02756 .48991 L s P p .001 w .02381 .52847 m .02756 .52847 L s P p .001 w .02381 .54775 m .02756 .54775 L s P p .001 w .02381 .56704 m .02756 .56704 L s P p .001 w .02381 .58632 m .02756 .58632 L s P p .001 w .02381 .00783 m .02756 .00783 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p .008 w .03363 -4.89009 Mdot .04345 -3.06957 Mdot .05326 -2.0069 Mdot .06308 -1.34002 Mdot .0729 -0.89642 Mdot .08272 -0.58733 Mdot .09254 -0.36373 Mdot .10236 -0.19694 Mdot .11217 -0.06931 Mdot .12199 .03049 Mdot .13181 .10996 Mdot .14163 .17426 Mdot .15145 .22702 Mdot .16127 .27082 Mdot .17108 .30759 Mdot .1809 .33875 Mdot .19072 .36538 Mdot .20054 .38833 Mdot .21036 .40823 Mdot .22018 .42561 Mdot .23 .44087 Mdot .23981 .45435 Mdot .24963 .4663 Mdot .25945 .47696 Mdot .26927 .4865 Mdot .27909 .49507 Mdot .28891 .5028 Mdot .29872 .5098 Mdot .30854 .51616 Mdot .31836 .52194 Mdot .32818 .52723 Mdot .338 .53207 Mdot .34782 .53651 Mdot .35763 .5406 Mdot .36745 .54437 Mdot .37727 .54785 Mdot .38709 .55108 Mdot .39691 .55407 Mdot .40673 .55685 Mdot .41654 .55945 Mdot .42636 .56186 Mdot .43618 .56412 Mdot .446 .56623 Mdot .45582 .56821 Mdot .46564 .57007 Mdot .47545 .57181 Mdot .48527 .57345 Mdot .49509 .575 Mdot .50491 .57646 Mdot .51473 .57783 Mdot .52455 .57913 Mdot .53436 .58036 Mdot .54418 .58153 Mdot .554 .58263 Mdot .56382 .58368 Mdot .57364 .58467 Mdot .58346 .58562 Mdot .59327 .58652 Mdot .60309 .58737 Mdot .61291 .58819 Mdot .62273 .58897 Mdot .63255 .58971 Mdot .64237 .59042 Mdot .65218 .59109 Mdot .662 .59174 Mdot .67182 .59236 Mdot .68164 .59295 Mdot .69146 .59352 Mdot .70128 .59407 Mdot .71109 .59459 Mdot .72091 .59509 Mdot .73073 .59557 Mdot .74055 .59604 Mdot .75037 .59648 Mdot .76019 .59691 Mdot .77 .59732 Mdot .77982 .59772 Mdot .78964 .5981 Mdot .79946 .59847 Mdot .80928 .59882 Mdot .8191 .59916 Mdot .82892 .59949 Mdot .83873 .59981 Mdot .84855 .60012 Mdot .85837 .60042 Mdot .86819 .6007 Mdot .87801 .60098 Mdot .88783 .60125 Mdot .89764 .60151 Mdot .90746 .60176 Mdot .91728 .60201 Mdot .9271 .60224 Mdot .93692 .60247 Mdot .94674 .60269 Mdot .95655 .60291 Mdot .96637 .60312 Mdot .97619 .60332 Mdot P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg7oo000KOol00`00Oomoo`0[Ool01000Oomoo`000Woo00<0 07ooOol09Goo00<007oo00000goo00@007ooOol002Ioo`03001oogoo00=oo`04001oogoo000WOol0 1000Oomoo`000Woo00@007ooOol003Qoo`006goo00<007ooOol0:7oo00@007ooOol0009oo`04001o ogoo000XOol20003Ool01000Oomoo`009goo00<007ooOol00Woo00@007ooOol002Moo`04001oogoo 0002Ool01000Oomoo`00>7oo000KOol00`00Oomoo`0YOol20004Ool2000ZOol00`00Oomoo`02Ool2 000YOol20003Ool2000YOol20004Ool2000iOol001]oo`03001oogoo0?aoo`006goo00<007ooOol0 :7oo00<007ooOol0dGoo000KOol00`00Oomoo`3lOol001]oo`03001oogoo0?aoo`006goo00<007oo Ool0mGoo0`0000=oo`0000000Goo000KOol00`00Oomoo`3fOol01000Oomoo`000Woo000KOol00`00 Oomoo`0ZOol00`00Oomoo`39Ool01000Oomoo`000Woo000EOooh0007Ool200000goo001oo`01Ool0 01]oo`03001oogoo00Ioo`03001oogoo00Moo`03001oogoo00Moo`03001oogoo00Ioo`03001oogoo 00Moo`03001oogoo00Moo`03001oogoo00Moo`03001oogoo00Ioo`03001oogoo00Moo`03001oogoo 00Moo`03001oogoo00Moo`03001oogoo00Ioo`03001oogoo00Moo`03001oogoo00Moo`03001oogoo 00Ioo`03001oogoo00Moo`03001oogoo00Moo`03001oogoo00Moo`03001oogoo00Ioo`03001oogoo 00Moo`03001oogoo00Moo`03001oogoo00Moo`03001oogoo00Ioo`03001oogoo00Moo`03001oogoo 00aoo`800003Ool007oo009oo`006goo00<007ooOol0o7oo000KOol00`00Oomoo`0]Ool00`00Oomo o`3goo00<007oo Ool0_Woo0002Ool20004Ool00`00Oomoo`02Ool500000goo000000020004Ool00`00Oomoo`3lOol0 0005Ool007ooOol0000:Ool01@00Oomoogoo00000Woo00<007ooOol00Woo00<007ooOol0?Woo00<0 07ooOol0^goo0004Ool00`00Oomoo`08Ool00`00Oomoo`02Ool00`00Oomoo`04Ool00`00Oomoo`3l Ool0009oo`8000]oo`03001oogoo00=oo`03001oogoo00=oo`80045oo`03001oogoo0;Uoo`0017oo 00<007ooOol027oo00<007ooOol017oo00<007ooOol00Woo00<007ooOol0o7oo00001Goo001oogoo 000027oo0`000goo00@007ooOol000Aoo`03001oogoo04=oo`03001oogoo0;Ioo`000Woo0P002goo 00<007ooOol00Woo0P001Goo00<007ooOol0AGoo00<007ooOol0]7oo000KOol00`00Oomoo`18Ool0 0`00Oomoo`2aOol001]oo`03001oogoo0?aoo`006goo00<007ooOol0BWoo00<007ooOol0[goo000K Ool00`00Oomoo`1"], ImageRangeCache->{{{0, 281}, {173, 0}} -> {-11.1155, 3.00696, 0.411146, 0.000837339}}]}, Open]], Cell[CellGroupData[{Cell[TextData[ "ListPlot[Table[n(Tan[Pi/n]) ,{n,4,100}],\n AxesLabel->{\"n\ \",\"\"}];"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.009818 -29.816285 9.492378 [ [(20)] .22018 .55933 0 2 Msboxa [(40)] .41654 .55933 0 2 Msboxa [(60)] .61291 .55933 0 2 Msboxa [(80)] .80928 .55933 0 2 Msboxa [(n)] 1.025 .55933 -1 0 Msboxa [(3.15)] .01131 .08471 1 0 Msboxa [(3.16)] .01131 .17963 1 0 Msboxa [(3.17)] .01131 .27455 1 0 Msboxa [(3.18)] .01131 .36948 1 0 Msboxa [(3.19)] .01131 .4644 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .22018 .55933 m .22018 .56558 L s P [(20)] .22018 .55933 0 2 Mshowa p .002 w .41654 .55933 m .41654 .56558 L s P [(40)] .41654 .55933 0 2 Mshowa p .002 w .61291 .55933 m .61291 .56558 L s P [(60)] .61291 .55933 0 2 Mshowa p .002 w .80928 .55933 m .80928 .56558 L s P [(80)] .80928 .55933 0 2 Mshowa p .001 w .06308 .55933 m .06308 .56308 L s P p .001 w .10236 .55933 m .10236 .56308 L s P p .001 w .14163 .55933 m .14163 .56308 L s P p .001 w .1809 .55933 m .1809 .56308 L s P p .001 w .25945 .55933 m .25945 .56308 L s P p .001 w .29872 .55933 m .29872 .56308 L s P p .001 w .338 .55933 m .338 .56308 L s P p .001 w .37727 .55933 m .37727 .56308 L s P p .001 w .45582 .55933 m .45582 .56308 L s P p .001 w .49509 .55933 m .49509 .56308 L s P p .001 w .53436 .55933 m .53436 .56308 L s P p .001 w .57364 .55933 m .57364 .56308 L s P p .001 w .65218 .55933 m .65218 .56308 L s P p .001 w .69146 .55933 m .69146 .56308 L s P p .001 w .73073 .55933 m .73073 .56308 L s P p .001 w .77 .55933 m .77 .56308 L s P p .001 w .84855 .55933 m .84855 .56308 L s P p .001 w .88783 .55933 m .88783 .56308 L s P p .001 w .9271 .55933 m .9271 .56308 L s P p .001 w .96637 .55933 m .96637 .56308 L s P [(n)] 1.025 .55933 -1 0 Mshowa p .002 w 0 .55933 m 1 .55933 L s P p .002 w .02381 .08471 m .03006 .08471 L s P [(3.15)] .01131 .08471 1 0 Mshowa p .002 w .02381 .17963 m .03006 .17963 L s P [(3.16)] .01131 .17963 1 0 Mshowa p .002 w .02381 .27455 m .03006 .27455 L s P [(3.17)] .01131 .27455 1 0 Mshowa p .002 w .02381 .36948 m .03006 .36948 L s P [(3.18)] .01131 .36948 1 0 Mshowa p .002 w .02381 .4644 m .03006 .4644 L s P [(3.19)] .01131 .4644 1 0 Mshowa p .001 w .02381 .10369 m .02756 .10369 L s P p .001 w .02381 .12268 m .02756 .12268 L s P p .001 w .02381 .14166 m .02756 .14166 L s P p .001 w .02381 .16065 m .02756 .16065 L s P p .001 w .02381 .19861 m .02756 .19861 L s P p .001 w .02381 .2176 m .02756 .2176 L s P p .001 w .02381 .23658 m .02756 .23658 L s P p .001 w .02381 .25557 m .02756 .25557 L s P p .001 w .02381 .29354 m .02756 .29354 L s P p .001 w .02381 .31252 m .02756 .31252 L s P p .001 w .02381 .33151 m .02756 .33151 L s P p .001 w .02381 .35049 m .02756 .35049 L s P p .001 w .02381 .38846 m .02756 .38846 L s P p .001 w .02381 .40745 m .02756 .40745 L s P p .001 w .02381 .42643 m .02756 .42643 L s P p .001 w .02381 .44542 m .02756 .44542 L s P p .001 w .02381 .48339 m .02756 .48339 L s P p .001 w .02381 .50237 m .02756 .50237 L s P p .001 w .02381 .52136 m .02756 .52136 L s P p .001 w .02381 .54034 m .02756 .54034 L s P p .001 w .02381 .06572 m .02756 .06572 L s P p .001 w .02381 .04674 m .02756 .04674 L s P p .001 w .02381 .02775 m .02756 .02775 L s P p .001 w .02381 .00877 m .02756 .00877 L s P p .001 w .02381 .57831 m .02756 .57831 L s P p .001 w .02381 .59729 m .02756 .59729 L s P p .001 w .02381 .61628 m .02756 .61628 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p .008 w .03363 8.15323 Mdot .04345 4.6668 Mdot .05326 3.06628 Mdot .06308 2.18273 Mdot .0729 1.63869 Mdot .08272 1.2782 Mdot .09254 1.02632 Mdot .10236 .84307 Mdot .11217 .70542 Mdot .12199 .59931 Mdot .13181 .51574 Mdot .14163 .44872 Mdot .15145 .39414 Mdot .16127 .34908 Mdot .17108 .31144 Mdot .1809 .27967 Mdot .19072 .25261 Mdot .20054 .22938 Mdot .21036 .20927 Mdot .22018 .19175 Mdot .23 .1764 Mdot .23981 .16287 Mdot .24963 .15088 Mdot .25945 .14021 Mdot .26927 .13067 Mdot .27909 .12211 Mdot .28891 .11439 Mdot .29872 .10741 Mdot .30854 .10108 Mdot .31836 .09532 Mdot .32818 .09006 Mdot .338 .08525 Mdot .34782 .08083 Mdot .35763 .07677 Mdot .36745 .07303 Mdot .37727 .06957 Mdot .38709 .06637 Mdot .39691 .0634 Mdot .40673 .06064 Mdot .41654 .05807 Mdot .42636 .05568 Mdot .43618 .05344 Mdot .446 .05135 Mdot .45582 .04939 Mdot .46564 .04756 Mdot .47545 .04583 Mdot .48527 .04421 Mdot .49509 .04268 Mdot .50491 .04124 Mdot .51473 .03988 Mdot .52455 .03859 Mdot .53436 .03738 Mdot .54418 .03622 Mdot .554 .03513 Mdot .56382 .0341 Mdot .57364 .03312 Mdot .58346 .03218 Mdot .59327 .03129 Mdot .60309 .03045 Mdot .61291 .02964 Mdot .62273 .02888 Mdot .63255 .02814 Mdot .64237 .02744 Mdot .65218 .02677 Mdot .662 .02614 Mdot .67182 .02552 Mdot .68164 .02494 Mdot .69146 .02438 Mdot .70128 .02384 Mdot .71109 .02332 Mdot .72091 .02283 Mdot .73073 .02235 Mdot .74055 .0219 Mdot .75037 .02146 Mdot .76019 .02104 Mdot .77 .02063 Mdot .77982 .02024 Mdot .78964 .01986 Mdot .79946 .0195 Mdot .80928 .01915 Mdot .8191 .01881 Mdot .82892 .01849 Mdot .83873 .01817 Mdot .84855 .01787 Mdot .85837 .01758 Mdot .86819 .01729 Mdot .87801 .01702 Mdot .88783 .01675 Mdot .89764 .0165 Mdot .90746 .01625 Mdot .91728 .01601 Mdot .9271 .01578 Mdot .93692 .01555 Mdot .94674 .01533 Mdot .95655 .01512 Mdot .96637 .01491 Mdot .97619 .01472 Mdot P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgGoo00<007ooOol0`7oo000KOol00`00 Oomoo`3lOol001]oo`03001oogoo0?aoo`006goo00<007ooOol0=Woo00<007ooOol0`goo000KOol0 0`00Oomoo`3lOol001]oo`03001oogoo03Aoo`03001oogoo07oo000KOol00`00Oomoo`0XOol01000Oomoo`000Woo00@007ooOol002Qoo`80 00=oo`04001oogoo000WOol00`00Oomoo`02Ool01000Oomoo`009goo00@007ooOol0009oo`04001o ogoo000hOol001]oo`03001oogoo02Uoo`8000Aoo`8002Yoo`03001oogoo009oo`8002Uoo`8000=o o`8002Uoo`8000Aoo`8003Uoo`006goo00<007ooOol0o7oo000KOol00`00Oomoo`3lOol001]oo`03 001oogoo0?aoo`006goo00<007ooOol0o7oo000KOol00`00Oomoo`3eOol300000goo00000001Ool0 01]oo`03001oogoo0?Ioo`04001oogoo0002Ool001EoooP000Moo`04001oogoo0002Ool001]oo`03 001oogoo00Ioo`03001oogoo00Moo`03001oogoo00Moo`03001oogoo00Ioo`03001oogoo00Moo`03 001oogoo00Moo`03001oogoo00Moo`03001oogoo00Ioo`03001oogoo00Moo`03001oogoo00Moo`03 001oogoo00Moo`03001oogoo00Ioo`03001oogoo00Moo`03001oogoo00Moo`03001oogoo00Ioo`03 001oogoo00Moo`03001oogoo00Moo`03001oogoo00Moo`03001oogoo00Ioo`03001oogoo00Moo`03 001oogoo00Moo`03001oogoo00Moo`03001oogoo00Ioo`03001oogoo00Moo`03001oogoo00eoo`80 0003Ool007oo005oo`006goo00<007ooOol0;Goo00<007ooOol0;Woo00<007ooOol0;Goo00<007oo Ool0;Woo00<007ooOol0Eo o`006goo00<007ooOol0o7oo000KOol00`00Oomoo`3lOol001]oo`03001oogoo0?aoo`006goo00<0 07ooOol0o7oo000KOol00`00Oomoo`3lOol00?mooa]oo`00ogoo6goo003oOolKOol00?mooa]oo`00 ogoo6goo003oOolKOol00?mooa]oo`00ogoo6goo003oOolKOol00001\ \>"], ImageRangeCache->{{{0, 281}, {173, 0}} -> {-11.1155, 3.13685, 0.411146, 0.00042525}}]}, Open]], Cell[CellGroupData[{Cell[TextData["Show[%,%%];"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.009818 -20.077646 6.497038 [ [(20)] .22018 .06317 0 2 Msboxa [(40)] .41654 .06317 0 2 Msboxa [(60)] .61291 .06317 0 2 Msboxa [(80)] .80928 .06317 0 2 Msboxa [(n)] 1.025 .06317 -1 0 Msboxa [(3.12)] .01131 .19311 1 0 Msboxa [(3.14)] .01131 .32305 1 0 Msboxa [(3.16)] .01131 .45299 1 0 Msboxa [(3.18)] .01131 .58293 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .22018 .06317 m .22018 .06942 L s P [(20)] .22018 .06317 0 2 Mshowa p .002 w .41654 .06317 m .41654 .06942 L s P [(40)] .41654 .06317 0 2 Mshowa p .002 w .61291 .06317 m .61291 .06942 L s P [(60)] .61291 .06317 0 2 Mshowa p .002 w .80928 .06317 m .80928 .06942 L s P [(80)] .80928 .06317 0 2 Mshowa p .001 w .06308 .06317 m .06308 .06692 L s P p .001 w .10236 .06317 m .10236 .06692 L s P p .001 w .14163 .06317 m .14163 .06692 L s P p .001 w .1809 .06317 m .1809 .06692 L s P p .001 w .25945 .06317 m .25945 .06692 L s P p .001 w .29872 .06317 m .29872 .06692 L s P p .001 w .338 .06317 m .338 .06692 L s P p .001 w .37727 .06317 m .37727 .06692 L s P p .001 w .45582 .06317 m .45582 .06692 L s P p .001 w .49509 .06317 m .49509 .06692 L s P p .001 w .53436 .06317 m .53436 .06692 L s P p .001 w .57364 .06317 m .57364 .06692 L s P p .001 w .65218 .06317 m .65218 .06692 L s P p .001 w .69146 .06317 m .69146 .06692 L s P p .001 w .73073 .06317 m .73073 .06692 L s P p .001 w .77 .06317 m .77 .06692 L s P p .001 w .84855 .06317 m .84855 .06692 L s P p .001 w .88783 .06317 m .88783 .06692 L s P p .001 w .9271 .06317 m .9271 .06692 L s P p .001 w .96637 .06317 m .96637 .06692 L s P [(n)] 1.025 .06317 -1 0 Mshowa p .002 w 0 .06317 m 1 .06317 L s P p .002 w .02381 .19311 m .03006 .19311 L s P [(3.12)] .01131 .19311 1 0 Mshowa p .002 w .02381 .32305 m .03006 .32305 L s P [(3.14)] .01131 .32305 1 0 Mshowa p .002 w .02381 .45299 m .03006 .45299 L s P [(3.16)] .01131 .45299 1 0 Mshowa p .002 w .02381 .58293 m .03006 .58293 L s P [(3.18)] .01131 .58293 1 0 Mshowa p .001 w .02381 .08916 m .02756 .08916 L s P p .001 w .02381 .11515 m .02756 .11515 L s P p .001 w .02381 .14114 m .02756 .14114 L s P p .001 w .02381 .16712 m .02756 .16712 L s P p .001 w .02381 .2191 m .02756 .2191 L s P p .001 w .02381 .24509 m .02756 .24509 L s P p .001 w .02381 .27108 m .02756 .27108 L s P p .001 w .02381 .29706 m .02756 .29706 L s P p .001 w .02381 .34904 m .02756 .34904 L s P p .001 w .02381 .37503 m .02756 .37503 L s P p .001 w .02381 .40102 m .02756 .40102 L s P p .001 w .02381 .42701 m .02756 .42701 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .50497 m .02756 .50497 L s P p .001 w .02381 .53096 m .02756 .53096 L s P p .001 w .02381 .55695 m .02756 .55695 L s P p .001 w .02381 .03718 m .02756 .03718 L s P p .001 w .02381 .0112 m .02756 .0112 L s P p .001 w .02381 .60892 m .02756 .60892 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p .008 w .03363 5.91051 Mdot .04345 3.52423 Mdot .05326 2.42875 Mdot .06308 1.82401 Mdot .0729 1.45164 Mdot .08272 1.20491 Mdot .09254 1.03251 Mdot .10236 .90708 Mdot .11217 .81287 Mdot .12199 .74024 Mdot .13181 .68304 Mdot .14163 .63717 Mdot .15145 .59981 Mdot .16127 .56897 Mdot .17108 .54321 Mdot .1809 .52147 Mdot .19072 .50295 Mdot .20054 .48704 Mdot .21036 .47328 Mdot .22018 .46129 Mdot .23 .45078 Mdot .23981 .44152 Mdot .24963 .43332 Mdot .25945 .42601 Mdot .26927 .41948 Mdot .27909 .41362 Mdot .28891 .40834 Mdot .29872 .40356 Mdot .30854 .39923 Mdot .31836 .39529 Mdot .32818 .39169 Mdot .338 .38839 Mdot .34782 .38537 Mdot .35763 .38259 Mdot .36745 .38003 Mdot .37727 .37766 Mdot .38709 .37547 Mdot .39691 .37344 Mdot .40673 .37155 Mdot .41654 .36979 Mdot .42636 .36816 Mdot .43618 .36663 Mdot .446 .36519 Mdot .45582 .36385 Mdot .46564 .3626 Mdot .47545 .36141 Mdot .48527 .3603 Mdot .49509 .35926 Mdot .50491 .35827 Mdot .51473 .35734 Mdot .52455 .35646 Mdot .53436 .35563 Mdot .54418 .35484 Mdot .554 .35409 Mdot .56382 .35339 Mdot .57364 .35271 Mdot .58346 .35207 Mdot .59327 .35147 Mdot .60309 .35089 Mdot .61291 .35034 Mdot .62273 .34981 Mdot .63255 .34931 Mdot .64237 .34883 Mdot .65218 .34837 Mdot .662 .34793 Mdot .67182 .34752 Mdot .68164 .34712 Mdot .69146 .34673 Mdot .70128 .34636 Mdot .71109 .34601 Mdot .72091 .34567 Mdot .73073 .34535 Mdot .74055 .34503 Mdot .75037 .34473 Mdot .76019 .34444 Mdot .77 .34417 Mdot .77982 .3439 Mdot .78964 .34364 Mdot .79946 .34339 Mdot .80928 .34315 Mdot .8191 .34292 Mdot .82892 .3427 Mdot .83873 .34248 Mdot .84855 .34228 Mdot .85837 .34208 Mdot .86819 .34188 Mdot .87801 .34169 Mdot .88783 .34151 Mdot .89764 .34134 Mdot .90746 .34117 Mdot .91728 .341 Mdot .9271 .34084 Mdot .93692 .34069 Mdot .94674 .34054 Mdot .95655 .3404 Mdot .96637 .34025 Mdot .97619 .34012 Mdot P p .008 w .03363 -7.08357 Mdot .04345 -4.63002 Mdot .05326 -3.19785 Mdot .06308 -2.29909 Mdot .0729 -1.70125 Mdot .08272 -1.28468 Mdot .09254 -0.98333 Mdot .10236 -0.75854 Mdot .11217 -0.58653 Mdot .12199 -0.45204 Mdot .13181 -0.34493 Mdot .14163 -0.25827 Mdot .15145 -0.18718 Mdot .16127 -0.12814 Mdot .17108 -0.07859 Mdot .1809 -0.03659 Mdot .19072 -0.00069 Mdot .20054 .03023 Mdot .21036 .05705 Mdot .22018 .08047 Mdot .23 .10104 Mdot .23981 .1192 Mdot .24963 .13531 Mdot .25945 .14967 Mdot .26927 .16253 Mdot .27909 .17408 Mdot .28891 .18451 Mdot .29872 .19394 Mdot .30854 .2025 Mdot .31836 .2103 Mdot .32818 .21742 Mdot .338 .22394 Mdot .34782 .22993 Mdot .35763 .23544 Mdot .36745 .24052 Mdot .37727 .24522 Mdot .38709 .24957 Mdot .39691 .2536 Mdot .40673 .25735 Mdot .41654 .26084 Mdot .42636 .2641 Mdot .43618 .26714 Mdot .446 .26999 Mdot .45582 .27266 Mdot .46564 .27516 Mdot .47545 .27751 Mdot .48527 .27972 Mdot .49509 .28181 Mdot .50491 .28377 Mdot .51473 .28562 Mdot .52455 .28738 Mdot .53436 .28903 Mdot .54418 .2906 Mdot .554 .29209 Mdot .56382 .2935 Mdot .57364 .29484 Mdot .58346 .29612 Mdot .59327 .29733 Mdot .60309 .29848 Mdot .61291 .29958 Mdot .62273 .30063 Mdot .63255 .30163 Mdot .64237 .30258 Mdot .65218 .3035 Mdot .662 .30437 Mdot .67182 .3052 Mdot .68164 .306 Mdot .69146 .30677 Mdot .70128 .3075 Mdot .71109 .30821 Mdot .72091 .30888 Mdot .73073 .30953 Mdot .74055 .31016 Mdot .75037 .31076 Mdot .76019 .31133 Mdot .77 .31189 Mdot .77982 .31242 Mdot .78964 .31294 Mdot .79946 .31343 Mdot .80928 .31391 Mdot .8191 .31437 Mdot .82892 .31482 Mdot .83873 .31525 Mdot .84855 .31566 Mdot .85837 .31606 Mdot .86819 .31645 Mdot .87801 .31682 Mdot .88783 .31719 Mdot .89764 .31754 Mdot .90746 .31788 Mdot .91728 .3182 Mdot .9271 .31852 Mdot .93692 .31883 Mdot .94674 .31913 Mdot .95655 .31942 Mdot .96637 .3197 Mdot .97619 .31997 Mdot P P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg7oo000KOol00`00Oomoo`0XOol01000Oomoo`000Woo00@007ooOol002Qoo`8000=oo`04001oogoo 000WOol00`00Oomoo`02Ool01000Oomoo`009goo00@007ooOol0009oo`04001oogoo000hOol001]o o`03001oogoo02Qoo`<000Aoo`8002Yoo`03001oogoo009oo`8002Uoo`8000=oo`8002Uoo`8000Ao o`8003Uoo`006goo00<007ooOol0o7oo000KOol00`00Oomoo`3lOol001]oo`03001oogoo0?aoo`00 6goo00<007ooOol0o7oo000KOol00`00Oomoo`3eOol300000goo00000001Ool001]oo`03001oogoo 02Yoo`03001oogoo0goo00<007ooOol0_Woo000KOol00`00Oomoo`0iOol00`00Oomoo`30Ool001]oo`03 001oogoo0?aoo`006goo00<007ooOol0=Woo00<007ooOol0`goo000KOol00`00Oomoo`3lOol001]o o`03001oogoo03Aoo`03001oogoo0"], ImageRangeCache->{{{0, 281}, {173, 0}} -> {-11.1155, 3.08391, 0.411146, 0.000621304}}]}, Open]], Cell[TextData[StyleBox[ "It is always a good idea to look at series expansions of new functions:", AspectRatioFixed->True, FontFamily->"courier", FontWeight->"Plain", PrivateFontOptions->{"FontPostScriptName"->Automatic}]], "Input", AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["Series[Sin[x],{x,0,10}]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ SeriesData[x, 0, {1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880}, 1, 11, 1]\ \>", "\<\ 3 5 7 9 x x x x 11 x - -- + --- - ---- + ------ + O[x] 6 120 5040 362880\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["Series[Cos[x],{x,0,10}]"], "Input", AspectRatioFixed->True], Cell[OutputFormData[ "\<\ SeriesData[x, 0, {1, 0, -1/2, 0, 1/24, 0, -1/720, 0, 1/40320, 0, -1/3628800}, 0, 11, 1]\ \>", "\<\ 2 4 6 8 10 x x x x x 11 1 - -- + -- - --- + ----- - ------- + O[x] 2 24 720 40320 3628800\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["Series[Tan[x],{x,0,10}]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ SeriesData[x, 0, {1, 0, 1/3, 0, 2/15, 0, 17/315, 0, 62/2835}, 1, 11, 1]\ \>", "\<\ 3 5 7 9 x 2 x 17 x 62 x 11 x + -- + ---- + ----- + ----- + O[x] 3 15 315 2835\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[TextData[StyleBox[ "Do the same series investigation for the other trigonometric and hyperbolic\n\ functions.. ", AspectRatioFixed->True, FontFamily->"courier", FontWeight->"Plain", PrivateFontOptions->{"FontPostScriptName"->Automatic}]], "Input", AspectRatioFixed->True]}, Open]]}, Open]]}, Open]] }, FrontEndVersion->"Macintosh 3.0", ScreenRectangle->{{0, 640}, {0, 460}}, WindowToolbars->{}, CellGrouping->Manual, WindowSize->{520, 365}, WindowMargins->{{4, Automatic}, {30, Automatic}}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, -1}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, MacintoshSystemPageSetup->"\<\ AVU/IFiQKFD000000V7E<09QgO0000000OZ:d096/NP0AP1Y06`0I@1^0642HMD` 0V7N40000001nXZ`0TJaj000000000000000009QeC0000000000000000000000 00000000000000000000000000000000\>" ] (*********************************************************************** 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->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1731, 51, 742, 23, 70, "Title", Evaluatable->False], Cell[2476, 76, 488, 17, 70, "Subtitle", Evaluatable->False], Cell[2967, 95, 1189, 36, 70, "Subsubtitle", Evaluatable->False], Cell[CellGroupData[{ Cell[4179, 133, 115, 2, 70, "Section", Evaluatable->False], Cell[4297, 137, 537, 10, 70, "Input"], Cell[4837, 149, 78, 1, 70, "Input"], Cell[CellGroupData[{ Cell[4938, 152, 64, 1, 70, "Input"], Cell[5005, 155, 214, 4, 70, "Print", Evaluatable->False] }, Open ]], Cell[CellGroupData[{ Cell[5251, 161, 88, 2, 70, "Subsection", Evaluatable->False], Cell[5342, 165, 168, 3, 70, "Input"], Cell[5513, 170, 333, 7, 70, "Input"], Cell[CellGroupData[{ Cell[5869, 179, 146, 3, 70, "Input"], Cell[6018, 184, 13670, 599, 70, 5560, 494, "GraphicsData", "PostScript", "Graphics", Evaluatable->False] }, Open ]], Cell[CellGroupData[{ Cell[19720, 785, 142, 3, 70, "Input"], Cell[19865, 790, 13389, 600, 70, 5527, 498, "GraphicsData", "PostScript", "Graphics", Evaluatable->False] }, Open ]], Cell[CellGroupData[{ Cell[33286, 1392, 64, 1, 70, "Input"], Cell[33353, 1395, 15274, 652, 70, 6917, 544, "GraphicsData", "PostScript", "Graphics", Evaluatable->False] }, Open ]], Cell[48639, 2049, 266, 6, 70, "Input"], Cell[CellGroupData[{ Cell[48928, 2057, 76, 1, 70, "Input"], Cell[49007, 2060, 312, 11, 70, "Output", Evaluatable->False] }, Open ]], Cell[CellGroupData[{ Cell[49351, 2073, 76, 1, 70, "Input"], Cell[49430, 2076, 354, 13, 70, "Output", Evaluatable->False] }, Open ]], Cell[CellGroupData[{ Cell[49816, 2091, 76, 1, 70, "Input"], Cell[49895, 2094, 313, 11, 70, "Output", Evaluatable->False] }, Open ]], Cell[50220, 2107, 286, 7, 70, "Input"] }, Open ]] }, Closed]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)