(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. 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[ 143367, 4607]*) (*NotebookOutlinePosition[ 144081, 4632]*) (* CellTagsIndexPosition[ 144037, 4628]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Plot[ x^3 - 2 x^2 - 5, {x, 1, 4}]\)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\(\ \[IndentingNewLine]\)\)\)], "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 -0.293651 0.31746 0.124421 0.0177369 [ [.18254 .11192 -9 -9 ] [.18254 .11192 9 0 ] [.34127 .11192 -3 -9 ] [.34127 .11192 3 0 ] [.5 .11192 -9 -9 ] [.5 .11192 9 0 ] [.65873 .11192 -3 -9 ] [.65873 .11192 3 0 ] [.81746 .11192 -9 -9 ] [.81746 .11192 9 0 ] [.97619 .11192 -3 -9 ] [.97619 .11192 3 0 ] [.01131 .03574 -12 -4.5 ] [.01131 .03574 0 4.5 ] [.01131 .21311 -6 -4.5 ] [.01131 .21311 0 4.5 ] [.01131 .30179 -12 -4.5 ] [.01131 .30179 0 4.5 ] [.01131 .39048 -12 -4.5 ] [.01131 .39048 0 4.5 ] [.01131 .47916 -12 -4.5 ] [.01131 .47916 0 4.5 ] [.01131 .56785 -12 -4.5 ] [.01131 .56785 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 .18254 .12442 m .18254 .13067 L s [(1.5)] .18254 .11192 0 1 Mshowa .34127 .12442 m .34127 .13067 L s [(2)] .34127 .11192 0 1 Mshowa .5 .12442 m .5 .13067 L s [(2.5)] .5 .11192 0 1 Mshowa .65873 .12442 m .65873 .13067 L s [(3)] .65873 .11192 0 1 Mshowa .81746 .12442 m .81746 .13067 L s [(3.5)] .81746 .11192 0 1 Mshowa .97619 .12442 m .97619 .13067 L s [(4)] .97619 .11192 0 1 Mshowa .125 Mabswid .05556 .12442 m .05556 .12817 L s .0873 .12442 m .0873 .12817 L s .11905 .12442 m .11905 .12817 L s .15079 .12442 m .15079 .12817 L s .21429 .12442 m .21429 .12817 L s .24603 .12442 m .24603 .12817 L s .27778 .12442 m .27778 .12817 L s .30952 .12442 m .30952 .12817 L s .37302 .12442 m .37302 .12817 L s .40476 .12442 m .40476 .12817 L s .43651 .12442 m .43651 .12817 L s .46825 .12442 m .46825 .12817 L s .53175 .12442 m .53175 .12817 L s .56349 .12442 m .56349 .12817 L s .59524 .12442 m .59524 .12817 L s .62698 .12442 m .62698 .12817 L s .69048 .12442 m .69048 .12817 L s .72222 .12442 m .72222 .12817 L s .75397 .12442 m .75397 .12817 L s .78571 .12442 m .78571 .12817 L s .84921 .12442 m .84921 .12817 L s .88095 .12442 m .88095 .12817 L s .9127 .12442 m .9127 .12817 L s .94444 .12442 m .94444 .12817 L s .25 Mabswid 0 .12442 m 1 .12442 L s .02381 .03574 m .03006 .03574 L s [(-5)] .01131 .03574 1 0 Mshowa .02381 .21311 m .03006 .21311 L s [(5)] .01131 .21311 1 0 Mshowa .02381 .30179 m .03006 .30179 L s [(10)] .01131 .30179 1 0 Mshowa .02381 .39048 m .03006 .39048 L s [(15)] .01131 .39048 1 0 Mshowa .02381 .47916 m .03006 .47916 L s [(20)] .01131 .47916 1 0 Mshowa .02381 .56785 m .03006 .56785 L s [(25)] .01131 .56785 1 0 Mshowa .125 Mabswid .02381 .05347 m .02756 .05347 L s .02381 .07121 m .02756 .07121 L s .02381 .08895 m .02756 .08895 L s .02381 .10668 m .02756 .10668 L s .02381 .14216 m .02756 .14216 L s .02381 .1599 m .02756 .1599 L s .02381 .17763 m .02756 .17763 L s .02381 .19537 m .02756 .19537 L s .02381 .23084 m .02756 .23084 L s .02381 .24858 m .02756 .24858 L s .02381 .26632 m .02756 .26632 L s .02381 .28405 m .02756 .28405 L s .02381 .31953 m .02756 .31953 L s .02381 .33726 m .02756 .33726 L s .02381 .355 m .02756 .355 L s .02381 .37274 m .02756 .37274 L s .02381 .40821 m .02756 .40821 L s .02381 .42595 m .02756 .42595 L s .02381 .44369 m .02756 .44369 L s .02381 .46142 m .02756 .46142 L s .02381 .4969 m .02756 .4969 L s .02381 .51463 m .02756 .51463 L s .02381 .53237 m .02756 .53237 L s .02381 .55011 m .02756 .55011 L s .02381 .018 m .02756 .018 L s .02381 .00026 m .02756 .00026 L s .02381 .58558 m .02756 .58558 L s .02381 .60332 m .02756 .60332 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 .018 m .04262 .01701 L .06244 .01614 L .08255 .01544 L .09396 .01514 L .09905 .01503 L .10458 .01493 L .11004 .01485 L .11508 .01479 L .11989 .01475 L .12232 .01473 L .12369 .01473 L .125 .01472 L .12615 .01472 L .12741 .01472 L .12855 .01472 L .12962 .01472 L .13088 .01472 L .13202 .01472 L .13334 .01472 L .13459 .01472 L .13684 .01473 L .1389 .01475 L .14357 .01479 L .14827 .01484 L .15331 .01492 L .1624 .01511 L .17321 .01543 L .18306 .0158 L .20215 .01678 L .22291 .01823 L .24268 .02001 L .26369 .02238 L .30144 .02792 L .34164 .03582 L .38033 .04557 L .42147 .05847 L .46109 .07358 L .4992 .09077 L .53976 .11217 L .57881 .13597 L .62031 .16495 L .66029 .19668 L .69875 .23092 L .73967 .27157 L .77908 .31504 L .81696 .36102 L .8573 .41471 L .89613 .47117 L .9374 .53659 L Mistroke .97619 .60332 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg000QOol;003GOol000mo o`03001oogoo03Moo``00<]oo`003goo00<007ooOol0@goo1@00aWoo0008Ool20005Ool00`00Oomo o`18Ool50031Ool000Moo`04001oogoo0004Ool00`00Oomoo`1=Ool6002kOol000Yoo`03001oogoo 009oo`<005=oo`@00;Moo`0000=oo`0000000P000goo0P001Goo00<007ooOol0Egoo1000/goo0008 Ool00`00Oomoo`04Ool00`00Oomoo`1KOol4002_Ool000Qoo`<000Aoo`03001oogoo05moo`<00:ao o`003goo00<007ooOol0HWoo1000Z7oo000?Ool2001WOol4002TOol000moo`03001oogoo06Yoo`@0 0:1oo`003goo00<007ooOol0KWoo0P00WWoo000?Ool00`00Oomoo`1`Ool2002LOol000moo`03001o ogoo079oo`8009Yoo`003goo0P00MGoo0P00V7oo000?Ool00`00Oomoo`1fOol3002EOol000moo`03 001oogoo07Uoo`8009=oo`003goo00<007ooOol08Goo1@000Woo0P0017oo0P008goo10008Woo1@00 0Woo0P0017oo0P009Goo0P0097oo0P0017oo0P0017oo0P009Goo0`001Goo000?Ool00`00Oomoo`0S Ool00`00Oomoo`07Ool01000Oomoo`008Woo00<007ooOol08goo00<007ooOol00Woo0P001Goo00@0 07ooOol002=oo`04001oogoo000ROol01000Oomoo`0027oo00@007ooOol002Eoo`03001oogoo00Ao o`003goo0P0097oo00<007ooOol02Woo00<007ooOol08Goo00<007ooOol08goo00<007ooOol00goo 0P001Woo00<007ooOol08goo00<007ooOol08goo00<007ooOol02Woo00<007ooOol087oo1@001Goo 000?Ool00`00Oomoo`0SOol00`00Oomoo`08Ool2000UOol00`00Oomoo`0SOol00`00Oomoo`04Ool2 0002Ool2000WOol00`00Oomoo`0SOol00`00Oomoo`07Ool2000SOol01000Oomoo`001Woo000?Ool0 0`00Oomoo`0SOol00`00Oomoo`08Ool00`00Oomoo`0ROol01000Oomoo`008Woo00@007ooOol000Mo o`<002Eoo`04001oogoo000ROol01000Oomoo`002Goo00<007ooOol08goo00<007oo00001Woo000? Ool00`00Oomoo`0ROol2000:Ool3000SOol2000TOol2000:Ool3000TOol2000TOol2000:Ool3000T Ool20006Ool000moo`03001oogoo08Qoo`8008Aoo`003goo0P00Rgoo0P00PWoo000?Ool00`00Oomo o`2Ool000moo`800;moo`03 001oogoo04eoo`003goo00<007ooOol0_goo00<007ooOol0C7oo000?Ool00`00Oomoo`2oOol00`00 Oomoo`1Ool00`00Oomoo`0mOol000mo o`03001oogoo0goo000?Ool00`00Oomo o`3AOol00`00Oomoo`0jOol000moo`03001oogoo0=9oo`03001oogoo03Uoo`003goo00<007ooOol0 dgoo00<007ooOol0>7oo000?Ool00`00Oomoo`3DOol00`00Oomoo`0gOol000moo`800=Ioo`03001o ogoo03Ioo`003goo00<007ooOol0eGoo00<007ooOol0=Woo000?Ool00`00Oomoo`3FOol00`00Oomo o`0eOol000moo`03001oogoo0=Moo`03001oogoo03Aoo`003goo00<007ooOol0f7oo00<007ooOol0 5oo`03001oogoo02Yo o`000goo00<007ooOol00Woo00<007ooOol017oo00<007ooOol0hWoo00<007ooOol0:Goo0002Ool2 0004Ool30004Ool00`00Oomoo`3SOol00`00Oomoo`0XOol000moo`03001oogoo0>Aoo`03001oogoo 02Moo`003goo0P00iGoo00<007ooOol09goo000?Ool00`00Oomoo`3UOol00`00Oomoo`0VOol000mo o`03001oogoo0>Ioo`03001oogoo02Eoo`003goo00<007ooOol0iWoo00<007ooOol09Goo000?Ool0 0`00Oomoo`3WOol00`00Oomoo`0TOol000moo`800>Uoo`03001oogoo02=oo`003goo00<007ooOol0 j7oo00<007ooOol08goo000?Ool00`00Oomoo`3YOol00`00Oomoo`0ROol000moo`03001oogoo0>Yo o`03001oogoo025oo`003goo0P00k7oo00<007ooOol087oo000?Ool00`00Oomoo`3[Ool00`00Oomo o`0POol000moo`03001oogoo0>aoo`03001oogoo01moo`003goo00<007ooOol0kGoo00<007ooOol0 7Woo000?Ool00`00Oomoo`3]Ool00`00Oomoo`0NOol000moo`800>moo`03001oogoo01eoo`003goo 00<007ooOol0kgoo00<007ooOol077oo000?Ool00`00Oomoo`3_Ool00`00Oomoo`0LOol00003Ool0 0000008000=oo`8000Eoo`03001oogoo0?1oo`03001oogoo01]oo`0000=oo`00Ool017oo00@007oo Ool000Aoo`03001oogoo0?5oo`03001oogoo01Yoo`000Woo00<007ooOol00Woo00@007ooOol000Ao o`<00?5oo`03001oogoo01Yoo`000goo00D007ooOomoo`00009oo`03001oogoo009oo`03001oogoo 0?9oo`03001oogoo01Uoo`0000Eoo`00Oomoo`00009oo`04001oogoo0004Ool00`00Oomoo`3bOol0 0`00Oomoo`0IOol0009oo`8000Aoo`8000Eoo`03001oogoo0?=oo`03001oogoo01Qoo`003goo00<0 07ooOol0m7oo00<007ooOol05goo000?Ool2003eOol00`00Oomoo`0GOol000moo`03001oogoo0?Eo o`03001oogoo01Ioo`003goo00<007ooOol0mWoo00<007ooOol05Goo000?Ool00`00Oomoo`3fOol0 0`00Oomoo`0EOol000moo`03001oogoo0?Moo`03001oogoo01Aoo`003goo0P00n7oo00<007ooOol0 57oo000?Ool00`00Oomoo`3hOol00`00Oomoo`0COol000moo`03001oogoo0?Uoo`03001oogoo019o o`003goo00<007ooOol0nGoo00<007ooOol04Woo000?Ool00`00Oomoo`3jOol00`00Oomoo`0AOol0 00moo`800?]oo`03001oogoo015oo`003goo00<007ooOol0ngoo00<007ooOol047oo000?Ool00`00 Oomoo`3lOol00`00Oomoo`0?Ool000moo`03001oogoo0?aoo`03001oogoo00moo`003goo00<007oo Ool0oGoo00<007ooOol03Woo000?Ool2003nOol00`00Oomoo`0>Ool000moo`03001oogoo0?ioo`03 001oogoo00eoo`003goo00<007ooOol0oWoo00<007ooOol03Goo00000goo000000020003Ool20005 Ool00`00Oomoo`3oOol00`00Oomoo`0"], ImageRangeCache->{{{73.5625, 302.938}, {258.75, 117.438}} -> {-0.217874, \ 22.2727, 0.0113367, 0.202908}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[x^3 + 3 x^2 - 1, {x, \(-3\), \(-2\)}]\)], "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 2.88095 0.952381 0.161866 0.147151 [ [.21429 .14937 -12 -9 ] [.21429 .14937 12 0 ] [.40476 .14937 -12 -9 ] [.40476 .14937 12 0 ] [.59524 .14937 -12 -9 ] [.59524 .14937 12 0 ] [.78571 .14937 -12 -9 ] [.78571 .14937 12 0 ] [.97619 .14937 -6 -9 ] [.97619 .14937 6 0 ] [.01131 .01472 -12 -4.5 ] [.01131 .01472 0 4.5 ] [.01131 .30902 -6 -4.5 ] [.01131 .30902 0 4.5 ] [.01131 .45617 -6 -4.5 ] [.01131 .45617 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .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 .21429 .16187 m .21429 .16812 L s [(-2.8)] .21429 .14937 0 1 Mshowa .40476 .16187 m .40476 .16812 L s [(-2.6)] .40476 .14937 0 1 Mshowa .59524 .16187 m .59524 .16812 L s [(-2.4)] .59524 .14937 0 1 Mshowa .78571 .16187 m .78571 .16812 L s [(-2.2)] .78571 .14937 0 1 Mshowa .97619 .16187 m .97619 .16812 L s [(-2)] .97619 .14937 0 1 Mshowa .125 Mabswid .07143 .16187 m .07143 .16562 L s .11905 .16187 m .11905 .16562 L s .16667 .16187 m .16667 .16562 L s .2619 .16187 m .2619 .16562 L s .30952 .16187 m .30952 .16562 L s .35714 .16187 m .35714 .16562 L s .45238 .16187 m .45238 .16562 L s .5 .16187 m .5 .16562 L s .54762 .16187 m .54762 .16562 L s .64286 .16187 m .64286 .16562 L s .69048 .16187 m .69048 .16562 L s .7381 .16187 m .7381 .16562 L s .83333 .16187 m .83333 .16562 L s .88095 .16187 m .88095 .16562 L s .92857 .16187 m .92857 .16562 L s .25 Mabswid 0 .16187 m 1 .16187 L s .02381 .01472 m .03006 .01472 L s [(-1)] .01131 .01472 1 0 Mshowa .02381 .30902 m .03006 .30902 L s [(1)] .01131 .30902 1 0 Mshowa .02381 .45617 m .03006 .45617 L s [(2)] .01131 .45617 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(3)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .13244 m .02756 .13244 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .25016 m .02756 .25016 L s .02381 .27959 m .02756 .27959 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 .01472 m .06244 .067 L .10458 .12077 L .14415 .16826 L .18221 .21123 L .22272 .25414 L .26171 .29274 L .30316 .33092 L .34309 .36501 L .3815 .39537 L .42237 .4251 L .46172 .4513 L .49955 .4743 L .53984 .4965 L .57861 .51568 L .61984 .5338 L .65954 .54911 L .69774 .5619 L .73838 .5735 L .77751 .58277 L .81909 .59065 L .83996 .59386 L .85916 .59638 L .8791 .59857 L .89771 .60024 L .91654 .60155 L .92715 .60213 L .9372 .60257 L .94695 .6029 L .95246 .60304 L .95755 .60315 L .96183 .60322 L .96429 .60325 L .96655 .60327 L .96892 .60329 L .97014 .6033 L .97148 .60331 L .97265 .60331 L .97373 .60332 L .97488 .60332 L .97611 .60332 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgaoo`003goo00<0 07ooOol087oo00<007ooOol0jgoo000?Ool00`00Oomoo`0QOol00`00Oomoo`3ZOol000moo`03001o ogoo029oo`03001oogoo0>Uoo`003goo00<007ooOol08goo00<007ooOol0j7oo000?Ool2000UOol0 0`00Oomoo`3WOol000moo`03001oogoo02Aoo`03001oogoo0>Moo`003goo00<007ooOol09Goo00<0 07ooOol0iWoo000?Ool00`00Oomoo`0VOol00`00Oomoo`3UOol000moo`03001oogoo02Moo`03001o ogoo0>Aoo`003goo00<007ooOol0:7oo00<007ooOol0hgoo000?Ool00`00Oomoo`0YOol00`00Oomo o`3ROol000moo`03001oogoo02Yoo`03001oogoo0>5oo`003goo0P00;7oo00<007ooOol0h7oo000? Ool00`00Oomoo`0/Ool00`00Oomoo`3OOol000moo`03001oogoo02eoo`03001oogoo0=ioo`003goo 00<007ooOol0;Woo00<007ooOol0gGoo000?Ool00`00Oomoo`0_Ool00`00Oomoo`3LOol000moo`03 001oogoo02moo`03001oogoo0=aoo`003goo00<007ooOol0<7oo00<007ooOol0fgoo000?Ool00`00 Oomoo`0aOol00`00Oomoo`3JOol000moo`03001oogoo039oo`03001oogoo0=Uoo`003goo0P00=7oo 00<007ooOol0f7oo000?Ool00`00Oomoo`0dOol00`00Oomoo`3GOol000moo`03001oogoo03Eoo`03 001oogoo0=Ioo`003goo00<007ooOol0=Woo00<007ooOol0eGoo000?Ool00`00Oomoo`0gOol00`00 Oomoo`3DOol000moo`03001oogoo03Qoo`03001oogoo0==oo`003goo00<007ooOol0>Goo00<007oo Ool0dWoo000?Ool00`00Oomoo`0jOol00`00Oomoo`3AOol000moo`8003aoo`03001oogoo0=1oo`00 3goo00<007ooOol0?7oo00<007ooOol0cgoo000?Ool00`00Oomoo`0mOol00`00Oomoo`3>Ool000mo o`03001oogoo03ioo`03001oogoo0Ool00`00Oomoo`2mOol000moo`03001oogoo 04moo`03001oogoo0;aoo`003goo00<007ooOol0D7oo0P00_7oo000?Ool00`00Oomoo`1BOol00`00 Oomoo`2iOol000moo`03001oogoo05=oo`03001oogoo0;Qoo`003goo00<007ooOol0E7oo00<007oo Ool0]goo000?Ool00`00Oomoo`1EOol00`00Oomoo`2fOol000moo`8005Moo`03001oogoo0;Eoo`00 3goo00<007ooOol0Egoo00<007ooOol0]7oo000?Ool00`00Oomoo`1HOol2002dOol000moo`03001o ogoo05Yoo`03001oogoo0;5oo`003goo00<007ooOol0Fgoo00<007ooOol0/7oo000?Ool00`00Oomo o`1LOol00`00Oomoo`2_Ool000moo`03001oogoo05eoo`800:moo`003goo00<007ooOol0Ggoo00<0 07ooOol0[7oo000?Ool00`00Oomoo`1POol00`00Oomoo`2[Ool000moo`80069oo`800:]oo`003goo 00<007ooOol0Hgoo00<007ooOol0Z7oo000?Ool00`00Oomoo`1TOol2002XOol000moo`03001oogoo 06Ioo`03001oogoo0:Eoo`003goo00<007ooOol0Igoo0P00YGoo000?Ool00`00Oomoo`1YOol00`00 Oomoo`2ROol000moo`03001oogoo06Yoo`800:9oo`003goo00<007ooOol0K7oo00<007ooOol0Wgoo 000?Ool2001^Ool2002OOol000moo`03001oogoo06moo`03001oogoo09aoo`003goo00<007ooOol0 L7oo00<007ooOol0Vgoo000?Ool00`00Oomoo`1aOol2002KOol000moo`03001oogoo07=oo`03001o ogoo09Qoo`003goo00<007ooOol0M7oo00<007ooOol0Ugoo0007Ool40004Ool00`00Oomoo`1eOol2 002GOol000Moo`03001oogoo00Eoo`03001oogoo07Moo`03001oogoo09Aoo`0027oo00<007ooOol0 17oo0`00N7oo0P00U7oo0009Ool00`00Oomoo`03Ool00`00Oomoo`1jOol2002BOol000Moo`04001o ogoo0004Ool00`00Oomoo`1lOol00`00Oomoo`2?Ool000Qoo`8000Eoo`03001oogoo07eoo`8008mo o`003goo00<007ooOol0Ogoo0P00SGoo000?Ool00`00Oomoo`21Ool00`00Oomoo`2:Ool000moo`03 001oogoo089oo`8008Yoo`003goo00<007ooOol0Q7oo0P00R7oo000?Ool20027Ool20026Ool000mo o`03001oogoo08Qoo`8008Aoo`003goo00<007ooOol0RWoo0P00PWoo000?Ool00`00Oomoo`2=oo`D002Ioo`001goo00@007ooOol000Ao o`03001oogoo0>Qoo`l001Moo`002Goo00<007ooOol00goo0`00mgoo40001goo000:Ool00`00Oomo o`02Ool00`00Oomoo`3oOol?Ool000Moo`04001oogoo0004Ool00`00Oomoo`3oOol?Ool000Qoo`80 00Eoo`03001oogoo0?moo`moo`003goo00<007ooOol0ogoo3goo003oOolQOol00?moob5oo`00\ \>"], ImageRangeCache->{{{73.5625, 302.938}, {451.625, 310.313}} -> {-3.40596, \ 8.32678, 0.0037789, 0.0244576}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[x - Cos[x], {x, 0, Pi/2}]\)], "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 0.0238095 0.606305 0.243673 0.228958 [ [.17539 .23117 -12 -9 ] [.17539 .23117 12 0 ] [.32696 .23117 -9 -9 ] [.32696 .23117 9 0 ] [.47854 .23117 -12 -9 ] [.47854 .23117 12 0 ] [.63011 .23117 -3 -9 ] [.63011 .23117 3 0 ] [.78169 .23117 -12 -9 ] [.78169 .23117 12 0 ] [.93327 .23117 -9 -9 ] [.93327 .23117 9 0 ] [.01131 .01472 -12 -4.5 ] [.01131 .01472 0 4.5 ] [.01131 .12919 -24 -4.5 ] [.01131 .12919 0 4.5 ] [.01131 .35815 -18 -4.5 ] [.01131 .35815 0 4.5 ] [.01131 .47263 -6 -4.5 ] [.01131 .47263 0 4.5 ] [.01131 .58711 -18 -4.5 ] [.01131 .58711 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 .24367 m .17539 .24992 L s [(0.25)] .17539 .23117 0 1 Mshowa .32696 .24367 m .32696 .24992 L s [(0.5)] .32696 .23117 0 1 Mshowa .47854 .24367 m .47854 .24992 L s [(0.75)] .47854 .23117 0 1 Mshowa .63011 .24367 m .63011 .24992 L s [(1)] .63011 .23117 0 1 Mshowa .78169 .24367 m .78169 .24992 L s [(1.25)] .78169 .23117 0 1 Mshowa .93327 .24367 m .93327 .24992 L s [(1.5)] .93327 .23117 0 1 Mshowa .125 Mabswid .05412 .24367 m .05412 .24742 L s .08444 .24367 m .08444 .24742 L s .11476 .24367 m .11476 .24742 L s .14507 .24367 m .14507 .24742 L s .2057 .24367 m .2057 .24742 L s .23602 .24367 m .23602 .24742 L s .26633 .24367 m .26633 .24742 L s .29665 .24367 m .29665 .24742 L s .35728 .24367 m .35728 .24742 L s .38759 .24367 m .38759 .24742 L s .41791 .24367 m .41791 .24742 L s .44822 .24367 m .44822 .24742 L s .50885 .24367 m .50885 .24742 L s .53917 .24367 m .53917 .24742 L s .56948 .24367 m .56948 .24742 L s .5998 .24367 m .5998 .24742 L s .66043 .24367 m .66043 .24742 L s .69074 .24367 m .69074 .24742 L s .72106 .24367 m .72106 .24742 L s .75138 .24367 m .75138 .24742 L s .81201 .24367 m .81201 .24742 L s .84232 .24367 m .84232 .24742 L s .87264 .24367 m .87264 .24742 L s .90295 .24367 m .90295 .24742 L s .96358 .24367 m .96358 .24742 L s .9939 .24367 m .9939 .24742 L s .25 Mabswid 0 .24367 m 1 .24367 L s .02381 .01472 m .03006 .01472 L s [(-1)] .01131 .01472 1 0 Mshowa .02381 .12919 m .03006 .12919 L s [(-0.5)] .01131 .12919 1 0 Mshowa .02381 .35815 m .03006 .35815 L s [(0.5)] .01131 .35815 1 0 Mshowa .02381 .47263 m .03006 .47263 L s [(1)] .01131 .47263 1 0 Mshowa .02381 .58711 m .03006 .58711 L s [(1.5)] .01131 .58711 1 0 Mshowa .125 Mabswid .02381 .03761 m .02756 .03761 L s .02381 .06051 m .02756 .06051 L s .02381 .0834 m .02756 .0834 L s .02381 .1063 m .02756 .1063 L s .02381 .15209 m .02756 .15209 L s .02381 .17499 m .02756 .17499 L s .02381 .19788 m .02756 .19788 L s .02381 .22078 m .02756 .22078 L s .02381 .26657 m .02756 .26657 L s .02381 .28946 m .02756 .28946 L s .02381 .31236 m .02756 .31236 L s .02381 .33526 m .02756 .33526 L s .02381 .38105 m .02756 .38105 L s .02381 .40394 m .02756 .40394 L s .02381 .42684 m .02756 .42684 L s .02381 .44973 m .02756 .44973 L s .02381 .49553 m .02756 .49553 L s .02381 .51842 m .02756 .51842 L s .02381 .54132 m .02756 .54132 L s .02381 .56421 m .02756 .56421 L s .02381 .61001 m .02756 .61001 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 .02977 L .10458 .04724 L .14415 .06465 L .18221 .0823 L .22272 .10204 L .26171 .12195 L .30316 .14408 L .34309 .1663 L .3815 .18849 L .42237 .21293 L .46172 .23725 L .49955 .26131 L .53984 .28762 L .57861 .31358 L .61984 .34179 L .65954 .36953 L .69774 .39667 L .73838 .426 L .77751 .4546 L .81909 .48533 L .85916 .51521 L .89771 .54413 L .93871 .57502 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgioo`006goo00<007ooOol057oo0`00jgoo000KOol0 0`00Oomoo`0GOol2003YOol001]oo`8001Yoo`<00>Ioo`006goo00<007ooOol077oo0P00i7oo000K Ool00`00Oomoo`0NOol2003ROol001]oo`03001oogoo021oo`800>1oo`006goo00<007ooOol08Woo 0P00gWoo000KOol00`00Oomoo`0TOol2003LOol001]oo`8002Moo`<00=Uoo`006goo00<007ooOol0 :Goo0P00egoo000KOol00`00Oomoo`0[Ool2003EOol001]oo`03001oogoo02eoo`800==oo`006goo 00<007ooOol0;goo0P00dGoo000KOol00`00Oomoo`0aOol2003?Ool001]oo`8003Aoo`800Woo0P00aWoo0007Ool0 1000Oomoo`0027oo00@007ooOol000Aoo`03001oogoo03aoo`800goo000KOol00`00Oomoo`35Ool00`00Oomoo`0jOol001]oo`03001o ogoo09oo`8001ioo`006goo0P00iGoo00<007ooOol06goo000KOol00`00Oomoo`3U Ool00`00Oomoo`0JOol001]oo`03001oogoo0>Ioo`8001Yoo`006goo00<007ooOol0j7oo00<007oo Ool05goo000KOol00`00Oomoo`3YOol00`00Oomoo`0FOol001]oo`03001oogoo0>Yoo`8001Ioo`00 6goo0P00kGoo00<007ooOol04goo000KOol00`00Oomoo`3]Ool00`00Oomoo`0BOol001]oo`03001o ogoo0>ioo`80019oo`006goo00<007ooOol0l7oo00<007ooOol03goo0007Ool50002Ool20004Ool2 0005Ool00`00Oomoo`3aOol00`00Oomoo`0>Ool000Uoo`03001oogoo00Moo`04001oogoo0004Ool0 0`00Oomoo`3bOol2000>Ool000Uoo`03001oogoo00Yoo`03001oogoo009oo`800?Eoo`03001oogoo 00]oo`002Goo00<007ooOol027oo0P001Goo00<007ooOol0mGoo00<007ooOol02Woo0009Ool00`00 Oomoo`08Ool00`00Oomoo`04Ool00`00Oomoo`3fOol00`00Oomoo`09Ool000Qoo`8000Yoo`<000Ao o`03001oogoo0?Moo`8000Uoo`006goo00<007ooOol0nGoo00<007ooOol01Woo000KOol00`00Oomo o`3jOol00`00Oomoo`05Ool001]oo`800?moo`Aoo`006goo00<007ooOol0ogoo0goo000KOol00`00 Oomoo`3oOol3Ool001]oo`03001oogoo0?moo`=oo`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo 8Goo003oOolQOol00001\ \>"], ImageRangeCache->{{{73.5625, 302.938}, {644.5, 503.188}} -> {-0.740346, \ 9.16735, 0.00620701, 0.0164368}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[x - 0.8 - 0.2 Sin[x], {x, 0, Pi/2}]\)], "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 0.0238095 0.606305 0.358226 0.429388 [ [.17539 .34573 -12 -9 ] [.17539 .34573 12 0 ] [.32696 .34573 -9 -9 ] [.32696 .34573 9 0 ] [.47854 .34573 -12 -9 ] [.47854 .34573 12 0 ] [.63011 .34573 -3 -9 ] [.63011 .34573 3 0 ] [.78169 .34573 -12 -9 ] [.78169 .34573 12 0 ] [.93327 .34573 -9 -9 ] [.93327 .34573 9 0 ] [.01131 .01472 -24 -4.5 ] [.01131 .01472 0 4.5 ] [.01131 .10059 -24 -4.5 ] [.01131 .10059 0 4.5 ] [.01131 .18647 -24 -4.5 ] [.01131 .18647 0 4.5 ] [.01131 .27235 -24 -4.5 ] [.01131 .27235 0 4.5 ] [.01131 .4441 -18 -4.5 ] [.01131 .4441 0 4.5 ] [.01131 .52998 -18 -4.5 ] [.01131 .52998 0 4.5 ] [.01131 .61586 -18 -4.5 ] [.01131 .61586 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 .35823 m .17539 .36448 L s [(0.25)] .17539 .34573 0 1 Mshowa .32696 .35823 m .32696 .36448 L s [(0.5)] .32696 .34573 0 1 Mshowa .47854 .35823 m .47854 .36448 L s [(0.75)] .47854 .34573 0 1 Mshowa .63011 .35823 m .63011 .36448 L s [(1)] .63011 .34573 0 1 Mshowa .78169 .35823 m .78169 .36448 L s [(1.25)] .78169 .34573 0 1 Mshowa .93327 .35823 m .93327 .36448 L s [(1.5)] .93327 .34573 0 1 Mshowa .125 Mabswid .05412 .35823 m .05412 .36198 L s .08444 .35823 m .08444 .36198 L s .11476 .35823 m .11476 .36198 L s .14507 .35823 m .14507 .36198 L s .2057 .35823 m .2057 .36198 L s .23602 .35823 m .23602 .36198 L s .26633 .35823 m .26633 .36198 L s .29665 .35823 m .29665 .36198 L s .35728 .35823 m .35728 .36198 L s .38759 .35823 m .38759 .36198 L s .41791 .35823 m .41791 .36198 L s .44822 .35823 m .44822 .36198 L s .50885 .35823 m .50885 .36198 L s .53917 .35823 m .53917 .36198 L s .56948 .35823 m .56948 .36198 L s .5998 .35823 m .5998 .36198 L s .66043 .35823 m .66043 .36198 L s .69074 .35823 m .69074 .36198 L s .72106 .35823 m .72106 .36198 L s .75138 .35823 m .75138 .36198 L s .81201 .35823 m .81201 .36198 L s .84232 .35823 m .84232 .36198 L s .87264 .35823 m .87264 .36198 L s .90295 .35823 m .90295 .36198 L s .96358 .35823 m .96358 .36198 L s .9939 .35823 m .9939 .36198 L s .25 Mabswid 0 .35823 m 1 .35823 L s .02381 .01472 m .03006 .01472 L s [(-0.8)] .01131 .01472 1 0 Mshowa .02381 .10059 m .03006 .10059 L s [(-0.6)] .01131 .10059 1 0 Mshowa .02381 .18647 m .03006 .18647 L s [(-0.4)] .01131 .18647 1 0 Mshowa .02381 .27235 m .03006 .27235 L s [(-0.2)] .01131 .27235 1 0 Mshowa .02381 .4441 m .03006 .4441 L s [(0.2)] .01131 .4441 1 0 Mshowa .02381 .52998 m .03006 .52998 L s [(0.4)] .01131 .52998 1 0 Mshowa .02381 .61586 m .03006 .61586 L s [(0.6)] .01131 .61586 1 0 Mshowa .125 Mabswid .02381 .03618 m .02756 .03618 L s .02381 .05765 m .02756 .05765 L s .02381 .07912 m .02756 .07912 L s .02381 .12206 m .02756 .12206 L s .02381 .14353 m .02756 .14353 L s .02381 .165 m .02756 .165 L s .02381 .20794 m .02756 .20794 L s .02381 .22941 m .02756 .22941 L s .02381 .25088 m .02756 .25088 L s .02381 .29382 m .02756 .29382 L s .02381 .31529 m .02756 .31529 L s .02381 .33676 m .02756 .33676 L s .02381 .3797 m .02756 .3797 L s .02381 .40116 m .02756 .40116 L s .02381 .42263 m .02756 .42263 L s .02381 .46557 m .02756 .46557 L s .02381 .48704 m .02756 .48704 L s .02381 .50851 m .02756 .50851 L s .02381 .55145 m .02756 .55145 L s .02381 .57292 m .02756 .57292 L s .02381 .59439 m .02756 .59439 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 .03661 L .10458 .06051 L .14415 .08301 L .18221 .10471 L .22272 .12791 L .26171 .15036 L .30316 .17437 L .34309 .19767 L .3815 .22026 L .42237 .2445 L .46172 .26807 L .49955 .29096 L .53984 .31559 L .57861 .33956 L .61984 .36536 L .65954 .39052 L .69774 .41502 L .73838 .44142 L .77751 .46718 L .81909 .49493 L .85916 .52203 L .89771 .54846 L .93871 .57694 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgeoo`006goo00<007ooOol05Goo0P00jgoo000KOol00`00Oomoo`0GOol2003YOol001]oo`03 001oogoo01Uoo`800>Moo`006goo0P0077oo0P00iGoo000KOol00`00Oomoo`0MOol00`00Oomoo`3R Ool001]oo`03001oogoo01ioo`800>9oo`006goo00<007ooOol087oo0P00h7oo0008Ool20004Ool2 0003Ool30005Ool00`00Oomoo`0ROol00`00Oomoo`3MOol000Moo`04001oogoo0008Ool01000Oomo o`0017oo00<007ooOol08goo0P00gGoo0007Ool01000Oomoo`0027oo00@007ooOol000Aoo`8002Io o`800=]oo`0000=oo`0000000P000Woo00@007ooOol000Qoo`<000Eoo`03001oogoo02Moo`03001o ogoo0=Qoo`001goo00@007ooOol000Uoo`03001oogoo00Aoo`03001oogoo02Qoo`800=Qoo`0027oo 0P002Woo0`0017oo00<007ooOol0:Woo0P00eWoo000KOol00`00Oomoo`0/Ool2003DOol001]oo`03 001oogoo02ioo`800=9oo`006goo0P00Woo0P00aWoo000K Ool00`00Oomoo`0lOol00`00Oomoo`33Ool001]oo`03001oogoo03eoo`800<=oo`006goo00<007oo Ool0?goo00<007ooOol0`7oo000KOol00`00Oomoo`10Ool20030Ool001]oo`8004=oo`800;ioo`00 6goo00<007ooOol0A7oo00<007ooOol0^goo000KOol00`00Oomoo`15Ool2002kOol001]oo`03001o ogoo04Moo`03001oogoo0;Qoo`0027oo0P0017oo0P001Goo0`000goo00<007ooOol0B7oo0P00^7oo 0007Ool01000Oomoo`002goo00<007ooOol00Woo00<007ooOol0BWoo0P00]Woo0007Ool01000Oomo o`0027oo1@000goo0P00CGoo0P00]7oo00000goo000000020002Ool01000Oomoo`0027oo00@007oo Ool000Aoo`03001oogoo04ioo`800;9oo`001goo00@007ooOol000Uoo`03001oo`0000Aoo`03001o ogoo051oo`800;1oo`0027oo0P002goo0P0017oo00<007ooOol0DWoo00<007ooOol0[Goo000KOol0 0`00Oomoo`1COol2002]Ool001]oo`8005Ioo`800:]oo`006goo00<007ooOol0Egoo00<007ooOol0 Z7oo000KOol00`00Oomoo`1HOol2002XOol001]oo`03001oogoo05Yoo`800:Ioo`006goo00<007oo Ool0G7oo00<007ooOol0Xgoo000KOol00`00Oomoo`1MOol2002SOol001]oo`80061oo`800:5oo`00 6goo00<007ooOol0HGoo0P00Wgoo000KOol00`00Oomoo`1SOol2002MOol001]oo`03001oogoo06Eo o`8009]oo`006goo00<007ooOol0Igoo00<007ooOol0V7oo000KOol00`00Oomoo`1XOol2002HOol0 01]oo`8006]oo`8009Ioo`006goo00<007ooOol0K7oo00<007ooOol0Tgoo000KOol00`00Oomoo`1] Ool2002COol001]oo`03001oogoo06moo`80095oo`0027oo0P0017oo0P000goo100017oo00<007oo Ool0LGoo00<007ooOol0SWoo0007Ool01000Oomoo`0027oo00<007ooOol01Goo00<007ooOol0LWoo 0P00SWoo0007Ool01000Oomoo`002Goo00<007ooOol017oo0P00MGoo00<007ooOol0Rgoo00000goo 000000020002Ool01000Oomoo`002Woo00<007ooOol00goo00<007ooOol0MGoo00<007ooOol0RWoo 0007Ool01000Oomoo`0027oo00@007ooOol000Aoo`03001oogoo07Ioo`8008Yoo`0027oo0P002Woo 0P001Goo00<007ooOol0N7oo00<007ooOol0Qgoo000KOol00`00Oomoo`1iOol20027Ool001]oo`80 07aoo`03001oogoo08Aoo`006goo00<007ooOol0O7oo0P00Q7oo000KOol00`00Oomoo`1nOol20022 Ool001]oo`03001oogoo081oo`80081oo`006goo00<007ooOol0PWoo0P00OWoo000KOol00`00Oomo o`24Ool2001lOol001]oo`8001aoo`8000Aoo`8000=oo`@000=oo`8001Moo`8000Aoo`8000Aoo`80 01Qoo`8000Aoo`8000Eoo`03001oogoo009oo`8000Ioo`03001oogoo01=oo`D001Yoo`D0009oo`80 00=oo`@000=oo`8001Moo`D0009oo`8000Aoo`8000aoo`006goo00<007ooOol06Woo00@007ooOol0 00Qoo`03001oogoo00=oo`04001oogoo000EOol01000Oomoo`0027oo00@007ooOol001Ioo`04001o ogoo000:Ool01@00Oomoogoo00000Woo00<007ooOol017oo0P005Goo00<007ooOol077oo00<007oo Ool01goo00<007ooOol00goo00@007ooOol001Qoo`03001oogoo00Moo`04001oogoo000;Ool001]o o`03001oogoo01Yoo`04001oogoo0009Ool00`00Oomoo`05Ool00`00Oomoo`0COol01000Oomoo`00 2goo00<007ooOol057oo00@007ooOol000Yoo`03001oogoo00Aoo`03001oogoo00Ioo`8001=oo`03 001oogoo01aoo`03001oogoo00Qoo`03001oogoo00Eoo`03001oogoo01Ioo`03001oogoo00Yoo`03 001oogoo00Uoo`006goo00<007ooOol06Woo00@007ooOol000Yoo`03001oogoo009oo`8001Ioo`04 001oogoo0009Ool2000GOol01000Oomoo`002goo00@007ooOomoo`8000]oo`03001oogoo011oo`03 001oogoo01aoo`03001oogoo00Uoo`03001oogoo009oo`8001Uoo`03001oogoo00Qoo`8000aoo`00 6goo00<007ooOol06Woo00@007ooOol000Qoo`04001oogoo0003Ool00`00Oomoo`0EOol01000Oomo o`002Goo00<007ooOol05Woo00@007ooOol000Qoo`04001oogoo0003Ool00`00Oomoo`0;Ool2000@ Ool00`00Oomoo`0LOol00`00Oomoo`07Ool01000Oomoo`000goo00<007ooOol067oo00<007ooOol0 27oo00<007ooOol02goo000KOol00`00Oomoo`0KOol2000:Ool20004Ool3000FOol2000:Ool3000G Ool20009Ool40003Ool3000=Ool2000=Ool2000MOol2000:Ool20004Ool3000GOol2000:Ool3000; Ool001]oo`80095oo`03001oogoo06moo`006goo00<007ooOol0TGoo0P00Kgoo000KOol00`00Oomo o`2COol00`00Oomoo`1/Ool001]oo`03001oogoo09Aoo`8006aoo`006goo00<007ooOol0UWoo0P00 JWoo000DOooo000=000001]oo`03001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Eoo`03001o ogoo00Eoo`03001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Eoo`03001o ogoo00Eoo`03001oogoo00Eoo`03001oogoo00Ioo`03001oogoo00Eoo`03001oogoo00Eoo`03001o ogoo00Eoo`03001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Eoo`03001o ogoo00Eoo`03001oogoo008000=oo`03001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Eoo`03 001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Ioo`03001oogoo00Eoo`03 001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Eoo`40005oo`5oo`006goo 00<007ooOol09Goo00<007ooOol09Goo00<007ooOol09Woo00<007ooOol08Woo00@007ooOol002Mo o`03001oogoo02Ioo`03001oogoo011oo`006goo00<007ooOol0W7oo0P00I7oo000KOol00`00Oomo o`2NOol00`00Oomoo`1QOol001]oo`03001oogoo09moo`80065oo`006goo0P00XWoo0P00Ggoo000K Ool00`00Oomoo`2SOol00`00Oomoo`1LOol001]oo`03001oogoo0:Aoo`8005aoo`006goo00<007oo Ool0YWoo00<007ooOol0FGoo000KOol00`00Oomoo`2WOol2001IOol001]oo`03001oogoo0:Uoo`03 001oogoo05Ioo`006goo0P00Zgoo00<007ooOol0EGoo000KOol00`00Oomoo`2[Ool2001EOol001]o o`03001oogoo0:eoo`03001oogoo059oo`006goo00<007ooOol0[Woo0P00DWoo000KOol00`00Oomo o`2`Ool00`00Oomoo`1?Ool001]oo`03001oogoo0;5oo`8004moo`006goo0P00]7oo00<007ooOol0 C7oo000KOol00`00Oomoo`2dOol2001Woo000KOol00`00Oomoo`36Ool2000j Ool001]oo`03001oogoo0Ool2000bOol001]oo`03001oogoo0=1oo`03001o ogoo02moo`006goo00<007ooOol0dGoo0P00;goo000KOol00`00Oomoo`3COol00`00Oomoo`0/Ool0 01]oo`800=Eoo`8002aoo`006goo00<007ooOol0eWoo0P00:Woo000KOol00`00Oomoo`3HOol00`00 Oomoo`0WOol001]oo`03001oogoo0=Uoo`8002Moo`0027oo0P0017oo0P001Goo0`000goo00<007oo Ool0fgoo00<007ooOol097oo0007Ool01000Oomoo`002goo00<007ooOol00Woo00<007ooOol0g7oo 0P0097oo0007Ool01000Oomoo`0027oo1@000goo0P00ggoo00<007ooOol08Goo0007Ool01000Oomo o`0027oo00@007ooOol000Aoo`03001oogoo0=moo`03001oogoo021oo`001goo00@007ooOol000Uo o`03001oo`0000Aoo`03001oogoo0>1oo`80021oo`0027oo0P002goo0P0017oo00<007ooOol0hWoo 00<007ooOol07Goo000KOol00`00Oomoo`3SOol2000MOol001]oo`03001oogoo0>Eoo`03001oogoo 01Yoo`006goo0P00igoo0P006Woo000KOol00`00Oomoo`3XOol00`00Oomoo`0GOol001]oo`03001o ogoo0>Uoo`03001oogoo01Ioo`006goo00<007ooOol0jWoo0P005Woo000KOol00`00Oomoo`3/Ool0 0`00Oomoo`0COol001]oo`03001oogoo0>eoo`03001oogoo019oo`006goo0P00kgoo0P004Woo000K Ool00`00Oomoo`3`Ool00`00Oomoo`0?Ool001]oo`03001oogoo0?5oo`8000moo`006goo00<007oo Ool0lgoo00<007ooOol037oo000KOol00`00Oomoo`3dOol00`00Oomoo`0;Ool001]oo`800?Ioo`80 00]oo`006goo00<007ooOol0mgoo00<007ooOol027oo000KOol00`00Oomoo`3hOol20008Ool001]o o`03001oogoo0?Yoo`03001oogoo00Eoo`0027oo0P0017oo0P000goo0`001Goo00<007ooOol0ogoo 0goo0007Ool01000Oomoo`0027oo00@007ooOol000Aoo`03001oogoo0?moo`=oo`001goo00@007oo Ool000Qoo`04001oogoo0004Ool2003oOol4Ool000Moo`04001oogoo0008Ool30005Ool00`00Oomo o`3oOol3Ool000Moo`04001oogoo0009Ool00`00Oomoo`3oOol:Ool000Qoo`8000Yoo`<00?moo`Yo o`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol00001\ \>"], ImageRangeCache->{{{73.5625, 302.938}, {220.688, 79.375}} -> {-0.740346, \ -0.00447492, 0.00620701, 0.00876443}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[BoxData[ \(f[x_] := \ Sin[3 x]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(g = D[f[x], {x, 1}]\)], "Input"], Cell[BoxData[ \(3\ Cos[3\ x]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(g /. x \[Rule] Pi\)], "Input"], Cell[BoxData[ \(\(-3\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(T\)], "Input"], Cell[BoxData[ \(T\)], "Output"] }, Open ]], Cell[BoxData[ \(Taypol[n_, a_] := \((\[IndentingNewLine]T = 0; \[IndentingNewLine]x =. ; \[IndentingNewLine]For[i = 0, \ i \[LessEqual] n, i = i + 1, \[IndentingNewLine]dd = D[f[x], {x, i}]; \[IndentingNewLine]cc = \ dd /. \ x \[Rule] a; \[IndentingNewLine]T = T + \ cc\ \((x - a)\)^i/\((\(i!\))\)])\)\)], "Input"], Cell[BoxData[ \(Taypol[1, 1]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(T\)], "Input"], Cell[BoxData[ \(3\ \((\(-1\) + x)\)\ Cos[3] + Sin[3]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(Plot[{T, f[x]}, {x, 0, 2 Pi}]\)\)\)], "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 0.345398 0.0829036 [ [.17539 .3329 -3 -9 ] [.17539 .3329 3 0 ] [.32696 .3329 -3 -9 ] [.32696 .3329 3 0 ] [.47854 .3329 -3 -9 ] [.47854 .3329 3 0 ] [.63011 .3329 -3 -9 ] [.63011 .3329 3 0 ] [.78169 .3329 -3 -9 ] [.78169 .3329 3 0 ] [.93327 .3329 -3 -9 ] [.93327 .3329 3 0 ] [.01131 .01378 -12 -4.5 ] [.01131 .01378 0 4.5 ] [.01131 .09669 -12 -4.5 ] [.01131 .09669 0 4.5 ] [.01131 .17959 -12 -4.5 ] [.01131 .17959 0 4.5 ] [.01131 .26249 -12 -4.5 ] [.01131 .26249 0 4.5 ] [.01131 .4283 -6 -4.5 ] [.01131 .4283 0 4.5 ] [.01131 .5112 -6 -4.5 ] [.01131 .5112 0 4.5 ] [.01131 .59411 -6 -4.5 ] [.01131 .59411 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 .3454 m .17539 .35165 L s [(1)] .17539 .3329 0 1 Mshowa .32696 .3454 m .32696 .35165 L s [(2)] .32696 .3329 0 1 Mshowa .47854 .3454 m .47854 .35165 L s [(3)] .47854 .3329 0 1 Mshowa .63011 .3454 m .63011 .35165 L s [(4)] .63011 .3329 0 1 Mshowa .78169 .3454 m .78169 .35165 L s [(5)] .78169 .3329 0 1 Mshowa .93327 .3454 m .93327 .35165 L s [(6)] .93327 .3329 0 1 Mshowa .125 Mabswid .05412 .3454 m .05412 .34915 L s .08444 .3454 m .08444 .34915 L s .11476 .3454 m .11476 .34915 L s .14507 .3454 m .14507 .34915 L s .2057 .3454 m .2057 .34915 L s .23602 .3454 m .23602 .34915 L s .26633 .3454 m .26633 .34915 L s .29665 .3454 m .29665 .34915 L s .35728 .3454 m .35728 .34915 L s .38759 .3454 m .38759 .34915 L s .41791 .3454 m .41791 .34915 L s .44822 .3454 m .44822 .34915 L s .50885 .3454 m .50885 .34915 L s .53917 .3454 m .53917 .34915 L s .56948 .3454 m .56948 .34915 L s .5998 .3454 m .5998 .34915 L s .66043 .3454 m .66043 .34915 L s .69074 .3454 m .69074 .34915 L s .72106 .3454 m .72106 .34915 L s .75138 .3454 m .75138 .34915 L s .81201 .3454 m .81201 .34915 L s .84232 .3454 m .84232 .34915 L s .87264 .3454 m .87264 .34915 L s .90295 .3454 m .90295 .34915 L s .96358 .3454 m .96358 .34915 L s .9939 .3454 m .9939 .34915 L s .25 Mabswid 0 .3454 m 1 .3454 L s .02381 .01378 m .03006 .01378 L s [(-4)] .01131 .01378 1 0 Mshowa .02381 .09669 m .03006 .09669 L s [(-3)] .01131 .09669 1 0 Mshowa .02381 .17959 m .03006 .17959 L s [(-2)] .01131 .17959 1 0 Mshowa .02381 .26249 m .03006 .26249 L s [(-1)] .01131 .26249 1 0 Mshowa .02381 .4283 m .03006 .4283 L s [(1)] .01131 .4283 1 0 Mshowa .02381 .5112 m .03006 .5112 L s [(2)] .01131 .5112 1 0 Mshowa .02381 .59411 m .03006 .59411 L s [(3)] .01131 .59411 1 0 Mshowa .125 Mabswid .02381 .03036 m .02756 .03036 L s .02381 .04694 m .02756 .04694 L s .02381 .06353 m .02756 .06353 L s .02381 .08011 m .02756 .08011 L s .02381 .11327 m .02756 .11327 L s .02381 .12985 m .02756 .12985 L s .02381 .14643 m .02756 .14643 L s .02381 .16301 m .02756 .16301 L s .02381 .19617 m .02756 .19617 L s .02381 .21275 m .02756 .21275 L s .02381 .22933 m .02756 .22933 L s .02381 .24591 m .02756 .24591 L s .02381 .27907 m .02756 .27907 L s .02381 .29566 m .02756 .29566 L s .02381 .31224 m .02756 .31224 L s .02381 .32882 m .02756 .32882 L s .02381 .36198 m .02756 .36198 L s .02381 .37856 m .02756 .37856 L s .02381 .39514 m .02756 .39514 L s .02381 .41172 m .02756 .41172 L s .02381 .44488 m .02756 .44488 L s .02381 .46146 m .02756 .46146 L s .02381 .47804 m .02756 .47804 L s .02381 .49462 m .02756 .49462 L s .02381 .52779 m .02756 .52779 L s .02381 .54437 m .02756 .54437 L s .02381 .56095 m .02756 .56095 L s .02381 .57753 m .02756 .57753 L s .02381 .61069 m .02756 .61069 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 .06244 .54056 L .10458 .47211 L .14415 .40783 L .18221 .34601 L .22272 .28021 L .26171 .21687 L .30316 .14955 L .34309 .08468 L .3815 .02228 L s .3815 .02228 m .39522 0 L s .02381 .3454 m .04262 .37555 L .06244 .40279 L .07286 .41382 L .08255 .42149 L .08813 .42465 L .09076 .42581 L .0932 .42669 L .096 .42747 L .09748 .42778 L .09824 .42791 L .09905 .42802 L .09976 .42811 L .10041 .42818 L .10168 .42827 L .10239 .42829 L .10317 .4283 L .1039 .42829 L .10458 .42827 L .10587 .42818 L .10651 .42812 L .10722 .42804 L .10848 .42784 L .10966 .42762 L .11231 .42695 L .11515 .42598 L .12035 .42355 L .1251 .42062 L .13466 .41272 L .14371 .40302 L .18204 .34622 L .20142 .31513 L .21172 .30013 L .22282 .28609 L .23339 .27535 L .23801 .27159 L .24307 .26819 L .24787 .26567 L .25234 .26398 L .25481 .26331 L .25705 .26288 L .25829 .26271 L .259 .26263 L .25964 .26258 L .26083 .26251 L .26209 .26249 L .2633 .26253 L .26462 .26261 L .26586 .26275 L .26702 .26292 L Mistroke .2692 .26336 L .27152 .26399 L .27427 .26496 L .27684 .26609 L .28166 .26875 L .29046 .27539 L .29997 .28494 L .31995 .31145 L .34103 .345 L .36093 .37685 L .37905 .40178 L .3891 .41267 L .3986 .42054 L .40382 .42375 L .40863 .42597 L .41115 .42684 L .41392 .42757 L .41532 .42784 L .41605 .42796 L .41682 .42806 L .41749 .42814 L .41823 .42821 L .41953 .42828 L .42017 .4283 L .42086 .4283 L .42208 .42827 L .42339 .42818 L .42414 .4281 L .42483 .42802 L .42724 .42759 L .4286 .42727 L .42983 .42693 L .43463 .42514 L .43918 .42278 L .44922 .41539 L .46014 .40422 L .47989 .37752 L .50089 .34393 L .52056 .31258 L .53861 .28803 L .54802 .27794 L .55794 .26984 L .56309 .26676 L .56789 .26462 L .57065 .26373 L .57315 .26312 L .57454 .26287 L .57527 .26277 L .57605 .26267 L .57672 .26261 L Mistroke .57747 .26255 L .57878 .2625 L .58007 .2625 L .58127 .26255 L .58259 .26266 L .58332 .26275 L .58399 .26284 L .58653 .26333 L .58893 .26397 L .59339 .26567 L .59821 .26819 L .6035 .27177 L .60909 .27643 L .61909 .28683 L .65708 .34269 L .67824 .37662 L .69753 .40298 L .70711 .41319 L .71216 .41762 L .71752 .42152 L .7222 .42423 L .72468 .4254 L .72736 .42644 L .72981 .42719 L .73088 .42746 L .73205 .42771 L .73309 .42789 L .7342 .42805 L .73537 .42818 L .73645 .42826 L .73769 .4283 L .73839 .4283 L .73905 .42829 L .73974 .42826 L .74037 .42822 L .7411 .42815 L .74179 .42808 L .74301 .42791 L .74414 .42771 L .74671 .4271 L .74953 .42619 L .75209 .42514 L .75782 .42207 L .76281 .41858 L .7682 .41401 L .77797 .40379 L .81905 .34279 L .83953 .31033 L .84952 .29626 L .85861 .2851 L Mistroke .86742 .27614 L .87699 .2688 L .88224 .26592 L .88455 .26493 L .88709 .26403 L .88949 .26337 L .89173 .26291 L .89297 .26274 L .8941 .26261 L .89541 .26253 L .89665 .26249 L .89789 .26251 L .89859 .26254 L .89924 .26259 L .90042 .2627 L .90168 .26288 L .90385 .26329 L .90623 .26393 L .90878 .2648 L .91151 .26597 L .91645 .26867 L .92606 .27599 L .93483 .28486 L .95391 .31001 L .97467 .3429 L .97619 .3454 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgWoo00<007ooOol0dGoo000?Ool2000kOol00`00Oomoo`3AOol000mo o`03001oogoo03Uoo`03001oogoo0=9oo`001goo1@000goo00<007ooOol0>Goo00<007ooOol0dWoo 0009Ool00`00Oomoo`03Ool00`00Oomoo`0hOol00`00Oomoo`3COol000Uoo`03001oogoo00=oo`<0 03Moo`03001oogoo00Aoo`<005Ioo`<005Eoo`<001aoo`0000=oo`0000000P0017oo00<007ooOol0 0goo00<007ooOol0=goo00@007ooOomoo`@0009oo`<0051oo`<0009oo`<0051oo`<0009oo`@001Uo o`002Goo00<007ooOol00goo00<007ooOol0=Woo00D007ooOomoo`0000Uoo`8004aoo`8000Qoo`80 04aoo`8000Uoo`03001oogoo01Ioo`0027oo0P001Goo00<007ooOol0=Goo00D007ooOomoo`0000ao o`03001oogoo04Qoo`03001oogoo00Yoo`03001oogoo04Qoo`03001oogoo00Yoo`8001Ioo`003goo 00<007ooOol0=Goo00@007oo000000ioo`03001oogoo04Ioo`03001oogoo00aoo`8004Moo`03001o ogoo00eoo`03001oogoo01=oo`003goo0P00=Goo00<007oo00004Goo00<007ooOol0A7oo00<007oo Ool03goo00<007ooOol0@goo00<007ooOol03goo00<007ooOol04Woo000?Ool00`00Oomoo`0cOol0 0`00Ool0000COol00`00Oomoo`12Ool00`00Oomoo`0AOol00`00Oomoo`11Ool00`00Oomoo`0@Ool0 0`00Oomoo`0BOol000moo`03001oogoo03=oo`8001Eoo`03001oogoo041oo`03001oogoo01=oo`03 001oogoo03moo`03001oogoo019oo`03001oogoo015oo`003goo00<007ooOol0Goo00<007ooOol06Woo00<007ooOol0>Goo00<007ooOol067oo 00<007ooOol03Woo000?Ool00`00Oomoo`0UOol50006Ool00`00Oomoo`0KOol5000WOol2000=Ool0 0`00Oomoo`0JOol3000VOol2000@Ool00`00Oomoo`0DOol30003Ool00`00Oomoo`0=Ool000moo`03 001oogoo02Moo`03001oogoo00Eoo`03001oogoo01aoo`8002Uoo`04001oogoo000;Ool00`00Oomo o`0LOol00`00Oomoo`0TOol01000Oomoo`003goo00<007ooOol057oo00@007ooOol000=oo`03001o ogoo00aoo`003goo0P00:7oo00<007ooOol01Goo00<007ooOol07Goo0P00:Woo00<007ooOol02Goo 00<007ooOol06Woo1@00:7oo00<007ooOol037oo00<007ooOol05Goo00@007ooOol000Aoo`03001o ogoo00]oo`003goo00<007ooOol09goo00<007ooOol017oo00<007ooOol07goo0P00:Woo00<007oo Ool01goo00<007ooOol06goo00<007ooOol00P009Woo0P003Woo00<007ooOol05Woo0`001Woo00<0 07ooOol02Woo000?Ool00`00Oomoo`0WOol00`00Oomoo`03Ool2000POol200000goo001oo`0UOol0 1000Oomoo`002Goo00<007ooOol077oo00D007oo001oo`0002Eoo`03001oogoo00eoo`03001oogoo 01Moo`03001oogoo00Eoo`03001oogoo00Yoo`003goo00<007ooOol09Woo0P001Goo00<007ooOol0 87oo0P00:7oo0P002Goo00<007ooOol07Woo0P0000=oo`00Ool097oo0`0037oo00<007ooOol067oo 0`001Woo00<007ooOol02Goo000?Ool00`00Oomoo`0/Ool00`00Oomoo`0SOol00`00Oomoo`0`Ool0 0`00Oomoo`0ROol00`00Oomoo`0`Ool00`00Oomoo`0ROol00`00Oomoo`09Ool000moo`8002eoo`03 001oogoo02=oo`03001oogoo02moo`03001oogoo02Aoo`03001oogoo02moo`03001oogoo02=oo`03 001oogoo00Qoo`003goo00<007ooOol0:goo00<007ooOol09Goo00<007ooOol0;Woo00<007ooOol0 97oo00<007ooOol0;Woo00<007ooOol097oo00<007ooOol027oo000?Ool00`00Oomoo`0[Ool00`00 Oomoo`0VOol00`00Oomoo`0/Ool00`00Oomoo`0VOol00`00Oomoo`0/Ool00`00Oomoo`0VOol00`00 Oomoo`07Ool000moo`03001oogoo02Yoo`03001oogoo02Moo`03001oogoo02aoo`03001oogoo02Io o`03001oogoo02aoo`03001oogoo02Ioo`03001oogoo00Moo`0027ooo`006@00000?Ool20006Ool0 0`00Oomoo`06Ool00`00Oomoo`05Ool00`00Oomoo`06Ool00`00Oomoo`05Ool00`00Ool00006Ool0 0`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`06Ool00`00Oomoo`05Ool00`00Oomoo`02Ool0 1@00Oomoogoo00001goo00<007ooOol01Woo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol0 0goo00@007ooOol000Moo`03001oogoo00Ioo`03001oogoo00Eoo`03001oogoo00Ioo`03001oogoo 00Eoo`03001oogoo00Eoo`03001oogoo00Ioo`03001oogoo00Eoo`03001oogoo00Ioo`03001oogoo 00Eoo`8000Moo`03001oogoo00Eoo`03001oogoo00Ioo`03001oogoo00Eoo`03001oogoo00Eoo`03 001oogoo00Ioo`40005oo`5oo`003goo0P001Woo00<007ooOol01Woo00<007ooOol01Goo00<007oo Ool01Woo00<007ooOol01Goo0P001goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Woo 00<007ooOol01Goo00<007ooOol00Woo00D007ooOomoo`0000Moo`03001oogoo00Ioo`03001oogoo 00Eoo`03001oogoo00Eoo`03001oogoo00=oo`04001oogoo0007Ool00`00Oomoo`06Ool00`00Oomo o`05Ool00`00Oomoo`06Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`06Ool00`00Oomo o`05Ool00`00Oomoo`06Ool00`00Oomoo`05Ool20007Ool00`00Oomoo`05Ool00`00Oomoo`06Ool0 0`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`06Ool10001Ool1Ool000moo`03001oo`0002Qo o`03001oogoo02aoo`03001oogoo02Ioo`03001oogoo02aoo`03001oogoo02Ioo`03001oogoo03=o o`003goo00<007oo00009goo00<007ooOol0;Woo00<007ooOol097oo00<007ooOol0;Woo00<007oo Ool097oo00<007ooOol0=7oo000?Ool200000goo001oo`0TOol00`00Oomoo`0_Ool00`00Oomoo`0T Ool00`00Oomoo`0^Ool00`00Oomoo`0TOol00`00Oomoo`0dOol000moo`04001oogoo000UOol00`00 Oomoo`0`Ool00`00Oomoo`0ROol00`00Oomoo`0`Ool00`00Oomoo`0ROol00`00Oomoo`0eOol000mo o`05001oogooOol0000SOol00`00Oomoo`0bOol00`00Oomoo`0POol00`00Oomoo`0bOol00`00Oomo o`0POol00`00Oomoo`0fOol000moo`05001oogooOol0000ROol00`00Oomoo`0cOol00`00Oomoo`0P Ool00`00Oomoo`0bOol00`00Oomoo`0POol00`00Oomoo`0fOol000moo`03001oogoo009oo`03001o ogoo01ioo`8003Ioo`03001oogoo01ioo`03001oogoo03Aoo`03001oogoo01ioo`03001oogoo03Mo o`003goo0P0017oo00<007ooOol07Goo00<007ooOol0=Woo00<007ooOol077oo00<007ooOol0=Woo 00<007ooOol07Goo00<007ooOol0=goo000?Ool00`00Oomoo`04Ool00`00Oomoo`0KOol2000hOol0 0`00Oomoo`0KOol00`00Oomoo`0gOol00`00Oomoo`0LOol00`00Oomoo`0hOol000moo`03001oogoo 00Eoo`03001oogoo01Uoo`8003Yoo`03001oogoo01Yoo`03001oogoo03Qoo`03001oogoo01Yoo`03 001oogoo03Uoo`003goo00<007ooOol01Goo00<007ooOol06Goo00<007ooOol0>Woo00<007ooOol0 67oo00<007ooOol0>Woo00<007ooOol06Goo00<007ooOol0>Goo000?Ool20007Ool00`00Oomoo`0G Ool2000mOol00`00Oomoo`0FOol00`00Oomoo`0lOol00`00Oomoo`0GOol00`00Oomoo`0jOol000mo o`03001oogoo00Moo`03001oogoo01Eoo`8003ioo`03001oogoo01Eoo`03001oogoo03eoo`03001o ogoo01Ioo`03001oogoo03]oo`003goo00<007ooOol027oo00<007ooOol057oo00<007ooOol0?Woo 00<007ooOol057oo00<007ooOol0?Woo00<007ooOol05Goo00<007ooOol0>goo000?Ool00`00Oomo o`09Ool00`00Oomoo`0BOol20011Ool00`00Oomoo`0BOol00`00Oomoo`10Ool00`00Oomoo`0COol0 0`00Oomoo`0lOol000moo`03001oogoo00Yoo`03001oogoo011oo`8004=oo`03001oogoo011oo`03 001oogoo049oo`03001oogoo015oo`03001oogoo03eoo`003goo0P002goo00<007ooOol03goo0P00 AGoo00<007ooOol03Woo00<007ooOol0A7oo00<007ooOol03goo00<007ooOol0?Woo000?Ool00`00 Oomoo`0;Ool00`00Oomoo`0Ool000Qoo`8000Eoo`04001oogoo003oOol>Ool0 00Moo`04001oogoo0004Ool00`00Ool0003oOol?Ool000Uoo`03001oogoo00=oo`<00?moo`moo`00 2Woo00<007ooOol00Woo0P00ogoo47oo0007Ool01000Oomoo`0017oo00<007ooOol0ogoo3goo0008 Ool20005Ool00`00Oomoo`3oOol?Ool000moo`800?mooa1oo`003goo00<007ooOol0ogoo3goo000? Ool00`00Oomoo`3oOol?Ool00?moob5oo`00ogoo8Goo0000\ \>"], ImageRangeCache->{{{73.5625, 302.938}, {233.375, 92.0625}} -> {-2.55071, \ 0.708165, 0.0237436, 0.0434113}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(For[k = 1, k \[LessEqual] 10, \(k++\), \[IndentingNewLine]Print[ N[3^k/\((\(k!\))\)]]]\)], "Input"], Cell[BoxData[ \(3.`\)], "Print"], Cell[BoxData[ \(4.5`\)], "Print"], Cell[BoxData[ \(4.5`\)], "Print"], Cell[BoxData[ \(3.375`\)], "Print"], Cell[BoxData[ \(2.025`\)], "Print"], Cell[BoxData[ \(1.0125`\)], "Print"], Cell[BoxData[ \(0.43392857142857144`\)], "Print"], Cell[BoxData[ \(0.1627232142857143`\)], "Print"], Cell[BoxData[ \(0.05424107142857143`\)], "Print"], Cell[BoxData[ \(0.016272321428571428`\)], "Print"] }, Open ]], Cell[BoxData[ \(Taypol[8, 1]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(T\)], "Input"], Cell[BoxData[ \(3\ \((\(-1\) + x)\)\ Cos[3] - 9\/2\ \((\(-1\) + x)\)\^3\ Cos[3] + 81\/40\ \((\(-1\) + x)\)\^5\ Cos[3] - 243\/560\ \((\(-1\) + x)\)\^7\ Cos[3] + Sin[3] - 9\/2\ \((\(-1\) + x)\)\^2\ Sin[3] + 27\/8\ \((\(-1\) + x)\)\^4\ Sin[3] - 81\/80\ \((\(-1\) + x)\)\^6\ Sin[ 3] + \(729\ \((\(-1\) + x)\)\^8\ Sin[3]\)\/4480\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[{f[x], T}, {x, 0, 2 Pi}]\)], "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 0.13282 0.118105 [ [.17539 .12032 -3 -9 ] [.17539 .12032 3 0 ] [.32696 .12032 -3 -9 ] [.32696 .12032 3 0 ] [.47854 .12032 -3 -9 ] [.47854 .12032 3 0 ] [.63011 .12032 -3 -9 ] [.63011 .12032 3 0 ] [.78169 .12032 -3 -9 ] [.78169 .12032 3 0 ] [.93327 .12032 -3 -9 ] [.93327 .12032 3 0 ] [.01131 .01471 -12 -4.5 ] [.01131 .01471 0 4.5 ] [.01131 .25092 -6 -4.5 ] [.01131 .25092 0 4.5 ] [.01131 .36903 -6 -4.5 ] [.01131 .36903 0 4.5 ] [.01131 .48714 -6 -4.5 ] [.01131 .48714 0 4.5 ] [.01131 .60524 -6 -4.5 ] [.01131 .60524 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 .13282 m .17539 .13907 L s [(1)] .17539 .12032 0 1 Mshowa .32696 .13282 m .32696 .13907 L s [(2)] .32696 .12032 0 1 Mshowa .47854 .13282 m .47854 .13907 L s [(3)] .47854 .12032 0 1 Mshowa .63011 .13282 m .63011 .13907 L s [(4)] .63011 .12032 0 1 Mshowa .78169 .13282 m .78169 .13907 L s [(5)] .78169 .12032 0 1 Mshowa .93327 .13282 m .93327 .13907 L s [(6)] .93327 .12032 0 1 Mshowa .125 Mabswid .05412 .13282 m .05412 .13657 L s .08444 .13282 m .08444 .13657 L s .11476 .13282 m .11476 .13657 L s .14507 .13282 m .14507 .13657 L s .2057 .13282 m .2057 .13657 L s .23602 .13282 m .23602 .13657 L s .26633 .13282 m .26633 .13657 L s .29665 .13282 m .29665 .13657 L s .35728 .13282 m .35728 .13657 L s .38759 .13282 m .38759 .13657 L s .41791 .13282 m .41791 .13657 L s .44822 .13282 m .44822 .13657 L s .50885 .13282 m .50885 .13657 L s .53917 .13282 m .53917 .13657 L s .56948 .13282 m .56948 .13657 L s .5998 .13282 m .5998 .13657 L s .66043 .13282 m .66043 .13657 L s .69074 .13282 m .69074 .13657 L s .72106 .13282 m .72106 .13657 L s .75138 .13282 m .75138 .13657 L s .81201 .13282 m .81201 .13657 L s .84232 .13282 m .84232 .13657 L s .87264 .13282 m .87264 .13657 L s .90295 .13282 m .90295 .13657 L s .96358 .13282 m .96358 .13657 L s .9939 .13282 m .9939 .13657 L s .25 Mabswid 0 .13282 m 1 .13282 L s .02381 .01471 m .03006 .01471 L s [(-1)] .01131 .01471 1 0 Mshowa .02381 .25092 m .03006 .25092 L s [(1)] .01131 .25092 1 0 Mshowa .02381 .36903 m .03006 .36903 L s [(2)] .01131 .36903 1 0 Mshowa .02381 .48714 m .03006 .48714 L s [(3)] .01131 .48714 1 0 Mshowa .02381 .60524 m .03006 .60524 L s [(4)] .01131 .60524 1 0 Mshowa .125 Mabswid .02381 .03834 m .02756 .03834 L s .02381 .06196 m .02756 .06196 L s .02381 .08558 m .02756 .08558 L s .02381 .1092 m .02756 .1092 L s .02381 .15644 m .02756 .15644 L s .02381 .18006 m .02756 .18006 L s .02381 .20368 m .02756 .20368 L s .02381 .2273 m .02756 .2273 L s .02381 .27455 m .02756 .27455 L s .02381 .29817 m .02756 .29817 L s .02381 .32179 m .02756 .32179 L s .02381 .34541 m .02756 .34541 L s .02381 .39265 m .02756 .39265 L s .02381 .41627 m .02756 .41627 L s .02381 .43989 m .02756 .43989 L s .02381 .46351 m .02756 .46351 L s .02381 .51076 m .02756 .51076 L s .02381 .53438 m .02756 .53438 L s .02381 .558 m .02756 .558 L s .02381 .58162 m .02756 .58162 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 .13282 m .04262 .17578 L .06244 .21458 L .07286 .23029 L .08255 .24122 L .08813 .24572 L .09076 .24738 L .0932 .24863 L .096 .24974 L .09748 .25018 L .09824 .25036 L .09905 .25053 L .09976 .25065 L .10041 .25075 L .10168 .25087 L .10239 .25091 L .10317 .25092 L .1039 .25091 L .10458 .25088 L .10587 .25076 L .10651 .25067 L .10722 .25055 L .10848 .25027 L .10966 .24995 L .11231 .249 L .11515 .24762 L .12035 .24416 L .1251 .23998 L .13466 .22873 L .14371 .21491 L .18204 .13399 L .20142 .0897 L .21172 .06834 L .22282 .04832 L .23339 .03303 L .23801 .02767 L .24307 .02282 L .24787 .01924 L .25234 .01683 L .25481 .01588 L .25705 .01526 L .25829 .01502 L .259 .01491 L .25964 .01483 L .26083 .01474 L .26209 .01472 L .2633 .01476 L .26462 .01488 L .26586 .01508 L .26702 .01532 L Mistroke .2692 .01594 L .27152 .01685 L .27427 .01823 L .27684 .01984 L .28166 .02363 L .29046 .03309 L .29997 .04668 L .31995 .08445 L .34103 .13226 L .36093 .17763 L .37905 .21314 L .3891 .22866 L .3986 .23987 L .40382 .24444 L .40863 .24761 L .41115 .24885 L .41392 .24988 L .41532 .25027 L .41605 .25044 L .41682 .25059 L .41749 .2507 L .41823 .25079 L .41953 .2509 L .42017 .25092 L .42086 .25092 L .42208 .25088 L .42339 .25075 L .42414 .25064 L .42483 .25052 L .42724 .24992 L .4286 .24946 L .42983 .24897 L .43463 .24642 L .43918 .24306 L .44922 .23253 L .46014 .21662 L .47989 .17859 L .50089 .13073 L .52056 .08607 L .53861 .05109 L .54802 .03672 L .55794 .02518 L .56309 .02079 L .56789 .01775 L .57065 .01647 L .57315 .01561 L .57454 .01525 L .57527 .0151 L .57605 .01497 L .57672 .01488 L Mistroke .57747 .0148 L .57878 .01472 L .58007 .01473 L .58127 .0148 L .58259 .01495 L .58332 .01508 L .58399 .01521 L .58653 .0159 L .58893 .01682 L .59339 .01923 L .59821 .02283 L .6035 .02793 L .60909 .03457 L .61909 .04938 L .65708 .12897 L .67824 .17731 L .69753 .21485 L .70711 .2294 L .71216 .2357 L .71752 .24127 L .7222 .24513 L .72468 .24679 L .72736 .24827 L .72981 .24934 L .73088 .24972 L .73205 .25008 L .73309 .25035 L .7342 .25057 L .73537 .25075 L .73645 .25086 L .73769 .25092 L .73839 .25092 L .73905 .2509 L .73974 .25086 L .74037 .25081 L .7411 .25072 L .74179 .25061 L .74301 .25037 L .74414 .25008 L .74671 .24921 L .74953 .24791 L .75209 .24642 L .75782 .24204 L .76281 .23707 L .7682 .23057 L .77797 .21601 L .81905 .12911 L .83953 .08287 L .84952 .06282 L .85861 .04692 L Mistroke .86742 .03416 L .87699 .0237 L .88224 .0196 L .88455 .01818 L .88709 .0169 L .88949 .01596 L .89173 .01531 L .89297 .01506 L .8941 .01489 L .89541 .01476 L .89665 .01472 L .89789 .01474 L .89859 .01479 L .89924 .01485 L .90042 .01501 L .90168 .01526 L .90385 .01585 L .90623 .01676 L .90878 .01801 L .91151 .01967 L .91645 .02351 L .92606 .03394 L .93483 .04658 L .95391 .08241 L .97467 .12925 L .97619 .13282 L Mfstroke .02381 .12722 m .04262 .17403 L .06244 .21417 L .07286 .23011 L .08255 .24115 L .08813 .24568 L .09076 .24735 L .0932 .2486 L .096 .24972 L .09748 .25016 L .09824 .25035 L .09905 .25052 L .09976 .25064 L .10041 .25074 L .10168 .25086 L .10239 .2509 L .10317 .25092 L .1039 .25091 L .10458 .25087 L .10587 .25075 L .10651 .25066 L .10722 .25054 L .10848 .25027 L .10966 .24995 L .11231 .249 L .11515 .24762 L .12035 .24416 L .1251 .23998 L .13466 .22873 L .14371 .21491 L .18204 .13399 L .20142 .0897 L .21172 .06834 L .22282 .04832 L .23339 .03303 L .23801 .02768 L .24307 .02283 L .24787 .01925 L .25234 .01684 L .25481 .0159 L .25705 .01528 L .25829 .01504 L .259 .01494 L .25964 .01486 L .26083 .01478 L .26209 .01476 L .2633 .01481 L .26462 .01494 L .26586 .01514 L .26702 .01539 L Mistroke .2692 .01603 L .27152 .01695 L .27427 .01837 L .27684 .02001 L .28166 .02389 L .29046 .03361 L .29997 .04775 L .31995 .08846 L .34103 .14568 L .36071 .21334 L .37905 .29621 L .38953 .35823 L .39945 .4323 L .40835 .51658 L Mfstroke .40835 .51658 m .41669 .61803 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol20005Ool2000IOol000Uoo`03001o ogoo00=oo`03001oogoo03Yoo`03001oogoo00Moo`8004eoo`03001oogoo00Ioo`8004aoo`8000Uo o`03001oogoo01Ioo`0027oo0P001Goo00<007ooOol0>Goo00<007ooOol02Woo00<007ooOol0BGoo 00<007ooOol02Goo00<007ooOol0B7oo00<007ooOol02Woo00<007ooOol05Goo000?Ool00`00Oomo o`0iOol00`00Oomoo`0:Ool00`00Oomoo`18Ool00`00Oomoo`0:Ool00`00Oomoo`18Ool00`00Oomo o`0;Ool00`00Oomoo`0DOol000moo`03001oogoo03Moo`8000ioo`03001oogoo04Ioo`03001oogoo 00aoo`8004Moo`03001oogoo00eoo`03001oogoo01=oo`003goo0P00=goo00<007ooOol03goo00<0 07ooOol0A7oo00<007ooOol03goo00<007ooOol0@goo00<007ooOol03goo00<007ooOol04Woo000? Ool00`00Oomoo`0eOol00`00Oomoo`0AOol00`00Oomoo`12Ool00`00Oomoo`0@Ool00`00Oomoo`12 Ool00`00Oomoo`0@Ool00`00Oomoo`0BOol000moo`03001oogoo03Eoo`03001oogoo015oo`03001o ogoo045oo`03001oogoo019oo`03001oogoo045oo`03001oogoo015oo`03001oogoo015oo`003goo 00<007ooOol0=7oo00<007ooOol04goo00<007ooOol0@7oo00<007ooOol04Woo00<007ooOol0@7oo 00<007ooOol04Woo00<007ooOol04Goo000?Ool00`00Oomoo`0cOol00`00Oomoo`0DOol20010Ool0 0`00Oomoo`0DOol00`00Oomoo`0nOol00`00Oomoo`0DOol00`00Oomoo`0@Ool000moo`03001oogoo 03=oo`03001oogoo01Eoo`03001oogoo03eoo`03001oogoo01Eoo`03001oogoo03ioo`03001oogoo 01Aoo`03001oogoo011oo`003goo00<007ooOol0Goo00<007ooOol06Goo00<007ooOol0>Woo00<007ooOol06Goo00<007ooOol03Goo000?Ool0 0`00Oomoo`0`Ool00`00Oomoo`0JOol2000jOol00`00Oomoo`0JOol00`00Oomoo`0hOol00`00Oomo o`0JOol00`00Oomoo`0=Ool000moo`03001oogoo031oo`03001oogoo01]oo`03001oogoo03Moo`03 001oogoo01]oo`03001oogoo03Qoo`03001oogoo01]oo`03001oogoo00aoo`003goo00<007ooOol0 ;goo00<007ooOol077oo0P00>7oo00<007ooOol077oo00<007ooOol0=Woo00<007ooOol077oo00<0 07ooOol037oo000?Ool00`00Oomoo`0_Ool00`00Oomoo`0MOol00`00Oomoo`0eOol00`00Oomoo`0M Ool00`00Oomoo`0fOol00`00Oomoo`0MOol00`00Oomoo`0;Ool000moo`8002moo`03001oogoo01io o`03001oogoo03Eoo`03001oogoo01ioo`03001oogoo03Eoo`03001oogoo01eoo`03001oogoo00]o o`003goo00<007ooOol09Goo1@0017oo00<007ooOol07Woo10009goo0P002goo00<007ooOol077oo 0`009Woo0P003Woo00<007ooOol05Woo0`001Woo00<007ooOol02Woo000?Ool00`00Oomoo`0WOol0 0`00Oomoo`04Ool00`00Oomoo`0NOol2000XOol01000Oomoo`002Goo00<007ooOol07Woo0P009Goo 00@007ooOol000eoo`03001oogoo01Ioo`04001oogoo0005Ool00`00Oomoo`0:Ool000moo`03001o ogoo02Moo`03001oogoo00=oo`03001oogoo021oo`8002Uoo`03001oogoo00Qoo`03001oogoo01]o o`H002Moo`03001oogoo00Yoo`03001oogoo01Moo`04001oogoo0006Ool00`00Oomoo`09Ool000mo o`03001oogoo02Moo`03001oogoo00=oo`03001oogoo025oo`03001oogoo02Qoo`03001oogoo00Io o`03001oogoo01aoo`06001oogoo001oo`009Goo0P003Goo00<007ooOol05goo0`001goo00<007oo Ool02Goo000?Ool00`00Oomoo`0WOol00`00Oomoo`02Ool00`00Oomoo`0POol01000Ool000009Woo 00@007ooOol000Qoo`03001oogoo01eoo`03001oo`00009oo`03001oogoo029oo`03001oogoo00]o o`03001oogoo01Uoo`03001oogoo00Ioo`03001oogoo00Uoo`003goo0P009goo0P0017oo00<007oo Ool08Goo0`009goo0P0027oo00<007ooOol07goo0P000Woo00<007ooOol08Woo0`002goo00<007oo Ool06Goo0`001goo00<007ooOol027oo000?Ool00`00Oomoo`0[Ool00`00Oomoo`0TOol00`00Oomo o`0_Ool00`00Oomoo`0TOol00`00Oomoo`0^Ool00`00Oomoo`0TOol00`00Oomoo`08Ool000moo`03 001oogoo02]oo`03001oogoo02Aoo`80031oo`03001oogoo02Aoo`03001oogoo02ioo`03001oogoo 02Aoo`03001oogoo00Qoo`003goo00<007ooOol0:goo00<007ooOol097oo0P00;goo00<007ooOol0 9Woo00<007ooOol0;7oo00<007ooOol09Woo00<007ooOol01goo000?Ool00`00Oomoo`0ZOol00`00 Oomoo`0VOol2000^Ool00`00Oomoo`0VOol00`00Oomoo`0/Ool00`00Oomoo`0VOol00`00Oomoo`07 Ool000moo`03001oogoo02Yoo`03001oogoo02Ioo`8002eoo`03001oogoo02Qoo`03001oogoo02Yo o`03001oogoo02Qoo`03001oogoo00Ioo`003goo00<007ooOol0:Goo00<007ooOol0:7oo0P00;7oo 00<007ooOol0:7oo00<007ooOol0:Woo00<007ooOol0:7oo00<007ooOol01Woo0008Oooo000I0000 00moo`8000Ioo`03001oogoo00Ioo`03001oogoo00Eoo`03001oogoo00Ioo`03001oogoo00Eoo`03 001oo`0000Ioo`03001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Ioo`03001oogoo00Eoo`06 001oogoo001oo`000goo00<007ooOol01Goo00<007ooOol01Woo00<007ooOol01Goo00<007ooOol0 1Goo00<007ooOol00goo00@007ooOol000Moo`03001oogoo00Ioo`03001oogoo00Eoo`03001oogoo 00Ioo`03001oogoo00Eoo`03001oogoo00Eoo`03001oogoo00Ioo`03001oogoo00Eoo`03001oogoo 00Ioo`03001oogoo00Eoo`8000Moo`03001oogoo00Eoo`03001oogoo00Ioo`03001oogoo00Eoo`03 001oogoo00Eoo`03001oogoo00Ioo`40005oo`5oo`003goo0`00:7oo00<007ooOol0:Woo0P00:Woo 00<007ooOol0:Woo00<007ooOol0:7oo00<007ooOol0goo00<007ooOol067oo00<007ooOol0>Woo000?Ool00`00Oomoo`07Ool0 0`00Oomoo`0EOol00`00Oomoo`0hOol00`00Oomoo`02Ool00`00Oomoo`0FOol00`00Oomoo`0lOol0 0`00Oomoo`0FOol00`00Oomoo`0kOol000moo`03001oogoo00Moo`03001oogoo01Eoo`03001oogoo 03Uoo`03001oogoo009oo`03001oogoo01Aoo`03001oogoo03eoo`03001oogoo01Ioo`03001oogoo 03]oo`003goo00<007ooOol027oo00<007ooOol04goo00<007ooOol0>Woo00<007ooOol00Woo00<0 07ooOol057oo00<007ooOol0?Woo00<007ooOol057oo00<007ooOol0?7oo000?Ool00`00Oomoo`09 Ool00`00Oomoo`0BOol00`00Oomoo`0jOol00`00Oomoo`03Ool00`00Oomoo`0BOol00`00Oomoo`0o Ool00`00Oomoo`0DOol00`00Oomoo`0lOol000moo`03001oogoo00Uoo`03001oogoo015oo`03001o ogoo03]oo`03001oogoo00Aoo`03001oogoo011oo`03001oogoo045oo`03001oogoo019oo`03001o ogoo03eoo`003goo00<007ooOol02Woo00<007ooOol047oo00<007ooOol0?7oo00<007ooOol00goo 00<007ooOol03goo00<007ooOol0@goo00<007ooOol047oo00<007ooOol0?Woo000?Ool2000;Ool0 0`00Oomoo`0?Ool00`00Oomoo`0mOol00`00Oomoo`04Ool00`00Oomoo`0>Ool00`00Oomoo`13Ool0 0`00Oomoo`0@Ool00`00Oomoo`0nOol000moo`03001oogoo00]oo`03001oogoo00eoo`03001oogoo 03ioo`03001oogoo00Eoo`03001oogoo00aoo`03001oogoo04Eoo`03001oogoo00ioo`03001oogoo 03moo`003goo00<007ooOol037oo00<007ooOol02goo00<007ooOol0?goo00<007ooOol01Goo00<0 07ooOol02goo00<007ooOol0Agoo00<007ooOol037oo00<007ooOol0@7oo000?Ool00`00Oomoo`0< Ool00`00Oomoo`0;Ool00`00Oomoo`10Ool00`00Oomoo`05Ool00`00Oomoo`0:Ool00`00Oomoo`18 Ool00`00Oomoo`0;Ool00`00Oomoo`10Ool000moo`03001oogoo00eoo`03001oogoo00Uoo`03001o ogoo045oo`03001oogoo00Eoo`03001oogoo00Uoo`03001oogoo04Yoo`03001oogoo00Qoo`8004=o o`001goo1@000goo00<007ooOol03Woo0P0027oo00<007ooOol0@Woo00<007ooOol01Woo0P001goo 0P00CWoo0P001goo00<007ooOol0@goo0009Ool00`00Oomoo`03Ool00`00Oomoo`0@Ool300000goo 000000020015Ool00`00Oomoo`08Ool30002Ool2001BOol20002Ool30016Ool000Uoo`03001oogoo 00=oo`<0019oo`<004Qoo`03001oogoo00Yoo`<005Ioo`<004Qoo`002Goo00<007ooOol00goo00<0 07ooOol0GWoo00<007ooOol0[Goo0009Ool00`00Oomoo`03Ool00`00Oomoo`1NOol00`00Oomoo`2] Ool000Qoo`8000Eoo`03001oogoo05ioo`03001oogoo0:eoo`003goo00<007ooOol0GWoo00<007oo Ool0[Goo000?Ool00`00Oomoo`1NOol00`00Oomoo`2]Ool000moo`80061oo`03001oogoo0:aoo`00 3goo00<007ooOol0Ggoo00<007ooOol0[7oo000?Ool00`00Oomoo`1OOol00`00Oomoo`2/Ool000mo o`03001oogoo05moo`03001oogoo0:aoo`003goo00<007ooOol0H7oo00<007ooOol0Zgoo000?Ool0 0`00Oomoo`1POol00`00Oomoo`2[Ool000moo`03001oogoo061oo`03001oogoo0:]oo`003goo0P00 HGoo00<007ooOol0Zgoo000?Ool00`00Oomoo`1POol00`00Oomoo`2[Ool000moo`03001oogoo065o o`03001oogoo0:Yoo`003goo00<007ooOol0HGoo00<007ooOol0ZWoo000?Ool00`00Oomoo`1QOol0 0`00Oomoo`2ZOol000moo`03001oogoo065oo`03001oogoo0:Yoo`003goo0P00HWoo00<007ooOol0 ZWoo000?Ool00`00Oomoo`1QOol00`00Oomoo`2ZOol000moo`03001oogoo069oo`03001oogoo0:Uo o`003goo00<007ooOol0HWoo00<007ooOol0ZGoo000?Ool00`00Oomoo`1ROol00`00Oomoo`2YOol0 00moo`03001oogoo069oo`03001oogoo0:Uoo`003goo00<007ooOol0HWoo00<007ooOol0ZGoo000? Ool2001SOol00`00Oomoo`2YOol000moo`03001oogoo06=oo`03001oogoo0:Qoo`003goo00<007oo Ool0Hgoo00<007ooOol0Z7oo000?Ool00`00Oomoo`1SOol00`00Oomoo`2XOol000Moo`@000Aoo`03 001oogoo06=oo`03001oogoo0:Qoo`001goo00<007ooOol01Goo00<007ooOol0Hgoo00<007ooOol0 Z7oo0008Ool00`00Oomoo`04Ool3001SOol00`00Oomoo`2XOol000Uoo`03001oogoo00=oo`03001o ogoo06=oo`03001oogoo0:Qoo`001goo00@007ooOol000Aoo`03001oogoo06=oo`03001oogoo0:Qo o`0027oo0P001Goo00<007ooOol0I7oo00<007ooOol0Ygoo000?Ool00`00Oomoo`1TOol00`00Oomo o`2WOol000moo`03001oogoo06Aoo`03001oogoo0:Moo`003goo00<007ooOol0I7oo00<007ooOol0 Ygoo000?Ool2001UOol00`00Oomoo`2WOol000moo`03001oogoo06Aoo`03001oogoo0:Moo`003goo 00<007ooOol0I7oo00<007ooOol0Ygoo000?Ool00`00Oomoo`1TOol00`00Oomoo`2WOol000moo`03 001oogoo06Aoo`03001oogoo0:Moo`003goo00<007ooOol0I7oo00<007ooOol0Ygoo000?Ool00`00 Oomoo`1UOol00`00Oomoo`2VOol000moo`8006Ioo`03001oogoo0:Ioo`003goo00<007ooOol0IGoo 00<007ooOol0YWoo000?Ool00`00Oomoo`1UOol00`00Oomoo`2VOol000moo`03001oogoo06Eoo`03 001oogoo0:Ioo`003goo00<007ooOol0IGoo00<007ooOol0YWoo000?Ool00`00Oomoo`1UOol00`00 Oomoo`2VOol000moo`8006Ioo`03001oogoo0:Ioo`003goo00<007ooOol0IGoo00<007ooOol0YWoo 000?Ool00`00Oomoo`1VOol00`00Oomoo`2UOol000moo`03001oogoo06Ioo`03001oogoo0:Eoo`00 3goo00<007ooOol0IWoo00<007ooOol0YGoo000?Ool00`00Oomoo`1VOol00`00Oomoo`2UOol000mo o`03001oogoo06Ioo`03001oogoo0:Eoo`003goo0P00Igoo00<007ooOol0YGoo000?Ool00`00Oomo o`1VOol00`00Oomoo`2UOol000moo`03001oogoo06Ioo`03001oogoo0:Eoo`003goo00<007ooOol0 Igoo00<007ooOol0Y7oo0008Ool20005Ool00`00Oomoo`1WOol00`00Oomoo`2TOol000Moo`04001o ogoo0004Ool00`00Oomoo`1WOol00`00Oomoo`2TOol000Uoo`03001oogoo00=oo`<006Moo`03001o ogoo0:Aoo`002Woo00<007ooOol00Woo00<007ooOol0Igoo00<007ooOol0Y7oo0007Ool01000Oomo o`0017oo00<007ooOol0Igoo00<007ooOol0Y7oo0008Ool20005Ool00`00Oomoo`1WOol00`00Oomo o`2TOol000moo`03001oogoo06Moo`03001oogoo0:Aoo`003goo00<007ooOol0J7oo00<007ooOol0 Xgoo000?Ool00`00Oomoo`1XOol00`00Oomoo`2SOol000moo`8006Uoo`03001oogoo0:=oo`003goo 00<007ooOol0J7oo00<007ooOol0Xgoo000?Ool00`00Oomoo`1XOol00`00Oomoo`2SOol000moo`03 001oogoo06Qoo`03001oogoo0:=oo`003goo00<007ooOol0J7oo00<007ooOol0Xgoo000?Ool00`00 Oomoo`1XOol00`00Oomoo`2SOol000moo`8006Uoo`03001oogoo0:=oo`003goo00<007ooOol0J7oo 00<007ooOol0Xgoo000?Ool00`00Oomoo`1XOol00`00Oomoo`2SOol000moo`03001oogoo06Uoo`03 001oogoo0:9oo`003goo00<007ooOol0JGoo00<007ooOol0XWoo000?Ool00`00Oomoo`1YOol00`00 Oomoo`2ROol000moo`03001oogoo06Uoo`03001oogoo0:9oo`003goo0P00JWoo00<007ooOol0XWoo 000?Ool00`00Oomoo`1YOol00`00Oomoo`2ROol000moo`03001oogoo06Uoo`03001oogoo0:9oo`00 3goo00<007ooOol0JGoo00<007ooOol0XWoo000?Ool00`00Oomoo`1YOol00`00Oomoo`2ROol000mo o`03001oogoo06Uoo`03001oogoo0:9oo`003goo00<007ooOol0JGoo00<007ooOol0XWoo000?Ool2 001ZOol00`00Oomoo`2ROol000moo`03001oogoo06Uoo`03001oogoo0:9oo`003goo00<007ooOol0 JGoo00<007ooOol0XWoo000?Ool00`00Oomoo`1ZOol00`00Oomoo`2QOol000Uoo`<000=oo`03001o ogoo06Yoo`03001oogoo0:5oo`002Woo00<007ooOol00Woo00<007ooOol0JWoo00<007ooOol0XGoo 0007Ool50003Ool3001ZOol00`00Oomoo`2QOol000Moo`04001oogoo0004Ool00`00Oomoo`1ZOol0 0`00Oomoo`2QOol000Qoo`03001oo`0000Aoo`03001oogoo06Yoo`03001oogoo0:5oo`002Goo0P00 17oo00<007ooOol0JWoo00<007ooOol0XGoo000?Ool00`00Oomoo`1ZOol00`00Oomoo`2QOol00?mo ob5oo`00ogoo8Goo0000\ \>"], ImageRangeCache->{{{73.5625, 302.938}, {220.688, 79.375}} -> {-2.55071, \ 1.83208, 0.0237436, 0.0304725}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[BoxData[ \(Bernpol[n_, a_, b_] := \((\[IndentingNewLine]BB = 0; \[IndentingNewLine]x =. ; \[IndentingNewLine]z = \((x - a)\)/\((b - a)\); \[IndentingNewLine]For[k = 0, k \[LessEqual] n, \(k++\), \[IndentingNewLine]BB\ = \ BB + Binomial[n, k]\ \ z^k\ \((1 - z)\)^\((n - k)\)\ f[ a + \((b - a)\) \((k/n)\)]]; \[IndentingNewLine]Plot[{f[x], BB}, {x, a, b}])\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Bernpol[3, 0, \ Pi/4]\)], "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 0.0238095 1.21261 0.0147151 0.588604 [ [.26633 .00222 -9 -9 ] [.26633 .00222 9 0 ] [.50885 .00222 -9 -9 ] [.50885 .00222 9 0 ] [.75138 .00222 -9 -9 ] [.75138 .00222 9 0 ] [.9939 .00222 -9 -9 ] [.9939 .00222 9 0 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .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 .26633 .01472 m .26633 .02097 L s [(0.2)] .26633 .00222 0 1 Mshowa .50885 .01472 m .50885 .02097 L s [(0.4)] .50885 .00222 0 1 Mshowa .75138 .01472 m .75138 .02097 L s [(0.6)] .75138 .00222 0 1 Mshowa .9939 .01472 m .9939 .02097 L s [(0.8)] .9939 .00222 0 1 Mshowa .125 Mabswid .08444 .01472 m .08444 .01847 L s .14507 .01472 m .14507 .01847 L s .2057 .01472 m .2057 .01847 L s .32696 .01472 m .32696 .01847 L s .38759 .01472 m .38759 .01847 L s .44822 .01472 m .44822 .01847 L s .56948 .01472 m .56948 .01847 L s .63011 .01472 m .63011 .01847 L s .69074 .01472 m .69074 .01847 L s .81201 .01472 m .81201 .01847 L s .87264 .01472 m .87264 .01847 L s .93327 .01472 m .93327 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 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 .01472 m .06244 .07089 L .10458 .13155 L .14415 .18738 L .18221 .23952 L .22272 .29282 L .26171 .34149 L .30316 .38988 L .34309 .43279 L .3815 .47022 L .42237 .50552 L .46172 .53477 L .49955 .55826 L .53984 .57804 L .55838 .58527 L .57861 .59179 L .59975 .59706 L .61028 .5991 L .61984 .6006 L .62997 .60183 L .63461 .60227 L .63951 .60265 L .64201 .60282 L .64476 .60297 L .64728 .60308 L .64958 .60317 L .6523 .60324 L .6538 .60328 L .65449 .60329 L .65522 .6033 L .65653 .60331 L .65774 .60332 L .65904 .60332 L .65978 .60332 L .66048 .60331 L .66166 .6033 L .66291 .60329 L .6641 .60327 L .66518 .60324 L .66782 .60317 L .67031 .60308 L .67528 .60283 L .68066 .60245 L .69029 .60153 L .69917 .60038 L .71793 .59702 L .73857 .59187 L .75802 .58565 L .77891 .57749 L .82019 .55698 L Mistroke .85995 .53188 L .89819 .50301 L .93889 .4675 L .97619 .43092 L Mfstroke .02381 .01472 m .06244 .06416 L .10458 .11529 L .14415 .16061 L .18221 .20169 L .22272 .24267 L .26171 .2794 L .30316 .31548 L .34309 .34729 L .3815 .37514 L .42237 .40175 L .46172 .42438 L .49955 .44334 L .53984 .46046 L .57861 .47391 L .59832 .4796 L .61984 .48491 L .64066 .48916 L .65954 .49225 L .67922 .49468 L .69002 .49567 L .70019 .49639 L .70524 .49666 L .70995 .49687 L .71487 .49704 L .71748 .49711 L .72027 .49717 L .72264 .4972 L .72399 .49722 L .72523 .49723 L .72631 .49724 L .72751 .49724 L .72876 .49724 L .72993 .49724 L .73101 .49724 L .73214 .49723 L .73311 .49722 L .73417 .49721 L .73654 .49718 L .73874 .49713 L .74379 .497 L .74926 .49679 L .75443 .49654 L .7592 .49626 L .77779 .49469 L .78748 .49357 L .79655 .49235 L .81719 .48891 L .85601 .47992 L .89729 .46673 L Mistroke .93705 .45044 L .9753 .43141 L .97619 .43092 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg Ool00`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0= Ool00`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0= Ool00`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0> Ool00`00Oomoo`07Ool001Eoo`<003eoo`03001oogoo03eoo`03001oogoo03eoo`03001oogoo03io o`03001oogoo00Moo`005Goo00<007oo0000ogoo2Goo000EOol01000Oomoo`00ogoo27oo000EOol0 0`00Oomoo`02003oOol7Ool001Eoo`04001oogooOol2003oOol6Ool001Eoo`03001oogoo009oo`03 001oogoo0?moo`Aoo`005Goo0P000goo0P00ogoo1Goo000EOol00`00Oomoo`03Ool2003oOol4Ool0 01Eoo`03001oogoo00Aoo`800?moo`=oo`005Goo00<007ooOol017oo0P00ogoo0goo000EOol00`00 Oomoo`05Ool2003oOol2Ool001Eoo`03001oogoo00Ioo`800?moo`5oo`005Goo00<007ooOol01Woo 00<007oo0000ogoo000EOol00`00Oomoo`07Ool00`00Ool0003nOol001Eoo`8000Uoo`800?ioo`00 5Goo00<007ooOol027oo00<007oo0000oGoo000EOol00`00Oomoo`09Ool00`00Ool0003lOol001Eo o`03001oogoo00Yoo`03001oo`000?]oo`005Goo00<007ooOol02Woo00@007ooOol00?Yoo`005Goo 00<007ooOol02goo00<007oo0000nWoo000EOol00`00Oomoo`0Uoo`005Goo0P006Goo00<007ooOol0 0Woo00<007ooOol0j7oo000EOol00`00Oomoo`0IOol00`00Oomoo`02Ool00`00Oomoo`3WOol001Eo o`03001oogoo01Uoo`03001oogoo00=oo`03001oogoo0>Ioo`005Goo00<007ooOol06Woo00<007oo Ool00goo00<007ooOol0iGoo000EOol00`00Oomoo`0KOol00`00Oomoo`03Ool00`00Oomoo`3TOol0 01Eoo`03001oogoo01aoo`03001oogoo00=oo`03001oogoo0>=oo`005Goo00<007ooOol077oo00<0 07ooOol00goo00<007ooOol0hgoo000EOol00`00Oomoo`0MOol00`00Oomoo`03Ool00`00Oomoo`3R Ool001Eoo`8001moo`03001oogoo00=oo`03001oogoo0>5oo`005Goo00<007ooOol07Woo00<007oo Ool017oo00<007ooOol0h7oo000EOol00`00Oomoo`0OOol00`00Oomoo`04Ool00`00Oomoo`3OOol0 01Eoo`03001oogoo021oo`03001oogoo00Aoo`03001oogoo0=ioo`005Goo00<007ooOol08Goo00<0 07ooOol017oo00<007ooOol0gGoo000EOol00`00Oomoo`0QOol00`00Oomoo`05Ool00`00Oomoo`3L Ool001Eoo`03001oogoo029oo`03001oogoo00Eoo`03001oogoo0=]oo`005Goo00<007ooOol08goo 00<007ooOol01Goo00<007ooOol0fWoo000EOol2000TOol00`00Oomoo`06Ool00`00Oomoo`3IOol0 01Eoo`03001oogoo02Aoo`03001oogoo00Ioo`03001oogoo0=Qoo`005Goo00<007ooOol09Goo00<0 07ooOol01Woo00<007ooOol0egoo000EOol00`00Oomoo`0VOol00`00Oomoo`06Ool00`00Oomoo`3F Ool001Eoo`03001oogoo02Ioo`03001oogoo00Moo`03001oogoo0=Eoo`000Woo0P0017oo0P001Goo 0`000goo00<007ooOol09goo00<007ooOol01goo00<007ooOol0e7oo00001Goo001oogoo00002goo 00<007ooOol00Woo00<007ooOol0:7oo00<007ooOol01goo00<007ooOol0dgoo00001Goo001oogoo 000027oo1@000goo0P00:Goo00<007ooOol027oo00<007ooOol0dWoo00001Goo001oogoo000027oo 00@007ooOol000Aoo`03001oogoo02Uoo`03001oogoo00Qoo`03001oogoo0=5oo`0000Eoo`00Oomo o`0000Uoo`03001oo`0000Aoo`03001oogoo02Yoo`03001oogoo00Qoo`03001oogoo0=1oo`000Woo 0P002goo0P0017oo00<007ooOol0:goo00<007ooOol027oo0P00d7oo000EOol00`00Oomoo`0[Ool0 0`00Oomoo`0:Ool00`00Oomoo`3=Ool001Eoo`03001oogoo02aoo`03001oogoo00Yoo`03001oogoo 0Ool00`00Oomoo`30Ool001Eoo`03001oogoo03Eoo`03001oogoo00ioo`03001oogoo0;moo`00 5Goo00<007ooOol0=Woo00<007ooOol03Woo00<007ooOol0_Woo000EOol00`00Oomoo`0gOol00`00 Oomoo`0>Ool00`00Oomoo`2mOol001Eoo`03001oogoo03Qoo`03001oogoo00ioo`800;eoo`005Goo 00<007ooOol0>Goo00<007ooOol03goo00<007ooOol0^Woo000EOol00`00Oomoo`0iOol00`00Oomo o`0@Ool00`00Oomoo`2iOol001Eoo`03001oogoo03Yoo`03001oogoo011oo`03001oogoo0;Qoo`00 5Goo0P00?7oo00<007ooOol047oo0P00^7oo000EOol00`00Oomoo`0lOol00`00Oomoo`0AOol00`00 Oomoo`2eOol001Eoo`03001oogoo03eoo`03001oogoo015oo`03001oogoo0;Aoo`005Goo00<007oo Ool0?Woo00<007ooOol04Goo0P00]7oo000EOol00`00Oomoo`0oOol00`00Oomoo`0BOol00`00Oomo o`2aOol001Eoo`03001oogoo041oo`03001oogoo019oo`03001oogoo0;1oo`000Woo0P0017oo0P00 0goo0`001Goo00<007ooOol0@Goo00<007ooOol04Woo0P00/7oo00001Goo001oogoo000027oo00@0 07ooOol000Aoo`03001oogoo049oo`03001oogoo01=oo`03001oogoo0:eoo`0000Eoo`00Oomoo`00 00Qoo`04001oogoo0004Ool20013Ool00`00Oomoo`0DOol2002]Ool00005Ool007ooOol00008Ool3 0005Ool00`00Oomoo`13Ool00`00Oomoo`0EOol00`00Oomoo`2ZOol00005Ool007ooOol00009Ool0 0`00Oomoo`04Ool00`00Oomoo`14Ool00`00Oomoo`0EOol2002ZOol0009oo`8000Yoo`<000Aoo`03 001oogoo04Eoo`03001oogoo01Ioo`03001oogoo0:Moo`005Goo00<007ooOol0AWoo00<007ooOol0 5Woo0P00Ygoo000EOol00`00Oomoo`17Ool00`00Oomoo`0GOol2002UOol001Eoo`03001oogoo04Qo o`03001oogoo01Qoo`03001oogoo0:9oo`005Goo0P00BWoo00<007ooOol067oo0P00XWoo000EOol0 0`00Oomoo`1:Ool00`00Oomoo`0IOol00`00Oomoo`2OOol001Eoo`03001oogoo04Yoo`03001oogoo 01Yoo`8009moo`005Goo00<007ooOol0Bgoo00<007ooOol06goo0P00WGoo000EOol00`00Oomoo`1< Ool00`00Oomoo`0LOol2002KOol001Eoo`03001oogoo04eoo`03001oogoo01eoo`8009Uoo`005Goo 00<007ooOol0CWoo00<007ooOol07Woo0P00Ugoo000EOol00`00Oomoo`1?Ool00`00Oomoo`0OOol0 0`00Oomoo`2DOol001Eoo`80051oo`03001oogoo021oo`8009Aoo`005Goo00<007ooOol0D7oo00<0 07ooOol08Goo0P00PWoo0P003Woo000EOol00`00Oomoo`1AOol00`00Oomoo`0ROol2001nOol3000? Ool001Eoo`03001oogoo059oo`03001oogoo02=oo`8007Yoo`800003Ool007oo00moo`005Goo00<0 07ooOol0Dgoo00<007ooOol097oo0P00MWoo0P000Woo00<007ooOol03goo000EOol00`00Oomoo`1D Ool00`00Oomoo`0UOol2001bOol20003Ool00`00Oomoo`0@Ool001Eoo`03001oogoo05Eoo`03001o ogoo02Ioo`8006ioo`8000Aoo`03001oogoo015oo`005Goo00<007ooOol0EWoo00<007ooOol09goo 0P00JWoo0P001Goo00<007ooOol04Woo000EOol2001HOol00`00Oomoo`0XOol2001VOol20006Ool0 0`00Oomoo`0COol001Eoo`03001oogoo05Qoo`03001oogoo02Uoo`<0065oo`8000Moo`03001oogoo 01Aoo`005Goo00<007ooOol0FGoo00<007ooOol0:goo0`00G7oo0P0027oo00<007ooOol05Goo000E Ool00`00Oomoo`1JOol00`00Oomoo`0]Ool2001GOol30009Ool00`00Oomoo`0FOol001Eoo`03001o ogoo05]oo`03001oogoo02ioo`<0051oo`@000]oo`03001oogoo01Moo`005Goo00<007ooOol0G7oo 00<007ooOol0<7oo1000B7oo10003Goo0P006Woo0002Ool20004Ool20004Ool20005Ool00`00Oomo o`1MOol2000dOol50010Ool3000@Ool00`00Oomoo`0JOol00005Ool007ooOol00008Ool01000Oomo o`0017oo00<007ooOol0Ggoo00<007ooOol0=Woo1@00>7oo0`004Woo00<007ooOol06goo00001Goo 001oogoo000027oo00@007ooOol000Aoo`80065oo`03001oogoo03Yoo`80039oo`@001Aoo`03001o ogoo01aoo`0000Eoo`00Oomoo`0000Uoo`8000Eoo`03001oogoo065oo`03001oogoo03]oo`T0025o o`P001Moo`03001oogoo01eoo`0000Eoo`00Oomoo`0000Qoo`04001oogoo0004Ool00`00Oomoo`1R Ool00`00Oomoo`13Ool7000@Ool:000MOol2000POol0009oo`8000Yoo`8000Eoo`03001oogoo06=o o`8004Yooa0002Ioo`03001oogoo021oo`005Goo00<007ooOol0IGoo00<007ooOol0O7oo00<007oo Ool08Goo000EOol00`00Oomoo`1VOol00`00Oomoo`1jOol00`00Oomoo`0ROol001Eoo`03001oogoo 06Moo`8007Qoo`8002Eoo`005Goo0P00JWoo00<007ooOol0M7oo00<007ooOol09Goo000EOol00`00 Oomoo`1ZOol00`00Oomoo`1bOol00`00Oomoo`0VOol001Eoo`03001oogoo06]oo`80075oo`03001o ogoo02Moo`005Goo00<007ooOol0KGoo00<007ooOol0K7oo0P00:Woo000EOol00`00Oomoo`1^Ool0 0`00Oomoo`1ZOol00`00Oomoo`0ZOol001Eoo`03001oogoo06moo`8006Uoo`03001oogoo02]oo`00 5Goo00<007ooOol0LGoo00<007ooOol0I7oo0P00;Woo000EOol00`00Oomoo`1bOol2001SOol00`00 Oomoo`0^Ool001Eoo`8007Eoo`80061oo`03001oogoo02moo`005Goo00<007ooOol0MWoo00<007oo Ool0Fgoo0P007oo0`00A7oo000EOol00`00Oomoo`29Ool3000b Ool30017Ool001Eoo`03001oogoo08aoo`<002eoo`8004Yoo`005Goo00<007ooOol0Sgoo10009Goo 1000C7oo000=Ool50003Ool00`00Oomoo`2COol4000LOol5001@Ool000moo`03001oogoo00=oo`03 001oogoo09Moo`L000moo`H005Eoo`003goo00<007ooOol00goo0P00Wgoo3`00Fgoo000?Ool00`00 Oomoo`03Ool00`00Oomoo`3oOol9Ool000moo`03001oogoo00=oo`03001oogoo0?moo`Uoo`003Woo 0P001Goo00<007ooOol0ogoo2Goo000EOol00`00Oomoo`3oOol9Ool00?moob5oo`00ogoo8Goo0000 \ \>"], ImageRangeCache->{{{73.5625, 302.938}, {511.875, 370.563}} -> {-0.353364, \ 2.88453, 0.00311998, 0.00642762}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(BB\)], "Input"], Cell[BoxData[ \(3\ \((1 - x)\)\^2\ x\ Sin[2] + 3\ \((1 - x)\)\ x\^2\ Sin[4] + x\^3\ Sin[6]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(f[x]\)], "Input"], Cell[BoxData[ \(Sin[3\ x]\)], "Output"] }, Open ]], Cell[BoxData[ \(f[x_] := \ 3 x^4 - 5 x^3 - 3 x + 2\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[f[x], {x, \(-3\), 3}]\)], "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 0.15873 0.0412051 0.00602025 [ [.02381 .02871 -6 -9 ] [.02381 .02871 6 0 ] [.18254 .02871 -6 -9 ] [.18254 .02871 6 0 ] [.34127 .02871 -6 -9 ] [.34127 .02871 6 0 ] [.65873 .02871 -3 -9 ] [.65873 .02871 3 0 ] [.81746 .02871 -3 -9 ] [.81746 .02871 3 0 ] [.97619 .02871 -3 -9 ] [.97619 .02871 3 0 ] [.4875 .16161 -12 -4.5 ] [.4875 .16161 0 4.5 ] [.4875 .28201 -12 -4.5 ] [.4875 .28201 0 4.5 ] [.4875 .40242 -12 -4.5 ] [.4875 .40242 0 4.5 ] [.4875 .52282 -12 -4.5 ] [.4875 .52282 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 .04121 m .02381 .04746 L s [(-3)] .02381 .02871 0 1 Mshowa .18254 .04121 m .18254 .04746 L s [(-2)] .18254 .02871 0 1 Mshowa .34127 .04121 m .34127 .04746 L s [(-1)] .34127 .02871 0 1 Mshowa .65873 .04121 m .65873 .04746 L s [(1)] .65873 .02871 0 1 Mshowa .81746 .04121 m .81746 .04746 L s [(2)] .81746 .02871 0 1 Mshowa .97619 .04121 m .97619 .04746 L s [(3)] .97619 .02871 0 1 Mshowa .125 Mabswid .05556 .04121 m .05556 .04496 L s .0873 .04121 m .0873 .04496 L s .11905 .04121 m .11905 .04496 L s .15079 .04121 m .15079 .04496 L s .21429 .04121 m .21429 .04496 L s .24603 .04121 m .24603 .04496 L s .27778 .04121 m .27778 .04496 L s .30952 .04121 m .30952 .04496 L s .37302 .04121 m .37302 .04496 L s .40476 .04121 m .40476 .04496 L s .43651 .04121 m .43651 .04496 L s .46825 .04121 m .46825 .04496 L s .53175 .04121 m .53175 .04496 L s .56349 .04121 m .56349 .04496 L s .59524 .04121 m .59524 .04496 L s .62698 .04121 m .62698 .04496 L s .69048 .04121 m .69048 .04496 L s .72222 .04121 m .72222 .04496 L s .75397 .04121 m .75397 .04496 L s .78571 .04121 m .78571 .04496 L s .84921 .04121 m .84921 .04496 L s .88095 .04121 m .88095 .04496 L s .9127 .04121 m .9127 .04496 L s .94444 .04121 m .94444 .04496 L s .25 Mabswid 0 .04121 m 1 .04121 L s .5 .16161 m .50625 .16161 L s [(20)] .4875 .16161 1 0 Mshowa .5 .28201 m .50625 .28201 L s [(40)] .4875 .28201 1 0 Mshowa .5 .40242 m .50625 .40242 L s [(60)] .4875 .40242 1 0 Mshowa .5 .52282 m .50625 .52282 L s [(80)] .4875 .52282 1 0 Mshowa .125 Mabswid .5 .07131 m .50375 .07131 L s .5 .10141 m .50375 .10141 L s .5 .13151 m .50375 .13151 L s .5 .19171 m .50375 .19171 L s .5 .22181 m .50375 .22181 L s .5 .25191 m .50375 .25191 L s .5 .31212 m .50375 .31212 L s .5 .34222 m .50375 .34222 L s .5 .37232 m .50375 .37232 L s .5 .43252 m .50375 .43252 L s .5 .46262 m .50375 .46262 L s .5 .49272 m .50375 .49272 L s .5 .0111 m .50375 .0111 L s .5 .55293 m .50375 .55293 L s .5 .58303 m .50375 .58303 L s .5 .61313 m .50375 .61313 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 .5 Mabswid .18277 .61803 m .20342 .50347 L .22272 .41345 L .26171 .27393 L .28086 .22301 L .30164 .17861 L .32148 .14528 L .34251 .11807 L .36204 .09901 L .38034 .08559 L .40059 .07473 L .41911 .06765 L .4381 .06249 L .44884 .06027 L .45882 .05854 L .49795 .05348 L .53953 .04835 L .5796 .04153 L .61815 .03293 L .65915 .02305 L .67958 .01881 L .68955 .01715 L .69864 .01595 L .70315 .01548 L .70553 .01528 L .70805 .0151 L .71025 .01496 L .71268 .01485 L .71375 .01481 L .71489 .01477 L .71598 .01475 L .71697 .01473 L .71811 .01472 L .71934 .01472 L .72049 .01472 L .72154 .01473 L .72277 .01476 L .72347 .01478 L .72411 .01479 L .72654 .0149 L .72887 .01503 L .73143 .01523 L .73661 .01579 L .74183 .01659 L .74678 .01757 L .75606 .02006 L .76606 .02378 L .77695 .02923 L .7873 .0359 L .79666 .04335 L Mistroke .81765 .06552 L .83694 .09368 L .85777 .13399 L .87775 .18386 L .89882 .25021 L .93685 .41221 L Mfstroke .93685 .41221 m .97101 .61803 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00`00Oomoo`0gOol008Uoo`T005Eoo`03001o ogoo03Ioo`00PWoo1`001Woo00<007ooOol0EWoo00<007ooOol0=Goo001lOol6000=Ool00`00Oomo o`1GOol00`00Oomoo`0dOol007Yoo`8001=oo`03001oogoo05Qoo`03001oogoo03=oo`00Mgoo0`00 5Goo00<007ooOol0FGoo00<007ooOol07oo 0P00Jgoo00<007ooOol08Goo001DOol00`00Oomoo`0hOol00`00Oomoo`1ZOol00`00Oomoo`0QOol0 05Aoo`03001oogoo03Qoo`03001oogoo06Yoo`03001oogoo025oo`00Dgoo00<007ooOol0>Goo00<0 07ooOol0Jgoo00<007ooOol087oo001COol00`00Oomoo`0iOol00`00Oomoo`1[Ool00`00Oomoo`0P Ool005=oo`03001oogoo03Uoo`03001oogoo06]oo`03001oogoo021oo`00DWoo00<007ooOol0>Woo 00<007ooOol0K7oo00<007ooOol07goo001BOol00`00Oomoo`0jOol00`00Oomoo`1/Ool00`00Oomo o`0OOol0055oo`03001oogoo03]oo`03001oogoo06aoo`03001oogoo01moo`00DGoo00<007ooOol0 >goo0P00KGoo00<007ooOol07goo001AOol00`00Oomoo`0kOol00`00Oomoo`1]Ool00`00Oomoo`0N Ool0051oo`03001oogoo03aoo`03001oogoo06eoo`03001oogoo01ioo`00D7oo00<007ooOol0?7oo 00<007ooOol0KGoo00<007ooOol07Woo001?Ool00`00Oomoo`0mOol00`00Oomoo`1^Ool00`00Oomo o`0MOol004moo`03001oogoo03eoo`03001oogoo06ioo`03001oogoo01eoo`00CWoo00<007ooOol0 ?Woo00<007ooOol0KWoo00<007ooOol07Goo001>Ool00`00Oomoo`0nOol00`00Oomoo`1_Ool00`00 Oomoo`0LOol004ioo`03001oogoo03ioo`80071oo`03001oogoo01aoo`00CGoo00<007ooOol0?goo 00<007ooOol0Kgoo00<007ooOol077oo001=Ool00`00Oomoo`0oOol00`00Oomoo`1_Ool00`00Oomo o`0LOol004aoo`03001oogoo041oo`03001oogoo071oo`03001oogoo01]oo`00C7oo00<007ooOol0 @7oo00<007ooOol0L7oo00<007ooOol06goo001;Ool00`00Oomoo`11Ool00`00Oomoo`1`Ool00`00 Oomoo`0KOol004]oo`03001oogoo045oo`03001oogoo071oo`03001oogoo01]oo`00Bgoo00<007oo Ool0=7oo0`000Woo0P001Woo00<007ooOol0LGoo00<007ooOol06Woo001:Ool00`00Oomoo`0fOol0 1000Oomoo`000Woo00<007ooOol00goo00<007ooOol0LGoo00<007ooOol06Woo001:Ool00`00Oomo o`0cOol500001Goo001oogoo00001Goo0`00LGoo00<007ooOol06Woo001:Ool00`00Oomoo`0cOol0 1000Oomoo`000Woo00@007ooOol000Eoo`03001oogoo075oo`03001oogoo01Yoo`00BWoo00<007oo Ool0=7oo00<007oo00000Woo00@007ooOol000Eoo`03001oogoo075oo`03001oogoo01Yoo`00BGoo 00<007ooOol0=Woo0P000goo0P001Woo00<007ooOol0LWoo00<007ooOol06Goo0019Ool00`00Oomo o`13Ool00`00Oomoo`1bOol00`00Oomoo`0IOol004Uoo`03001oogoo04=oo`03001oogoo079oo`03 001oogoo01Uoo`00BGoo00<007ooOol0@goo00<007ooOol0LWoo00<007ooOol06Goo0018Ool00`00 Oomoo`14Ool00`00Oomoo`1bOol00`00Oomoo`0IOol004Qoo`03001oogoo04Aoo`8007Aoo`03001o ogoo01Qoo`00B7oo00<007ooOol0A7oo00<007ooOol0Lgoo00<007ooOol067oo0017Ool00`00Oomo o`15Ool00`00Oomoo`1cOol00`00Oomoo`0HOol004Moo`03001oogoo04Eoo`03001oogoo07=oo`03 001oogoo01Qoo`00Agoo00<007ooOol0AGoo00<007ooOol0M7oo00<007ooOol05goo0017Ool00`00 Oomoo`15Ool00`00Oomoo`1dOol00`00Oomoo`0GOol004Ioo`03001oogoo04Ioo`03001oogoo07Ao o`03001oogoo01Moo`00AWoo00<007ooOol0AWoo00<007ooOol0M7oo00<007ooOol05goo0016Ool0 0`00Oomoo`16Ool00`00Oomoo`1dOol00`00Oomoo`0GOol004Eoo`03001oogoo04Moo`8007Ioo`03 001oogoo01Ioo`00AGoo00<007ooOol0Agoo00<007ooOol0MGoo00<007ooOol05Woo0015Ool00`00 Oomoo`17Ool00`00Oomoo`1eOol00`00Oomoo`0FOol004Eoo`03001oogoo04Moo`03001oogoo07Eo o`03001oogoo01Ioo`00A7oo00<007ooOol0B7oo00<007ooOol0MWoo00<007ooOol05Goo0014Ool0 0`00Oomoo`18Ool00`00Oomoo`1fOol00`00Oomoo`0EOol004Aoo`03001oogoo04Qoo`03001oogoo 07Ioo`03001oogoo01Eoo`00A7oo00<007ooOol0B7oo00<007ooOol0MWoo00<007ooOol05Goo0013 Ool00`00Oomoo`19Ool2001gOol00`00Oomoo`0EOol004=oo`03001oogoo04Uoo`03001oogoo07Mo o`03001oogoo01Aoo`00@goo00<007ooOol0BGoo00<007ooOol0Mgoo00<007ooOol057oo0012Ool0 0`00Oomoo`1:Ool00`00Oomoo`1gOol00`00Oomoo`0DOol0049oo`03001oogoo04Yoo`03001oogoo 07Moo`03001oogoo01Aoo`00@Woo00<007ooOol0BWoo00<007ooOol0Mgoo00<007ooOol057oo0012 Ool00`00Oomoo`1:Ool00`00Oomoo`1hOol00`00Oomoo`0COol0045oo`03001oogoo03aoo`<000Ao o`8000Ioo`03001oogoo07Qoo`03001oogoo01=oo`00@Goo00<007ooOol0?7oo00@007ooOol0009o o`04001oogoo0005Ool00`00Oomoo`1hOol00`00Oomoo`0COol0045oo`03001oogoo03aoo`04001o ogoo0002Ool01000Oomoo`001Goo0`00N7oo00<007ooOol04goo0011Ool00`00Oomoo`0lOol30003 Ool01000Oomoo`001Goo00<007ooOol0NGoo00<007ooOol04Woo0010Ool00`00Oomoo`0nOol00`00 Oomoo`02Ool01000Oomoo`001Goo00<007ooOol0NGoo00<007ooOol04Woo0010Ool00`00Oomoo`0n Ool30003Ool20006Ool00`00Oomoo`1iOol00`00Oomoo`0BOol0041oo`03001oogoo04aoo`03001o ogoo07Uoo`03001oogoo019oo`00@7oo00<007ooOol0C7oo00<007ooOol0NGoo00<007ooOol04Woo 000oOol00`00Oomoo`1=Ool00`00Oomoo`1jOol00`00Oomoo`0AOol003moo`03001oogoo04eoo`03 001oogoo07Yoo`03001oogoo015oo`00?goo00<007ooOol0CGoo00<007ooOol0NWoo00<007ooOol0 4Goo000oOol00`00Oomoo`1=Ool2001kOol00`00Oomoo`0AOol003ioo`03001oogoo04ioo`03001o ogoo07Yoo`03001oogoo015oo`00?Woo00<007ooOol0CWoo00<007ooOol0NWoo00<007ooOol04Goo 000nOol00`00Oomoo`1>Ool00`00Oomoo`1kOol00`00Oomoo`0@Ool003ioo`03001oogoo04ioo`03 001oogoo07]oo`03001oogoo011oo`00?Goo00<007ooOol0Cgoo00<007ooOol0Ngoo00<007ooOol0 47oo000mOol00`00Oomoo`1?Ool00`00Oomoo`1kOol00`00Oomoo`0@Ool003eoo`03001oogoo04mo o`03001oogoo07]oo`03001oogoo011oo`00?Goo00<007ooOol0Cgoo0P00O7oo00<007ooOol047oo 000mOol00`00Oomoo`1?Ool00`00Oomoo`1lOol00`00Oomoo`0?Ool003aoo`03001oogoo051oo`03 001oogoo07aoo`03001oogoo00moo`00?7oo00<007ooOol0D7oo00<007ooOol0O7oo00<007ooOol0 3goo000lOol00`00Oomoo`1@Ool00`00Oomoo`1lOol00`00Oomoo`0?Ool003aoo`03001oogoo051o o`03001oogoo07aoo`03001oogoo00moo`00>goo00<007ooOol0DGoo00<007ooOol0O7oo00<007oo Ool03goo000kOol00`00Oomoo`1AOol00`00Oomoo`1mOol00`00Oomoo`0>Ool003]oo`03001oogoo 055oo`03001oogoo07eoo`03001oogoo00ioo`00>goo00<007ooOol0DGoo0P00OWoo00<007ooOol0 3Woo000jOol00`00Oomoo`1BOol00`00Oomoo`1mOol00`00Oomoo`0>Ool003Yoo`03001oogoo059o o`03001oogoo07eoo`03001oogoo00ioo`00>Woo00<007ooOol0DWoo00<007ooOol0OGoo00<007oo Ool03Woo000jOol00`00Oomoo`1BOol00`00Oomoo`1nOol00`00Oomoo`0=Ool003Yoo`03001oogoo 059oo`03001oogoo07ioo`03001oogoo00eoo`00>Woo00<007ooOol0A7oo0P0017oo0P001Woo00<0 07ooOol0OWoo00<007ooOol03Goo000iOol00`00Oomoo`14Ool01000Oomoo`000Woo00@007ooOol0 00Eoo`03001oogoo07ioo`03001oogoo00eoo`00>Goo00<007ooOol0A7oo00@007ooOol0009oo`04 001oogoo0005Ool3001nOol00`00Oomoo`0=Ool003Uoo`03001oogoo04Eoo`8000=oo`04001oogoo 0005Ool00`00Oomoo`1oOol00`00Oomoo`07oo00<007ooOol0E7oo00<007ooOol0Ogoo00<007ooOol037oo000hOol00`00 Oomoo`1DOol00`00Oomoo`1oOol00`00Oomoo`07oo00<007ooOol0E7oo00<007ooOol0P7oo00<007ooOol02goo000hOol0 0`00Oomoo`1DOol20021Ool00`00Oomoo`0;Ool003Qoo`03001oogoo05Aoo`03001oogoo081oo`03 001oogoo00]oo`00=goo00<007ooOol0EGoo00<007ooOol0P7oo00<007ooOol02goo000gOol00`00 Oomoo`1EOol00`00Oomoo`20Ool00`00Oomoo`0;Ool003Moo`03001oogoo05Eoo`03001oogoo085o o`03001oogoo00Yoo`00=goo00<007ooOol0EGoo00<007ooOol0PGoo00<007ooOol02Woo000gOol0 0`00Oomoo`1EOol00`00Oomoo`21Ool00`00Oomoo`0:Ool003Moo`03001oogoo05Eoo`03001oogoo 085oo`03001oogoo00Yoo`00=goo00<007ooOol0EGoo00<007ooOol0PGoo00<007ooOol02Woo000f Ool00`00Oomoo`1FOol20022Ool00`00Oomoo`0:Ool003Ioo`03001oogoo05Ioo`03001oogoo089o o`03001oogoo00Uoo`00=Woo00<007ooOol0EWoo00<007ooOol0PWoo00<007ooOol02Goo000fOol0 0`00Oomoo`1FOol00`00Oomoo`22Ool00`00Oomoo`09Ool003Ioo`03001oogoo05Ioo`03001oogoo 089oo`03001oogoo00Uoo`00=Woo00<007ooOol0EWoo00<007ooOol0PWoo00<007ooOol02Goo000e Ool00`00Oomoo`1GOol00`00Oomoo`22Ool00`00Oomoo`09Ool003Eoo`03001oogoo05Moo`03001o ogoo08=oo`03001oogoo00Qoo`00=Goo00<007ooOol0Egoo0P00Q7oo00<007ooOol027oo000eOol0 0`00Oomoo`1GOol00`00Oomoo`23Ool00`00Oomoo`08Ool00001\ \>"], ImageRangeCache->{{{73.5625, 302.938}, {220.688, 79.375}} -> {-5.21149, \ 50.6055, 0.0221471, 0.583931}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Bernpol[10, \(-1\), 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 0.163561 0.0338275 [ [.02381 .15106 -6 -9 ] [.02381 .15106 6 0 ] [.18254 .15106 -12 -9 ] [.18254 .15106 12 0 ] [.5 .15106 -9 -9 ] [.5 .15106 9 0 ] [.65873 .15106 -3 -9 ] [.65873 .15106 3 0 ] [.81746 .15106 -9 -9 ] [.81746 .15106 9 0 ] [.97619 .15106 -3 -9 ] [.97619 .15106 3 0 ] [.32877 .07899 -24 -4.5 ] [.32877 .07899 0 4.5 ] [.32877 .24813 -18 -4.5 ] [.32877 .24813 0 4.5 ] [.32877 .3327 -6 -4.5 ] [.32877 .3327 0 4.5 ] [.32877 .41727 -18 -4.5 ] [.32877 .41727 0 4.5 ] [.32877 .50184 -12 -4.5 ] [.32877 .50184 0 4.5 ] [.32877 .58641 -24 -4.5 ] [.32877 .58641 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 .16356 m .02381 .16981 L s [(-1)] .02381 .15106 0 1 Mshowa .18254 .16356 m .18254 .16981 L s [(-0.5)] .18254 .15106 0 1 Mshowa .5 .16356 m .5 .16981 L s [(0.5)] .5 .15106 0 1 Mshowa .65873 .16356 m .65873 .16981 L s [(1)] .65873 .15106 0 1 Mshowa .81746 .16356 m .81746 .16981 L s [(1.5)] .81746 .15106 0 1 Mshowa .97619 .16356 m .97619 .16981 L s [(2)] .97619 .15106 0 1 Mshowa .125 Mabswid .05556 .16356 m .05556 .16731 L s .0873 .16356 m .0873 .16731 L s .11905 .16356 m .11905 .16731 L s .15079 .16356 m .15079 .16731 L s .21429 .16356 m .21429 .16731 L s .24603 .16356 m .24603 .16731 L s .27778 .16356 m .27778 .16731 L s .30952 .16356 m .30952 .16731 L s .37302 .16356 m .37302 .16731 L s .40476 .16356 m .40476 .16731 L s .43651 .16356 m .43651 .16731 L s .46825 .16356 m .46825 .16731 L s .53175 .16356 m .53175 .16731 L s .56349 .16356 m .56349 .16731 L s .59524 .16356 m .59524 .16731 L s .62698 .16356 m .62698 .16731 L s .69048 .16356 m .69048 .16731 L s .72222 .16356 m .72222 .16731 L s .75397 .16356 m .75397 .16731 L s .78571 .16356 m .78571 .16731 L s .84921 .16356 m .84921 .16731 L s .88095 .16356 m .88095 .16731 L s .9127 .16356 m .9127 .16731 L s .94444 .16356 m .94444 .16731 L s .25 Mabswid 0 .16356 m 1 .16356 L s .34127 .07899 m .34752 .07899 L s [(-2.5)] .32877 .07899 1 0 Mshowa .34127 .24813 m .34752 .24813 L s [(2.5)] .32877 .24813 1 0 Mshowa .34127 .3327 m .34752 .3327 L s [(5)] .32877 .3327 1 0 Mshowa .34127 .41727 m .34752 .41727 L s [(7.5)] .32877 .41727 1 0 Mshowa .34127 .50184 m .34752 .50184 L s [(10)] .32877 .50184 1 0 Mshowa .34127 .58641 m .34752 .58641 L s [(12.5)] .32877 .58641 1 0 Mshowa .125 Mabswid .34127 .09591 m .34502 .09591 L s .34127 .11282 m .34502 .11282 L s .34127 .12973 m .34502 .12973 L s .34127 .14665 m .34502 .14665 L s .34127 .18047 m .34502 .18047 L s .34127 .19739 m .34502 .19739 L s .34127 .2143 m .34502 .2143 L s .34127 .23122 m .34502 .23122 L s .34127 .26504 m .34502 .26504 L s .34127 .28196 m .34502 .28196 L s .34127 .29887 m .34502 .29887 L s .34127 .31578 m .34502 .31578 L s .34127 .34961 m .34502 .34961 L s .34127 .36653 m .34502 .36653 L s .34127 .38344 m .34502 .38344 L s .34127 .40035 m .34502 .40035 L s .34127 .43418 m .34502 .43418 L s .34127 .4511 m .34502 .4511 L s .34127 .46801 m .34502 .46801 L s .34127 .48492 m .34502 .48492 L s .34127 .51875 m .34502 .51875 L s .34127 .53566 m .34502 .53566 L s .34127 .55258 m .34502 .55258 L s .34127 .56949 m .34502 .56949 L s .34127 .06208 m .34502 .06208 L s .34127 .04516 m .34502 .04516 L s .34127 .02825 m .34502 .02825 L s .34127 .01134 m .34502 .01134 L s .34127 .60332 m .34502 .60332 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 .60332 m .06244 .49533 L .10458 .40834 L .14415 .3498 L .18221 .30973 L .20178 .29394 L .22272 .2799 L .26416 .25864 L .30409 .24339 L .34251 .23082 L .38337 .21739 L .42272 .20276 L .46056 .18613 L .50085 .1652 L .53962 .14202 L .58084 .11485 L .62055 .08757 L .65874 .06207 L .69939 .03827 L .71819 .02931 L .73852 .02164 L .74967 .01851 L .75456 .01741 L .75993 .01641 L .765 .01566 L .76974 .01516 L .77235 .01496 L .77474 .01483 L .77606 .01477 L .7768 .01475 L .77749 .01474 L .77876 .01472 L .7794 .01472 L .7801 .01472 L .78132 .01473 L .78245 .01475 L .78369 .01479 L .78502 .01485 L .78641 .01492 L .78773 .01502 L .79019 .01523 L .79463 .01577 L .79945 .01659 L .80472 .01777 L .8103 .01935 L .8203 .02309 L .82974 .02775 L .83988 .03406 L .85819 .04916 L .87937 .07321 L Mistroke .89947 .10334 L .93771 .18332 L .95635 .2345 L .97619 .29887 L Mfstroke .02381 .60332 m .06244 .52294 L .10458 .45202 L .14415 .39836 L .18221 .35616 L .22272 .31912 L .26171 .28922 L .30316 .26186 L .34309 .23838 L .3815 .21745 L .42237 .1962 L .46172 .17627 L .49955 .15745 L .53984 .13792 L .57861 .12004 L .61984 .10279 L .65954 .08896 L .67958 .08344 L .69774 .07949 L .70787 .07779 L .71741 .07655 L .72266 .07603 L .72748 .07566 L .73023 .07549 L .73278 .07537 L .73545 .07527 L .73687 .07523 L .73765 .07522 L .73838 .0752 L .7396 .07519 L .74025 .07518 L .74094 .07518 L .74164 .07517 L .74236 .07518 L .74367 .07518 L .74488 .0752 L .746 .07522 L .74724 .07525 L .74856 .07529 L .75154 .07542 L .75435 .07558 L .75962 .076 L .76465 .07655 L .76928 .07718 L .77974 .07907 L .78944 .08145 L .79851 .08423 L .81915 .09279 L .83943 .1045 L .85797 .11835 L Mistroke .8786 .13771 L .89773 .15971 L .93598 .2169 L .97516 .29646 L .97619 .29887 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggoo00<007ooOol097oo001ROol00`00Oomoo`1D Ool2000oOol00`00Oomoo`0SOol004eoo`@000=oo`8000Aoo`8000Ioo`03001oogoo05=oo`03001o ogoo041oo`03001oogoo029oo`00CGoo00<007ooOol02Goo00@007ooOol000Eoo`03001oogoo059o o`03001oogoo01=oo`l0021oo`03001oogoo025oo`00CWoo00<007ooOol02goo00<007ooOol00goo 0P00DWoo00<007ooOol03Goo1`003goo1@0077oo00<007ooOol087oo0017Ool40004Ool00`00Oomo o`08Ool20006Ool00`00Oomoo`1?Ool2000;Ool5000KOol2000JOol00`00Oomoo`0POol004eoo`04 001oogoo0009Ool00`00Oomoo`05Ool00`00Oomoo`1>Ool00`00Oomoo`09Ool2000ROol3000HOol0 0`00Oomoo`0OOol004ioo`8000Yoo`<000Eoo`03001oogoo04eoo`03001oogoo00Moo`<002Moo`<0 01Ioo`03001oogoo01ioo`00HWoo00<007ooOol0Bgoo0P001goo0`00;Goo0P0057oo00<007ooOol0 7Woo001ROol2001:Ool20006Ool3000bOol2000COol00`00Oomoo`0MOol0069oo`03001oogoo04Qo o`03001oogoo00=oo`<003Moo`80015oo`03001oogoo01eoo`00HWoo00<007ooOol0AWoo0P000goo 0`00?7oo0P0047oo00<007ooOol077oo001ROol00`00Oomoo`14Ool20003Ool20011Ool00`00Oomo o`0=Ool00`00Oomoo`0LOol0069oo`03001oogoo049oo`8000=oo`8004Aoo`8000ioo`03001oogoo 01]oo`00HWoo0P00@Woo00@007ooOomoo`8004Qoo`03001oogoo00]oo`03001oogoo01]oo`00HWoo 00<007ooOol0?goo0P000Woo0P00Bgoo00<007ooOol02goo00<007ooOol06Woo001ROol00`00Oomo o`0nOol00`00Ool00002001>Ool00`00Oomoo`0:Ool00`00Oomoo`0JOol000Qoo`D002=oo`8000Ao o`8000Aoo`8002Aoo`03001oogoo02=oo`8000Aoo`8000Aoo`8000]oo`@001Eoo`D002=oo`D0009o o`8000Aoo`8000Ioo`03001oogoo00Yoo`03001oogoo00ioo`@000Moo`002Woo00<007ooOol08Woo 00@007ooOol000Qoo`04001oogoo000SOol00`00Oomoo`0ROol01000Oomoo`0027oo00@007ooOol0 00Uoo`<001Uoo`03001oogoo02Eoo`03001oogoo00Moo`04001oogoo0006Ool00`00Oomoo`09Ool0 0`00Oomoo`0>Ool00`00Oomoo`08Ool000Yoo`03001oogoo029oo`04001oogoo000;Ool00`00Oomo o`0QOol2000SOol01000Oomoo`002goo00<007ooOol01Goo0`006goo00<007ooOol09Goo00<007oo Ool02Woo00<007ooOol01Goo00<007ooOol02Goo00<007ooOol03Woo00<007ooOol01goo0002Ool4 0004Ool00`00Oomoo`0LOol40002Ool01000Oomoo`002Goo0P0097oo00<007ooOol08Woo00@007oo Ool000Uoo`8000Ioo`8001ioo`03001oogoo02Eoo`03001oogoo00Qoo`8000Uoo`03001oogoo00Qo o`03001oogoo00moo`03001oogoo00Ioo`002Woo00<007ooOol08Woo00@007ooOol000Uoo`03001o ogoo02=oo`03001oogoo029oo`04001oogoo0009Ool00`00Oomoo`03Ool3000OOol00`00Oomoo`0U Ool00`00Oomoo`08Ool00`00Oomoo`09Ool00`00Oomoo`08Ool00`00Oomoo`0Ool00`00Oomoo`02Ool00`00Oomoo`0?Ool0069oo`03001oogoo00ioo`D0099oo`03001o ogoo009oo`03001oogoo00ioo`00HWoo00<007ooOol037oo1000UWoo00D007ooOomoo`00011oo`00 HWoo0P002goo1000V7oo00<007ooOol00Woo00<007ooOol03Goo001ROol00`00Oomoo`08Ool3002L Ool01@00Oomoogoo00003goo001ROol00`00Oomoo`05Ool3002POol01000Oomoo`003goo001ROol0 0`00Oomoo`02Ool4002ROol01@00Oomoogoo00003Woo001ROol00`00Ool00004002UOol01000Oomo o`003Woo001QOol300000goo0000002WOol01@00Oomoogoo00003Goo001MOol4000017oo00000000 ZWoo00@007ooOol000eoo`00FGoo10001Goo00<007ooOol0ZWoo00@007ooOol000eoo`00CGoo1000 0goo1@0000=oo`00000017oo0`00[Goo00@007ooOol000aoo`00CGoo00<007ooOol017oo0P000goo 00@007ooOol0009oo`04001oogoo002]Ool01000Oomoo`0037oo001>Ool01000Oomoogoo0P0027oo 0`000goo0P00[Goo00<007oo000037oo001?Ool30008Ool30005Ool00`00Oomoo`2/Ool00`00Ool0 000goo0P003Goo00<007ooOol05Goo00<007ooOol0/Goo0P0027oo000jOol0 0`00Oomoo`0;Ool2000HOol00`00Oomoo`2bOol00`00Oomoo`06Ool003Qoo`8000eoo`03001oogoo 01Qoo`800;=oo`03001oogoo00Ioo`00=goo00<007ooOol037oo00<007ooOol06Goo00<007ooOol0 ^goo000eOol2000>Ool00`00Oomoo`0JOol00`00Oomoo`2kOol003Aoo`03001oogoo00eoo`03001o ogoo01]oo`03001oogoo0;]oo`00Ool00`00Oomoo`2kOol0011oo`04001oogoo 001>Ool2002lOol000moo`04001oogoo001?Ool00`00Oomoo`2kOol000moo`04001oogoo001?Ool0 0`00Oomoo`2kOol000ioo`04001oogoo001@Ool00`00Oomoo`2kOol000ioo`04001oogoo001@Ool0 0`00Oomoo`2kOol000ioo`03001oo`00055oo`800;aoo`003Goo00@007ooOol0055oo`03001oogoo 0;]oo`003Goo00<007oo0000DWoo00<007ooOol0^goo000=Ool00`00Ool0001BOol00`00Oomoo`2k Ool000aoo`03001oo`0005=oo`03001oogoo0;]oo`0037oo00<007oo0000Dgoo0P00_7oo000"], ImageRangeCache->{{{73.5625, 302.938}, {413.563, 272.25}} -> {-2.09346, \ 30.3638, 0.0110213, 0.103432}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Factor[BB]\)], "Input"], Cell[BoxData[ \(\(2242 - 5295\ x + 1647\ x\^2 - 2304\ x\^3 + 1512\ x\^4\)\/1000\)], \ "Output"] }, Open ]] }, FrontEndVersion->"4.0 for Microsoft Windows", ScreenRectangle->{{0, 800}, {0, 527}}, WindowSize->{496, 369}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic} ] (*********************************************************************** 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[1739, 51, 161, 4, 90, "Input"], Cell[1903, 57, 13150, 440, 186, 4645, 331, "GraphicsData", "PostScript", \ "Graphics"], Cell[15056, 499, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15223, 507, 76, 1, 30, "Input"], Cell[15302, 510, 11404, 342, 186, 3457, 240, "GraphicsData", "PostScript", \ "Graphics"], Cell[26709, 854, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[26876, 862, 63, 1, 30, "Input"], Cell[26942, 865, 12271, 390, 186, 3975, 283, "GraphicsData", "PostScript", \ "Graphics"], Cell[39216, 1257, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[39383, 1265, 74, 1, 30, "Input"], Cell[39460, 1268, 13039, 408, 186, 4211, 295, "GraphicsData", "PostScript", \ "Graphics"], Cell[52502, 1678, 130, 3, 29, "Output"] }, Open ]], Cell[52647, 1684, 53, 1, 30, "Input"], Cell[CellGroupData[{ Cell[52725, 1689, 52, 1, 30, "Input"], Cell[52780, 1692, 46, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[52863, 1698, 50, 1, 30, "Input"], Cell[52916, 1701, 40, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[52993, 1707, 34, 1, 30, "Input"], Cell[53030, 1710, 35, 1, 29, "Output"] }, Open ]], Cell[53080, 1714, 399, 8, 150, "Input"], Cell[53482, 1724, 45, 1, 30, "Input"], Cell[CellGroupData[{ Cell[53552, 1729, 34, 1, 30, "Input"], Cell[53589, 1732, 70, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[53696, 1738, 103, 2, 50, "Input"], Cell[53802, 1742, 18890, 638, 186, 7001, 487, "GraphicsData", "PostScript", \ "Graphics"], Cell[72695, 2382, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[72862, 2390, 134, 3, 50, "Input"], Cell[72999, 2395, 36, 1, 25, "Print"], Cell[73038, 2398, 37, 1, 25, "Print"], Cell[73078, 2401, 37, 1, 25, "Print"], Cell[73118, 2404, 39, 1, 25, "Print"], Cell[73160, 2407, 39, 1, 25, "Print"], Cell[73202, 2410, 40, 1, 25, "Print"], Cell[73245, 2413, 53, 1, 25, "Print"], Cell[73301, 2416, 52, 1, 25, "Print"], Cell[73356, 2419, 53, 1, 25, "Print"], Cell[73412, 2422, 54, 1, 25, "Print"] }, Open ]], Cell[73481, 2426, 45, 1, 30, "Input"], Cell[CellGroupData[{ Cell[73551, 2431, 34, 1, 30, "Input"], Cell[73588, 2434, 386, 7, 147, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[74011, 2446, 63, 1, 30, "Input"], Cell[74077, 2449, 20464, 669, 186, 7390, 503, "GraphicsData", "PostScript", \ "Graphics"], Cell[94544, 3120, 130, 3, 29, "Output"] }, Open ]], Cell[94689, 3126, 471, 8, 170, "Input"], Cell[CellGroupData[{ Cell[95185, 3138, 54, 1, 30, "Input"], Cell[95242, 3141, 14458, 425, 186, 4397, 296, "GraphicsData", "PostScript", \ "Graphics"], Cell[109703, 3568, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[109870, 3576, 35, 1, 30, "Input"], Cell[109908, 3579, 115, 2, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[110060, 3586, 37, 1, 30, "Input"], Cell[110100, 3589, 43, 1, 29, "Output"] }, Open ]], Cell[110158, 3593, 70, 1, 30, "Input"], Cell[CellGroupData[{ Cell[110253, 3598, 59, 1, 30, "Input"], Cell[110315, 3601, 15292, 434, 186, 4050, 291, "GraphicsData", "PostScript", \ "Graphics"], Cell[125610, 4037, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[125777, 4045, 55, 1, 30, "Input"], Cell[125835, 4048, 17201, 541, 186, 5623, 394, "GraphicsData", "PostScript", \ "Graphics"], Cell[143039, 4591, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[143206, 4599, 43, 1, 30, "Input"], Cell[143252, 4602, 99, 2, 45, "Output"] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)