(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 139730, 4529]*) (*NotebookOutlinePosition[ 140421, 4553]*) (* CellTagsIndexPosition[ 140377, 4549]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Comparison of the Integral of 1/x with Riemann sums", "Subtitle"], Cell["\<\ Ivan Cnop Vrije universiteit Brussel icnop@vub.ac.be\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["Avoid messages", "Subsubsection"], Cell[BoxData[ \(Off[Plot::plnr]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Intervals with constantlength 1", "Section"], Cell[CellGroupData[{ Cell["We start with some useful list programming", "Subsection"], Cell[BoxData[ \(Clear[x]\)], "Input"], Cell[BoxData[ \(\(height = 5;\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(values = \ Table[1/j, {j, 14}]\)], "Input"], Cell[BoxData[ \({1, 1\/2, 1\/3, 1\/4, 1\/5, 1\/6, 1\/7, 1\/8, 1\/9, 1\/10, 1\/11, 1\/12, 1\/13, 1\/14}\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[{ \(\(howMany = Length[values];\)\), "\n", \(\(rightEnd = howMany;\)\), "\n", \(\(leftEnd = 0;\)\), "\n", \(delta\ = \((rightEnd - leftEnd)\)/howMany\)}], "Input"], Cell[BoxData[ \(1\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(xes = Table[x, {x, leftEnd + delta, rightEnd, delta}]\)], "Input"], Cell[BoxData[ \({1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}\)], "Output"] }, Closed]], Cell[BoxData[ \(\(slots = \ Map[\((\((# - delta)\) < x < \((#)\))\) &, xes];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(slots\)], "Input"], Cell[BoxData[ \({0 < x < 1, 1 < x < 2, 2 < x < 3, 3 < x < 4, 4 < x < 5, 5 < x < 6, 6 < x < 7, 7 < x < 8, 8 < x < 9, 9 < x < 10, 10 < x < 11, 11 < x < 12, 12 < x < 13, 13 < x < 14}\)], "Output"] }, Closed]], Cell[BoxData[ \(\(l = Flatten[Transpose[{slots, values}]];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(l /. Head[l] -> Which\)], "Input"], Cell[BoxData[ \(Which[0 < x < 1, 1, 1 < x < 2, 1\/2, 2 < x < 3, 1\/3, 3 < x < 4, 1\/4, 4 < x < 5, 1\/5, 5 < x < 6, 1\/6, 6 < x < 7, 1\/7, 7 < x < 8, 1\/8, 8 < x < 9, 1\/9, 9 < x < 10, 1\/10, 10 < x < 11, 1\/11, 11 < x < 12, 1\/12, 12 < x < 13, 1\/13, 13 < x < 14, 1\/14]\)], "Output"] }, Closed]], Cell[BoxData[ \(Clear[f]; f[x_] := l /. Head[l] -> Which\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{\(f[x]\), ",", \({x, leftEnd, howMany\ delta}\), "\n", StyleBox[",", FontColor->GrayLevel[0.500008]], StyleBox[\(AxesOrigin -> {leftEnd, 0}\), FontColor->GrayLevel[0.500008]], StyleBox[",", FontColor->GrayLevel[0.500008]], StyleBox[\(PlotRange -> {0, 2}\), FontColor->GrayLevel[0.500008]]}], "]"}]], "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 0.0680272 0 0.309017 [ [.15986 -0.0125 -3 -9 ] [.15986 -0.0125 3 0 ] [.29592 -0.0125 -3 -9 ] [.29592 -0.0125 3 0 ] [.43197 -0.0125 -3 -9 ] [.43197 -0.0125 3 0 ] [.56803 -0.0125 -3 -9 ] [.56803 -0.0125 3 0 ] [.70408 -0.0125 -6 -9 ] [.70408 -0.0125 6 0 ] [.84014 -0.0125 -6 -9 ] [.84014 -0.0125 6 0 ] [.97619 -0.0125 -6 -9 ] [.97619 -0.0125 6 0 ] [.01131 .07725 -24 -4.5 ] [.01131 .07725 0 4.5 ] [.01131 .15451 -18 -4.5 ] [.01131 .15451 0 4.5 ] [.01131 .23176 -24 -4.5 ] [.01131 .23176 0 4.5 ] [.01131 .30902 -6 -4.5 ] [.01131 .30902 0 4.5 ] [.01131 .38627 -24 -4.5 ] [.01131 .38627 0 4.5 ] [.01131 .46353 -18 -4.5 ] [.01131 .46353 0 4.5 ] [.01131 .54078 -24 -4.5 ] [.01131 .54078 0 4.5 ] [.01131 .61803 -6 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15986 0 m .15986 .00625 L s [(2)] .15986 -0.0125 0 1 Mshowa .29592 0 m .29592 .00625 L s [(4)] .29592 -0.0125 0 1 Mshowa .43197 0 m .43197 .00625 L s [(6)] .43197 -0.0125 0 1 Mshowa .56803 0 m .56803 .00625 L s [(8)] .56803 -0.0125 0 1 Mshowa .70408 0 m .70408 .00625 L s [(10)] .70408 -0.0125 0 1 Mshowa .84014 0 m .84014 .00625 L s [(12)] .84014 -0.0125 0 1 Mshowa .97619 0 m .97619 .00625 L s [(14)] .97619 -0.0125 0 1 Mshowa .125 Mabswid .05782 0 m .05782 .00375 L s .09184 0 m .09184 .00375 L s .12585 0 m .12585 .00375 L s .19388 0 m .19388 .00375 L s .22789 0 m .22789 .00375 L s .2619 0 m .2619 .00375 L s .32993 0 m .32993 .00375 L s .36395 0 m .36395 .00375 L s .39796 0 m .39796 .00375 L s .46599 0 m .46599 .00375 L s .5 0 m .5 .00375 L s .53401 0 m .53401 .00375 L s .60204 0 m .60204 .00375 L s .63605 0 m .63605 .00375 L s .67007 0 m .67007 .00375 L s .7381 0 m .7381 .00375 L s .77211 0 m .77211 .00375 L s .80612 0 m .80612 .00375 L s .87415 0 m .87415 .00375 L s .90816 0 m .90816 .00375 L s .94218 0 m .94218 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .07725 m .03006 .07725 L s [(0.25)] .01131 .07725 1 0 Mshowa .02381 .15451 m .03006 .15451 L s [(0.5)] .01131 .15451 1 0 Mshowa .02381 .23176 m .03006 .23176 L s [(0.75)] .01131 .23176 1 0 Mshowa .02381 .30902 m .03006 .30902 L s [(1)] .01131 .30902 1 0 Mshowa .02381 .38627 m .03006 .38627 L s [(1.25)] .01131 .38627 1 0 Mshowa .02381 .46353 m .03006 .46353 L s [(1.5)] .01131 .46353 1 0 Mshowa .02381 .54078 m .03006 .54078 L s [(1.75)] .01131 .54078 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(2)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .01545 m .02756 .01545 L s .02381 .0309 m .02756 .0309 L s .02381 .04635 m .02756 .04635 L s .02381 .0618 m .02756 .0618 L s .02381 .09271 m .02756 .09271 L s .02381 .10816 m .02756 .10816 L s .02381 .12361 m .02756 .12361 L s .02381 .13906 m .02756 .13906 L s .02381 .16996 m .02756 .16996 L s .02381 .18541 m .02756 .18541 L s .02381 .20086 m .02756 .20086 L s .02381 .21631 m .02756 .21631 L s .02381 .24721 m .02756 .24721 L s .02381 .26266 m .02756 .26266 L s .02381 .27812 m .02756 .27812 L s .02381 .29357 m .02756 .29357 L s .02381 .32447 m .02756 .32447 L s .02381 .33992 m .02756 .33992 L s .02381 .35537 m .02756 .35537 L s .02381 .37082 m .02756 .37082 L s .02381 .40172 m .02756 .40172 L s .02381 .41717 m .02756 .41717 L s .02381 .43262 m .02756 .43262 L s .02381 .44807 m .02756 .44807 L s .02381 .47898 m .02756 .47898 L s .02381 .49443 m .02756 .49443 L s .02381 .50988 m .02756 .50988 L s .02381 .52533 m .02756 .52533 L s .02381 .55623 m .02756 .55623 L s .02381 .57168 m .02756 .57168 L s .02381 .58713 m .02756 .58713 L s .02381 .60258 m .02756 .60258 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .30902 m .04262 .30902 L .06244 .30902 L .07216 .30902 L .08255 .30902 L .08562 .30902 L .08852 .30902 L .08979 .30902 L .09113 .30902 L .09183 .30902 L .0926 .15451 L .0933 .15451 L .09396 .15451 L .10458 .15451 L .12312 .15451 L .14335 .15451 L .14866 .15451 L .15431 .15451 L .15706 .15451 L .15841 .15451 L .15965 .15451 L .16078 .10301 L .16197 .10301 L .16449 .10301 L .18458 .10301 L .20444 .10301 L .21311 .10301 L .22255 .10301 L .22507 .10301 L .22645 .10301 L .22775 .10301 L .22885 .07725 L .23004 .07725 L .23257 .07725 L .24206 .07725 L .26297 .07725 L .28301 .07725 L .28788 .07725 L .29056 .07725 L .29309 .07725 L .29452 .07725 L .29533 .07725 L .29608 .0618 L .2974 .0618 L .2988 .0618 L .30411 .0618 L .342 .0618 L .35198 .0618 L .35689 .0618 L .35928 .0618 L Mistroke .36145 .0618 L .36275 .0618 L .36398 .0515 L .36527 .0515 L .36667 .0515 L .37236 .0515 L .38234 .0515 L .40192 .0515 L .41229 .0515 L .418 .0515 L .42339 .0515 L .42853 .0515 L .42993 .0515 L .4307 .0515 L .43143 .0515 L .4327 .04415 L .43338 .04415 L .4341 .04415 L .44386 .04415 L .46293 .04415 L .48301 .04415 L .4931 .04415 L .49587 .04415 L .49739 .04415 L .49813 .04415 L .49882 .04415 L .49947 .04415 L .50015 .03863 L .50084 .03863 L .5016 .03863 L .50413 .03863 L .52525 .03863 L .54452 .03863 L .55407 .03863 L .55911 .03863 L .56188 .03863 L .56447 .03863 L .56672 .03863 L .56798 .03863 L .56914 .03434 L .57034 .03434 L .57165 .03434 L .5743 .03434 L .58339 .03434 L .60462 .03434 L .62392 .03434 L .62859 .03434 L .63115 .03434 L .63354 .03434 L .63479 .03434 L Mistroke .63549 .03434 L .63613 .0309 L .63683 .0309 L .63759 .0309 L .63897 .0309 L .64398 .0309 L .66294 .0309 L .68427 .0309 L .69434 .0309 L .69876 .0309 L .70126 .0309 L .70249 .0309 L .7036 .0309 L .70477 .02809 L .70588 .02809 L .70831 .02809 L .71329 .02809 L .72377 .02809 L .74275 .02809 L .75241 .02809 L .76268 .02809 L .76689 .02809 L .76911 .02809 L .77031 .02809 L .77144 .02809 L .77268 .02575 L .77334 .02575 L .77404 .02575 L .77642 .02575 L .7811 .02575 L .80103 .02575 L .81152 .02575 L .82262 .02575 L .83253 .02575 L .83525 .02575 L .83675 .02575 L .83817 .02575 L .83949 .02575 L .84023 .02377 L .84092 .02377 L .84344 .02377 L .86262 .02377 L .88147 .02377 L .89138 .02377 L .90182 .02377 L .9044 .02377 L .90582 .02377 L .90716 .02377 L .90792 .02377 L .90875 .02207 L Mistroke .9095 .02207 L .91019 .02207 L .91301 .02207 L .92329 .02207 L .94348 .02207 L .97619 .02207 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]HGAYHf4PAg9QL6QYHggooooo000Nooooo`;o00004?ooool00ol0003oooooooooo`3]ooooo`007_oo ool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo0>gooooo000Nooooo`03o`000?oooooo oooo00oooooo00?o0000ooooooooool0kOooool001kooooo00?o0000ooooooooool03oooool00ol0 003oooooooooo`3]ooooo`007_ooool2o`00013ooooo00?o0000ooooooooool0kOooool001kooooo 00?o0000ooooooooool03oooool00ol0003oooooooooo`3]ooooo`007_ooool00ol0003ooooooooo o`0?ooooo`03o`000?oooooooooo0>gooooo000Nooooo`03o`000?oooooooooo00oooooo00?o0000 ooooooooool0kOooool001kooooo0_l0000@ooooo`03o`000?oooooooooo0>gooooo000Nooooo`03 o`000?oooooooooo00oooooo00?o0000ooooooooool0kOooool001kooooo00?o0000ooooooooool0 3oooool00ol0003oooooooooo`3]ooooo`007_ooool00ol0003oooooooooo`0?ooooo`03o`000?oo oooooooo0>gooooo000Nooooo`;o00004?ooool00ol0003oooooooooo`3]ooooo`001Oooool2o`00 00Cooooo00?o0000ooooooooool00oooool00ol0003oooooooooo`02ooooo`?o00001Oooool00ol0 003oooooooooo`0?ooooo`03o`000?oooooooooo0>gooooo0004ooooo`04o`000?ooooooooooo`00 00Wooooo00Go0000ooooooooooooooooo`000003ooooo`03o`000?oooooooooo00;ooooo00?o0000 ooooooooool03oooool00ol0003oooooooooo`3]ooooo`001?ooool01?l0003oooooooooool0000: ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool00_ooool00ol0003oooooooooo`0? ooooo`03o`000?oooooooooo0>gooooo0004ooooo`04o`000?ooooooooooo`0000[ooooo00?o0000 ooooooooool01?ooool00ol0003oooooooooo`02ooooo`?o00003oooool00ol0003oooooooooo`3] ooooo`001?ooool01?l0003oooooooooool0000;ooooo`03o`000?oooooo000000?o00001Oooool0 0ol0003oooooooooo`0?ooooo`03o`000?oooooooooo0>gooooo0004ooooo`04o`000?oooooooooo o`0000Oooooo00Oo0000ooooooooooooooooo`000?oooooo000000Sooooo00?o0000ooooooooool0 3oooool00ol0003oooooooooo`3]ooooo`001Oooool2o`0000Sooooo1Ol000000ooooooo0000o`00 0003o`0000Cooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`3]ooooo`007_ooool2 o`00013ooooo00?o0000ooooooooool0kOooool001kooooo00?o0000ooooooooool03oooool00ol0 003oooooooooo`3]ooooo`007_ooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo0>go oooo000Nooooo`03o`000?oooooooooo00oooooo00?o0000ooooooooool0kOooool001kooooo0_l0 000@ooooo`03o`000?oooooooooo0>gooooo000Nooooo`03o`000?oooooooooo00oooooo00?o0000 ooooooooool0kOooool001kooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`3]oooo o`007_ooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo0>gooooo000Nooooo`;o0000 4?ooool00ol0003oooooooooo`3]ooooo`007_ooool00ol0003oooooooooo`0?ooooo`03o`000?oo oooooooo0>gooooo000Nooooo`03o`000?oooooooooo00oooooo00?o0000ooooooooool0kOooool0 01kooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`3]ooooo`007_ooool2o`00013o oooo00?o0000ooooooooool0kOooool001Kooooo0ol00005ooooo`03o`000?oooooooooo00oooooo 00?o0000ooooooooool0kOooool001Oooooo00?o0000ooooooooool01?ooool00ol0003ooooooooo o`0?ooooo`03o`000?oooooooooo0>gooooo000Gooooo`03o`000?oooooooooo00Cooooo00?o0000 ooooooooool03oooool00ol0003oooooooooo`3]ooooo`005oooool00ol0003oooooooooo`04oooo oa?o0000koooool001Oooooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`3oooooo`00 5_ooool2o`0000Kooooo00?o0000ooooooooool0ooooool001Oooooo00?o0000ooooooooool01?oo ool00ol0003oooooooooo`3oooooo`007_ooool2o`000?oooooo0Oooool001kooooo00?o0000oooo ooooool0ooooool001kooooo00?o0000ooooooooool0ooooool001kooooo00?o0000ooooooooool0 ooooool001kooooo0_l0003oooooo`7ooooo000Nooooo`03o`000?oooooooooo0?oooooo000Noooo o`03o`000?oooooooooo0?oooooo000Nooooo`03o`000?oooooooooo0?oooooo000Nooooo`;o0000 ooooool1ooooo`007_ooool00ol0003oooooooooo`3oooooo`007_ooool00ol0003oooooooooo`3o ooooo`007_ooool00ol0003oooooooooo`3oooooo`007_ooool2o`000?oooooo0Oooool000Cooooo 0ol00004ooooo`04o`000?ooooooooooooooo`Go00000_ooool3o`0000Gooooo00?o0000oooooooo ool0ooooool000Gooooo00?o0000ooooooooool02?ooool01_l0003oooooooooool0003oooooo`00 00?ooooo00?o0000ooooooooool00_ooool00ol0003oooooooooo`3oooooo`001Oooool00ol0003o ooooooooo`09ooooo`03o`000?oooooooooo00Gooooo00?o0000ooooooooool00_ooool00ol0003o ooooooooo`3oooooo`001Oooool00ol0003oooooooooo`0:ooooo`03o`000?oooooooooo00Cooooo 00?o0000ooooooooool00_ooool3o`000?oooooo0005ooooo`03o`000?oooooooooo00Oooooo00Ko 0000ooooooooooooooooo`000?ooool4o`0000Gooooo00?o0000ooooooooool0ooooool000Cooooo 0_l00009ooooo`07o`000?ooooooooooooooool0003oooooo`000008ooooo`03o`000?oooooooooo 0?oooooo0005ooooo`03o`000?oooooooooo00Sooooo0ol00002ooooo`Go00001?ooool00ol0003o ooooooooo`3oooooo`007_ooool2o`000?oooooo0Oooool001kooooo00?o0000ooooooooool0oooo ool001kooooo00?o0000ooooooooool0ooooool001kooooo00?o0000ooooooooool0ooooool001ko oooo0_l0003oooooo`7ooooo000Nooooo`03o`000?oooooooooo0?oooooo000Nooooo`03o`000?oo oooooooo0?oooooo000Nooooo`03o`000?oooooooooo0?oooooo000Nooooo`;o0000ooooool1oooo o`007_ooool00ol0003oooooooooo`3oooooo`007_ooool00ol0003oooooooooo`3oooooo`007_oo ool00ol0003oooooooooo`3oooooo`007_ooool2o`000?oooooo0Oooool000[ooooo0ol00004oooo o`03o`000?oooooooooo00;ooooo0ol00005ooooo`03o`000?oooooooooo0?oooooo000;ooooo`03 o`000?oooooooooo00Oooooo00Go0000ooooooooooooooooo`000004ooooo`03o`000?oooooooooo 0?oooooo000;ooooo`03o`000?oooooooooo00_ooooo00?o0000ooooooooool00_ooool00ol0003o ooooooooo`3oooooo`002oooool00ol0003oooooooooo`0;ooooo`03o`000?oooooooooo00;ooooo 0ol0003oooooo`002oooool00ol0003oooooooooo`07ooooo`Co00001Oooool00ol0003ooooooooo o`3oooooo`002_ooool2o`0000Wooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`3o ooooo`002oooool00ol0003oooooooooo`07ooooo`Go00001?ooool00ol0003oooooooooo`3ooooo o`007_ooool2o`000?oooooo0Oooool001kooooo00?o0000ooooooooool0ooooool001kooooo00?o 0000ooooooooool0ooooool001kooooo00?o0000ooooooooool0ooooool001kooooo0_l0003ooooo o`7ooooo000Nooooo`03o`000?oooooooooo0?oooooo000Nooooo`03o`000?oooooooooo0?oooooo 000Nooooo`03o`000?oooooooooo0?oooooo000Nooooo`;o0000ooooool1ooooo`007_ooool00ol0 003oooooooooo`3oooooo`007_ooool00ol0003oooooooooo`3oooooo`007_ooool00ol0003ooooo ooooo`3oooooo`007_ooool2o`000?oooooo0Oooool000Cooooo0ol00004ooooo`03o`000?oooooo oooo00?ooooo00?o0000ooooooooool00_ooool3o`0000Gooooo00?o0000ooooooooool0ooooool0 00Gooooo00?o0000ooooooooool02Oooool01Ol0003ooooooooooooooooo000000?ooooo00?o0000 ooooooooool00_ooool00ol0003oooooooooo`3oooooo`001Oooool00ol0003oooooooooo`0:oooo o`03o`000?oooooooooo00Cooooo00?o0000ooooooooool00_ooool00ol0003oooooooooo`3ooooo o`001Oooool00ol0003oooooooooo`0:ooooo`03o`000?oooooooooo00Cooooo00?o0000oooooooo ool00_ooool3o`000?oooooo0005ooooo`03o`000?oooooooooo00_ooooo00?o0000ooooool00000 0ol00005ooooo`03o`000?oooooooooo0?oooooo0004ooooo`;o00002Oooool01ol0003ooooooooo oooooooo0000ooooool000002?ooool00ol0003oooooooooo`3oooooo`001Oooool00ol0003ooooo ooooo`07ooooo`Go000000?oooooo`000?l000000ol00004ooooo`03o`000?oooooooooo0?oooooo 000Nooooo`;o0000ooooool1ooooo`007_ooool00ol0003oooooooooo`3oooooo`007_ooool00ol0 003oooooooooo`3oooooo`007_ooool00ol0003oooooooooo`3oooooo`007_ooool2o`000?oooooo 0Oooool001kooooo00?o0000ooooooooool0ooooool001kooooo00?o0000ooooooooool0ooooool0 01kooooo00?o0000ooooooooool0ooooool001kooooo0_l0003oooooo`7ooooo000Nooooo`03o`00 0?oooooooooo0?oooooo000Nooooo`03o`000?oooooooooo0?oooooo000Nooooo`03o`000?oooooo oooo0?oooooo000Nooooo`;o0000ooooool1ooooo`005Oooool5o`0000Cooooo00?o0000oooooooo ool0ooooool001Kooooo00Co0000oooooooooooo00001?ooool00ol0003oooooooooo`3oooooo`00 5oooool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo0?oooooo000Hooooo`03o`000?oo oooooooo00?ooooo0ol0003oooooo`005Oooool01Ol0003ooooooooooooooooo00000?oooooo1ooo ool001Gooooo00Go0000ooooooooooooooooo`00003oooooo`Oooooo000Fooooo`?o0000ooooool8 ooooo`00oooooolQooooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-1.7356, -0.152823, \ 0.0567121, 0.0124846}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Closed]] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["left- and right values of the function", "Section"], Cell[BoxData[ \(f[x_] := 1/x\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(fLinks = \ Map[f, xes - delta\ ];\)\)], "Input"], Cell[BoxData[ \(Power::"infy" \(\(:\)\(\ \)\) "Infinite expression \!\(1\/0\) encountered."\)], "Message"] }, Closed]], Cell[BoxData[ \(\(l1 = Flatten[Transpose[{slots, fLinks}]];\)\)], "Input"], Cell[BoxData[ \(Clear[fL]; fL[x_] := l1 /. Head[l] -> Which\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{\({f[x], fL[x]}\), ",", \({x, leftEnd, howMany\ delta}\), "\n", StyleBox[",", FontColor->GrayLevel[0.500008]], StyleBox[\(AxesOrigin -> {leftEnd, 0}\), FontColor->GrayLevel[0.500008]]}], "]"}]], "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 0.0680272 0.0147151 0.249649 [ [.15986 .00222 -3 -9 ] [.15986 .00222 3 0 ] [.29592 .00222 -3 -9 ] [.29592 .00222 3 0 ] [.43197 .00222 -3 -9 ] [.43197 .00222 3 0 ] [.56803 .00222 -3 -9 ] [.56803 .00222 3 0 ] [.70408 .00222 -6 -9 ] [.70408 .00222 6 0 ] [.84014 .00222 -6 -9 ] [.84014 .00222 6 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.01131 .13954 -18 -4.5 ] [.01131 .13954 0 4.5 ] [.01131 .26436 -6 -4.5 ] [.01131 .26436 0 4.5 ] [.01131 .38919 -18 -4.5 ] [.01131 .38919 0 4.5 ] [.01131 .51401 -6 -4.5 ] [.01131 .51401 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15986 .01472 m .15986 .02097 L s [(2)] .15986 .00222 0 1 Mshowa .29592 .01472 m .29592 .02097 L s [(4)] .29592 .00222 0 1 Mshowa .43197 .01472 m .43197 .02097 L s [(6)] .43197 .00222 0 1 Mshowa .56803 .01472 m .56803 .02097 L s [(8)] .56803 .00222 0 1 Mshowa .70408 .01472 m .70408 .02097 L s [(10)] .70408 .00222 0 1 Mshowa .84014 .01472 m .84014 .02097 L s [(12)] .84014 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(14)] .97619 .00222 0 1 Mshowa .125 Mabswid .05782 .01472 m .05782 .01847 L s .09184 .01472 m .09184 .01847 L s .12585 .01472 m .12585 .01847 L s .19388 .01472 m .19388 .01847 L s .22789 .01472 m .22789 .01847 L s .2619 .01472 m .2619 .01847 L s .32993 .01472 m .32993 .01847 L s .36395 .01472 m .36395 .01847 L s .39796 .01472 m .39796 .01847 L s .46599 .01472 m .46599 .01847 L s .5 .01472 m .5 .01847 L s .53401 .01472 m .53401 .01847 L s .60204 .01472 m .60204 .01847 L s .63605 .01472 m .63605 .01847 L s .67007 .01472 m .67007 .01847 L s .7381 .01472 m .7381 .01847 L s .77211 .01472 m .77211 .01847 L s .80612 .01472 m .80612 .01847 L s .87415 .01472 m .87415 .01847 L s .90816 .01472 m .90816 .01847 L s .94218 .01472 m .94218 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .13954 m .03006 .13954 L s [(0.5)] .01131 .13954 1 0 Mshowa .02381 .26436 m .03006 .26436 L s [(1)] .01131 .26436 1 0 Mshowa .02381 .38919 m .03006 .38919 L s [(1.5)] .01131 .38919 1 0 Mshowa .02381 .51401 m .03006 .51401 L s [(2)] .01131 .51401 1 0 Mshowa .125 Mabswid .02381 .03968 m .02756 .03968 L s .02381 .06464 m .02756 .06464 L s .02381 .08961 m .02756 .08961 L s .02381 .11457 m .02756 .11457 L s .02381 .1645 m .02756 .1645 L s .02381 .18947 m .02756 .18947 L s .02381 .21443 m .02756 .21443 L s .02381 .2394 m .02756 .2394 L s .02381 .28933 m .02756 .28933 L s .02381 .31429 m .02756 .31429 L s .02381 .33926 m .02756 .33926 L s .02381 .36422 m .02756 .36422 L s .02381 .41415 m .02756 .41415 L s .02381 .43912 m .02756 .43912 L s .02381 .46408 m .02756 .46408 L s .02381 .48905 m .02756 .48905 L s .02381 .53898 m .02756 .53898 L s .02381 .56394 m .02756 .56394 L s .02381 .58891 m .02756 .58891 L s .02381 .61387 m .02756 .61387 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 .05198 .61803 m .0521 .61508 L .05489 .56111 L .05752 .51844 L .06244 .45429 L .06757 .4028 L .07299 .36006 L .08269 .30317 L .09312 .25973 L .10458 .22498 L .11478 .20139 L .12409 .18407 L .145 .15484 L .16409 .13578 L .18485 .12017 L .20462 .10864 L .22563 .09886 L .26338 .0856 L .30359 .07542 L .34227 .06804 L .38341 .06194 L .42304 .05725 L .46115 .05355 L .50171 .05025 L .54075 .04757 L .58225 .04513 L .62223 .04309 L .6607 .04138 L .70162 .03977 L .74102 .03839 L .77891 .03721 L .81925 .03607 L .85807 .03507 L .89935 .03411 L .93911 .03327 L .97619 .03255 L s .09184 .26436 m .09259 .26436 L .09396 .26436 L .10458 .26436 L .12341 .26436 L .13412 .26436 L .14415 .26436 L .15371 .26436 L .15646 .26436 L .15782 .26436 L .15908 .26436 L .16021 .13954 L .16143 .13954 L .16399 .13954 L .18502 .13954 L .20499 .13954 L .2155 .13954 L .22124 .13954 L .22404 .13954 L .22527 .13954 L .2266 .13954 L .22788 .13954 L .22907 .09793 L .2302 .09793 L .2314 .09793 L .23655 .09793 L .24747 .09793 L .26667 .09793 L .27604 .09793 L .28614 .09793 L .29078 .09793 L .29332 .09793 L .29455 .09793 L .29567 .09793 L .29671 .07713 L .29769 .07713 L .29985 .07713 L .30442 .07713 L .34288 .07713 L .35315 .07713 L .35817 .07713 L .36037 .07713 L .36153 .07713 L .36276 .07713 L .36405 .06464 L .36524 .06464 L .36759 .06464 L .37278 .06464 L .3838 .06464 L .40382 .06464 L Mistroke .41434 .06464 L .42008 .06464 L .42544 .06464 L .42791 .06464 L .43025 .06464 L .43155 .06464 L .43228 .05632 L .43295 .05632 L .43541 .05632 L .44634 .05632 L .46556 .05632 L .48426 .05632 L .48938 .05632 L .49207 .05632 L .4949 .05632 L .49739 .05632 L .49807 .05632 L .4988 .05632 L .50011 .05038 L .50139 .05038 L .50261 .05038 L .50487 .05038 L .54339 .05038 L .55369 .05038 L .55872 .05038 L .56331 .05038 L .5645 .05038 L .56579 .05038 L .56702 .05038 L .56815 .04592 L .56934 .04592 L .57066 .04592 L .57334 .04592 L .58436 .04592 L .60531 .04592 L .61449 .04592 L .62453 .04592 L .62925 .04592 L .63183 .04592 L .63311 .04592 L .63428 .04592 L .63539 .04592 L .63656 .04245 L .63774 .04245 L .63903 .04245 L .64336 .04245 L .66319 .04245 L .68424 .04245 L .69423 .04245 L .69909 .04245 L Mistroke .70121 .04245 L .70232 .04245 L .7035 .04245 L .70473 .03968 L .70587 .03968 L .7081 .03968 L .71301 .03968 L .72339 .03968 L .74229 .03968 L .75178 .03968 L .76194 .03968 L .76687 .03968 L .76929 .03968 L .77036 .03968 L .77154 .03968 L .77259 .03741 L .77357 .03741 L .77573 .03741 L .78028 .03741 L .81899 .03741 L .82938 .03741 L .83444 .03741 L .83665 .03741 L .83781 .03741 L .83904 .03741 L .84035 .03552 L .84155 .03552 L .84392 .03552 L .84913 .03552 L .86015 .03552 L .87996 .03552 L .89806 .03552 L .90283 .03552 L .90536 .03552 L .90674 .03552 L .90804 .03552 L .90928 .03392 L .90998 .03392 L .91062 .03392 L .91296 .03392 L .91752 .03392 L .93841 .03392 L .97619 .03392 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]HGAYHf4PAg9QL6QYHgOooool00ol0003ooooo ooooo`0Pooooo`Go00008?ooool01Ol0003ooooooooooooooooo0000023ooooo00Go0000oooooooo ooooooooo`00000Oooooo`03o`000?oooooooooo00;ooooo00Co0000oooooooooooo00007?ooool0 0ol0003oooooooooo`03ooooo`03o`000?oooooooooo01cooooo00Co0000oooooooooooooooo1Ol0 0003ooooo`00>_ooool00ol0003oooooooooo`0Oooooo`04o`000?ooooooooooo`00027ooooo1?l0 000Rooooo`?o00008?ooool00ol0003oooooooooo`02ooooo`04o`000?ooooooooooo`0001cooooo 00?o0000ooooooooool01?ooool00ol0003oooooooooo`0Kooooo`05o`000?ooooooooooooooool0 00000_ooool00ol0003oooooooooo`02ooooo`00=oooool01Ol0003ooooooooooooooooo0000027o oooo00?o0000ooooool000008Oooool00ol0003oooooooooo`0Rooooo`05o`000?oooooooooooooo ool000007oooool00ol0003oooooooooo`02ooooo`04o`000?ooooooooooo`0001cooooo00Go0000 ooooooooooooooooo`000003ooooo`03o`000?oooooooooo01[ooooo00?o0000ooooooooool00_oo ool00ol0003oooooo`000004ooooo`00=oooool01Ol0003ooooooooooooooooo000002;ooooo0_l0 000Rooooo`03o`000?oooooooooo027ooooo00Go0000ooooooooooooooooo`00000Nooooo`;o0000 1?ooool01?l0003oooooooooool0000Kooooo`;o00000oooool01Ol0003ooooooooooooooooo0000 01_ooooo0_l00005ooooo`;o00001?ooool003Sooooo0ol0000Tooooo`03o`000?oooooooooo027o oooo0_l0000Rooooo`?o00008?ooool00ol0003oooooooooo`03ooooo`;o00007Oooool00ol0003o ooooooooo`02ooooo`?o00007Oooool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo00;o oooo000Eooooo`03o`000?oooooooooo0?oooooo2Oooool001Gooooo00?o0000ooooooooool0oooo ool9ooooo`005Oooool00ol0003oooooooooo`3oooooo`Wooooo000Eooooo`03o`000?oooooooooo 0?oooooo2Oooool000koooooool0000Co`0000005Oooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01oooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`07ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Oooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01oooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`07ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Oooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Oooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Gooooo000Eooooo`03o`000?oooooooooo02;ooooo00?o0000ooooooooool08_oo ool00ol0003oooooooooo`0Rooooo`03o`000?oooooooooo02;ooooo00?o0000ooooooooool08_oo ool00ol0003oooooooooo`0Rooooo`03o`000?oooooooooo02;ooooo00?o0000ooooooooool01Ooo ool001Gooooo00?o0000ooooooooool0ooooool9ooooo`005Oooool00ol0003oooooooooo`3ooooo o`Wooooo000Eooooo`03o`000?oooooooooo0>Kooooo6ol00007ooooo`005Oooool00ol0003ooooo ooooo`35ooooobWo00006_ooool001Gooooo0_l0002VooooobCo0000?oooool001Gooooo00?o0000 ooooooooool0T?oooolWo`00057ooooo000Eooooo`03o`000?oooooooooo08Gooooo2ol000000ooo oooo0000o`00000Ao`0006Cooooo000Eooooo`03o`000?oooooooooo07[ooooo6?l0001fooooo`00 5Oooool00ol0003oooooooooo`1/oooooa?o0000ROooool001Gooooo00?o0000ooooooooool0IOoo ool:o`0009Wooooo000Eooooo`03o`000?oooooooooo05cooooo2Ol00007ooooo`03o`000?oooooo oooo09Wooooo000Eooooo`;o0000F?oooolFo`0009_ooooo000Eooooo`03o`000?oooooooooo057o oooo1_l00002ooooo`03o`000?oooooooooo0:cooooo000Eooooo`03o`000?oooooooooo04cooooo 1Ol00008ooooo`03o`000?oooooooooo0:cooooo000Eooooo`03o`000?oooooooooo04Kooooo5?l0 002^ooooo`005Oooool00ol0003oooooooooo`11ooooo`Go000000?oooooo`000?ooool0_oooool0 01Gooooo00?o0000ooooooooool0?Oooool4o`0000Kooooo00?o0000ooooooooool0__ooool001Go oooo00?o0000ooooooooool0>_ooool3o`0000[ooooo00?o0000ooooooooool0__ooool001Gooooo 0_l0000iooooo`;o00003Oooool00ol0003oooooooooo`2nooooo`005Oooool00ol0003ooooooooo o`0eooooo`?o00003oooool00ol0003oooooooooo`2nooooo`005Oooool00ol0003oooooooooo`0c oooooaGo0000`?ooool001Gooooo00?o0000ooooooooool0ooooo`03o`000?oooooooooo0=7ooooo00001Ooooooo0000oooo oooooooo000000_ooooo00?o0000ooooooooool00_ooool3o`0002;ooooo4ol0003Cooooo`0000Go ooooo`000?ooooooooooo`00000;ooooo`03o`000?oooooooooo00;ooooo00?o0000ooooooooool0 8Oooool2o`000>Gooooo00001Ooooooo0000oooooooooooo000000Oooooo1?l00005ooooo`03o`00 0?oooooooooo023ooooo00?o0000ooooool00000iOooool00005ooooool0003oooooooooool00000 1oooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo01oooooo00Co0000oooooooooooo 0000iOooool000;ooooo0_l00008ooooo`Go00001?ooool00ol0003oooooooooo`0Nooooo`05o`00 0?ooooooooooooooool00000iOooool001Gooooo00?o0000ooooooooool07_ooool01Ol0003ooooo oooooooooooo00000>Gooooo000Eooooo`03o`000?oooooooooo01gooooo00?o0000ooooooooool0 0_ooool00ol0003oooooooooo`3Sooooo`005Oooool2o`0001gooooo00?o0000ooooooooool00ooo ool00ol0003oooooooooo`3Sooooo`005Oooool00ol0003oooooooooo`0Kooooo`03o`000?oooooo oooo00Cooooo00?o0000ooooooooool0hoooool001Gooooo00?o0000ooooooooool06oooool00ol0 003oooooooooo`04ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`03o`000?oooooooooo01[o oooo00?o0000ooooooooool01Oooool00ol0003oooooooooo`3Sooooo`005Oooool00ol0003ooooo ooooo`0Iooooo`03o`000?oooooooooo00Kooooo00?o0000ooooooooool0hoooool001Gooooo00?o 0000ooooooooool06?ooool00ol0003oooooooooo`07ooooo`03o`000?oooooooooo0>?ooooo000E ooooo`03o`000?oooooooooo01Sooooo00?o0000ooooooooool01oooool00ol0003oooooooooo`3S ooooo`005Oooool2o`0001Sooooo00?o0000ooooooooool02?ooool00ol0003oooooooooo`3Soooo o`005Oooool00ol0003oooooooooo`0Gooooo`03o`000?oooooooooo00Sooooo00?o0000oooooooo ool0hoooool001Gooooo00?o0000ooooooooool05oooool00ol0003oooooooooo`08ooooo`03o`00 0?oooooooooo0>?ooooo000Eooooo`03o`000?oooooooooo01Kooooo00?o0000ooooooooool02Ooo ool00ol0003oooooooooo`3Sooooo`005Oooool00ol0003oooooooooo`0Fooooo`03o`000?oooooo oooo00Wooooo00?o0000ooooooooool0hoooool001Gooooo00?o0000ooooooooool05Oooool00ol0 003oooooooooo`0:ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`;o00005_ooool00ol0003o ooooooooo`0:ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`03o`000?oooooooooo01Cooooo 00?o0000ooooooooool02oooool00ol0003oooooooooo`3Sooooo`005Oooool00ol0003ooooooooo o`0Dooooo`03o`000?oooooooooo00_ooooo00?o0000ooooooooool0hoooool001Gooooo00?o0000 ooooooooool04oooool00ol0003oooooooooo`0?ooooo000Eoooo o`03o`000?oooooooooo01?ooooo00?o0000ooooooooool03?ooool00ol0003oooooooooo`3Soooo o`005Oooool00ol0003oooooooooo`0Cooooo`03o`000?oooooooooo00cooooo00?o0000oooooooo ool0hoooool001Gooooo00?o0000ooooooooool04_ooool00ol0003oooooooooo`0=ooooo`03o`00 0?oooooooooo0>?ooooo000Eooooo`;o00004oooool00ol0003oooooooooo`0=ooooo`03o`000?oo oooooooo0>?ooooo000Eooooo`03o`000?oooooooooo01;ooooo00?o0000ooooooooool03Oooool0 0ol0003oooooooooo`3Sooooo`005Oooool00ol0003oooooooooo`0Aooooo`03o`000?oooooooooo 00kooooo00?o0000ooooooooool0hoooool001Gooooo00?o0000ooooooooool04Oooool00ol0003o ooooooooo`0>ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`03o`000?oooooooooo017ooooo 00?o0000ooooooooool03_ooool00ol0003oooooooooo`3Sooooo`003Oooool3o`0000Gooooo00?o 0000ooooooooool04?ooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo0>?ooooo000> ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool04?ooool00ol0003oooooooooo`0? ooooo`03o`000?oooooooooo0>?ooooo000>ooooo`03o`000?oooooooooo00Cooooo0ol0000?oooo oaCo0000iOooool000kooooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`0@ooooo`03 o`000?oooooooooo0?Gooooo000>ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool0 3oooool00ol0003oooooooooo`3fooooo`003Oooool2o`0000Kooooo00?o0000ooooooooool03ooo ool00ol0003oooooooooo`3fooooo`003_ooool00ol0003oooooooooo`04ooooo`03o`000?oooooo oooo00oooooo00?o0000ooooooooool0m_ooool001Gooooo00?o0000ooooooooool03oooool00ol0 003oooooooooo`3fooooo`005Oooool00ol0003oooooooooo`0>ooooo`03o`000?oooooooooo0?Oo oooo000Eooooo`;o00003oooool00ol0003oooooooooo`3gooooo`005Oooool00ol0003ooooooooo o`0>ooooo`03o`000?oooooooooo0?Oooooo000Eooooo`03o`000?oooooooooo00kooooo00?o0000 ooooooooool0moooool001Gooooo00?o0000ooooooooool03Oooool00ol0003oooooooooo`3hoooo o`005Oooool00ol0003oooooooooo`0=ooooo`03o`000?oooooooooo0?Sooooo000Eooooo`03o`00 0?oooooooooo00gooooo00?o0000ooooooooool0n?ooool001Gooooo00?o0000ooooooooool03Ooo ool00ol0003oooooooooo`3hooooo`005Oooool2o`0000gooooo00?o0000ooooooooool0nOooool0 01Gooooo00?o0000ooooooooool03?ooool00ol0003oooooooooo`3iooooo`005Oooool00ol0003o ooooooooo`0ooooo`03o`000?oooooooooo00Cooooo0ol00006oooo o`03o`000?oooooooooo0?oooooo000?ooooo`03o`000?oooooooooo00?ooooo00?o0000oooooooo ool01_ooool00ol0003oooooooooo`3oooooo`003?ooool01Ol0003ooooooooooooooooo000000Co oooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`3oooooo`003?ooool01Ol0003ooooo oooooooooooo000000Cooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`3oooooo`00 3Oooool3o`0000Gooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`3oooooo`005Ooo ool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo0?oooooo000Eooooo`03o`000?oooooo oooo00Kooooo00?o0000ooooooooool0ooooool001Gooooo0_l00007ooooo`03o`000?oooooooooo 0?oooooo000Eooooo`03o`000?oooooooooo00Gooooo00?o0000ooooooooool0ooooool1ooooo`00 5Oooool00ol0003oooooooooo`05ooooo`03o`000?oooooooooo0?oooooo0Oooool001Gooooo00?o 0000ooooooooool01Oooool00ol0003oooooooooo`3oooooo`7ooooo000Eooooo`03o`000?oooooo oooo00Gooooo00?o0000ooooooooool0ooooool1ooooo`005Oooool00ol0003oooooooooo`05oooo o`03o`000?oooooooooo0?oooooo0Oooool001Gooooo00?o0000ooooooooool01Oooool00ol0003o ooooooooo`3oooooo`7ooooo000Eooooo`;o00001_ooool00ol0003oooooooooo`3oooooo`7ooooo 000Eooooo`03o`000?oooooooooo00Gooooo00?o0000ooooooooool0ooooool1ooooo`005Oooool0 0ol0003oooooooooo`05ooooo`03o`000?oooooooooo0?oooooo0Oooool001Gooooo00?o0000oooo ooooool01Oooool00ol0003oooooooooo`3oooooo`7ooooo000Eooooo`03o`000?oooooooooo00Go oooo00?o0000ooooooooool0ooooool1ooooo`005Oooool00ol0003oooooooooo`05ooooo`03o`00 0?oooooooooo0?oooooo0Oooool001Gooooo0_l00006ooooo`03o`000?oooooooooo0?oooooo0Ooo ool001Gooooo00?o0000ooooooooool01Oooool00ol0003oooooooooo`3oooooo`7ooooo000Eoooo o`03o`000?oooooooooo00Gooooo00?o0000ooooooooool0ooooool1ooooo`005Oooool00ol0003o ooooooooo`05ooooo`03o`000?oooooooooo0?oooooo0Oooool001Gooooo00?o0000ooooooooool0 1Oooool00ol0003oooooooooo`3oooooo`7ooooo000Eooooo`03o`000?oooooooooo00Gooooo00?o 0000ooooooooool0ooooool1ooooo`005Oooool00ol0003oooooooooo`05ooooo`03o`000?oooooo oooo0?oooooo0Oooool001Gooooo0_l00006ooooo`03o`000?oooooooooo0?oooooo0Oooool001Go oooo00?o0000ooooooooool01Oooool00ol0003oooooooooo`3oooooo`7ooooo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-1.15634, -0.185434, \ 0.0540293, 0.0147225}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(fRight = \ Map[f, xes]\)], "Input"], Cell[BoxData[ \({1, 1\/2, 1\/3, 1\/4, 1\/5, 1\/6, 1\/7, 1\/8, 1\/9, 1\/10, 1\/11, 1\/12, 1\/13, 1\/14}\)], "Output"] }, Closed]], Cell[BoxData[ \(\(l2 = Flatten[Transpose[{slots, fRight}]];\)\)], "Input"], Cell[BoxData[ \(Clear[fR]; fR[x_] := l2 /. Head[l] -> Which\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{\({f[x], fR[x]}\), ",", \({x, leftEnd, howMany\ delta}\), "\n", StyleBox[",", FontColor->GrayLevel[0.500008]], StyleBox[\(AxesOrigin -> {leftEnd, 0}\), FontColor->GrayLevel[0.500008]]}], "]"}]], "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 0.0680272 0.0147151 0.3394 [ [.15986 .00222 -3 -9 ] [.15986 .00222 3 0 ] [.29592 .00222 -3 -9 ] [.29592 .00222 3 0 ] [.43197 .00222 -3 -9 ] [.43197 .00222 3 0 ] [.56803 .00222 -3 -9 ] [.56803 .00222 3 0 ] [.70408 .00222 -6 -9 ] [.70408 .00222 6 0 ] [.84014 .00222 -6 -9 ] [.84014 .00222 6 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.01131 .09956 -24 -4.5 ] [.01131 .09956 0 4.5 ] [.01131 .18441 -18 -4.5 ] [.01131 .18441 0 4.5 ] [.01131 .26926 -24 -4.5 ] [.01131 .26926 0 4.5 ] [.01131 .35411 -6 -4.5 ] [.01131 .35411 0 4.5 ] [.01131 .43896 -24 -4.5 ] [.01131 .43896 0 4.5 ] [.01131 .52381 -18 -4.5 ] [.01131 .52381 0 4.5 ] [.01131 .60866 -24 -4.5 ] [.01131 .60866 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15986 .01472 m .15986 .02097 L s [(2)] .15986 .00222 0 1 Mshowa .29592 .01472 m .29592 .02097 L s [(4)] .29592 .00222 0 1 Mshowa .43197 .01472 m .43197 .02097 L s [(6)] .43197 .00222 0 1 Mshowa .56803 .01472 m .56803 .02097 L s [(8)] .56803 .00222 0 1 Mshowa .70408 .01472 m .70408 .02097 L s [(10)] .70408 .00222 0 1 Mshowa .84014 .01472 m .84014 .02097 L s [(12)] .84014 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(14)] .97619 .00222 0 1 Mshowa .125 Mabswid .05782 .01472 m .05782 .01847 L s .09184 .01472 m .09184 .01847 L s .12585 .01472 m .12585 .01847 L s .19388 .01472 m .19388 .01847 L s .22789 .01472 m .22789 .01847 L s .2619 .01472 m .2619 .01847 L s .32993 .01472 m .32993 .01847 L s .36395 .01472 m .36395 .01847 L s .39796 .01472 m .39796 .01847 L s .46599 .01472 m .46599 .01847 L s .5 .01472 m .5 .01847 L s .53401 .01472 m .53401 .01847 L s .60204 .01472 m .60204 .01847 L s .63605 .01472 m .63605 .01847 L s .67007 .01472 m .67007 .01847 L s .7381 .01472 m .7381 .01847 L s .77211 .01472 m .77211 .01847 L s .80612 .01472 m .80612 .01847 L s .87415 .01472 m .87415 .01847 L s .90816 .01472 m .90816 .01847 L s .94218 .01472 m .94218 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .09956 m .03006 .09956 L s [(0.25)] .01131 .09956 1 0 Mshowa .02381 .18441 m .03006 .18441 L s [(0.5)] .01131 .18441 1 0 Mshowa .02381 .26926 m .03006 .26926 L s [(0.75)] .01131 .26926 1 0 Mshowa .02381 .35411 m .03006 .35411 L s [(1)] .01131 .35411 1 0 Mshowa .02381 .43896 m .03006 .43896 L s [(1.25)] .01131 .43896 1 0 Mshowa .02381 .52381 m .03006 .52381 L s [(1.5)] .01131 .52381 1 0 Mshowa .02381 .60866 m .03006 .60866 L s [(1.75)] .01131 .60866 1 0 Mshowa .125 Mabswid .02381 .03169 m .02756 .03169 L s .02381 .04866 m .02756 .04866 L s .02381 .06563 m .02756 .06563 L s .02381 .0826 m .02756 .0826 L s .02381 .11653 m .02756 .11653 L s .02381 .1335 m .02756 .1335 L s .02381 .15047 m .02756 .15047 L s .02381 .16744 m .02756 .16744 L s .02381 .20138 m .02756 .20138 L s .02381 .21835 m .02756 .21835 L s .02381 .23532 m .02756 .23532 L s .02381 .25229 m .02756 .25229 L s .02381 .28623 m .02756 .28623 L s .02381 .3032 m .02756 .3032 L s .02381 .32017 m .02756 .32017 L s .02381 .33714 m .02756 .33714 L s .02381 .37108 m .02756 .37108 L s .02381 .38805 m .02756 .38805 L s .02381 .40502 m .02756 .40502 L s .02381 .42199 m .02756 .42199 L s .02381 .45593 m .02756 .45593 L s .02381 .4729 m .02756 .4729 L s .02381 .48987 m .02756 .48987 L s .02381 .50684 m .02756 .50684 L s .02381 .54078 m .02756 .54078 L s .02381 .55775 m .02756 .55775 L s .02381 .57472 m .02756 .57472 L s .02381 .59169 m .02756 .59169 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 .06212 .61803 m .06244 .61231 L .06757 .54231 L .07299 .48421 L .08269 .40687 L .09312 .34782 L .10458 .30057 L .11478 .2685 L .12409 .24495 L .145 .20522 L .16409 .1793 L .18485 .15809 L .20462 .14241 L .22563 .12911 L .26338 .11109 L .30359 .09724 L .34227 .08721 L .38341 .07892 L .42304 .07255 L .46115 .06751 L .50171 .06303 L .54075 .05938 L .58225 .05606 L .62223 .0533 L .6607 .05097 L .70162 .04878 L .74102 .04691 L .77891 .04529 L .81925 .04374 L .85807 .04239 L .89935 .04109 L .93911 .03994 L .97619 .03896 L s .02381 .35411 m .04262 .35411 L .06244 .35411 L .07216 .35411 L .08255 .35411 L .08562 .35411 L .08852 .35411 L .08979 .35411 L .09113 .35411 L .09183 .35411 L .0926 .18441 L .0933 .18441 L .09396 .18441 L .10458 .18441 L .12312 .18441 L .14335 .18441 L .14866 .18441 L .15431 .18441 L .15706 .18441 L .15841 .18441 L .15965 .18441 L .16078 .12785 L .16197 .12785 L .16449 .12785 L .18458 .12785 L .20444 .12785 L .21311 .12785 L .22255 .12785 L .22507 .12785 L .22645 .12785 L .22775 .12785 L .22885 .09956 L .23004 .09956 L .23257 .09956 L .24206 .09956 L .26297 .09956 L .28301 .09956 L .28788 .09956 L .29056 .09956 L .29309 .09956 L .29452 .09956 L .29533 .09956 L .29608 .0826 L .2974 .0826 L .2988 .0826 L .30411 .0826 L .342 .0826 L .35198 .0826 L .35689 .0826 L .35928 .0826 L Mistroke .36145 .0826 L .36275 .0826 L .36398 .07128 L .36527 .07128 L .36667 .07128 L .37236 .07128 L .38234 .07128 L .40192 .07128 L .41229 .07128 L .418 .07128 L .42339 .07128 L .42853 .07128 L .42993 .07128 L .4307 .07128 L .43143 .07128 L .4327 .0632 L .43338 .0632 L .4341 .0632 L .44386 .0632 L .46293 .0632 L .48301 .0632 L .4931 .0632 L .49587 .0632 L .49739 .0632 L .49813 .0632 L .49882 .0632 L .49947 .0632 L .50015 .05714 L .50084 .05714 L .5016 .05714 L .50413 .05714 L .52525 .05714 L .54452 .05714 L .55407 .05714 L .55911 .05714 L .56188 .05714 L .56447 .05714 L .56672 .05714 L .56798 .05714 L .56914 .05243 L .57034 .05243 L .57165 .05243 L .5743 .05243 L .58339 .05243 L .60462 .05243 L .62392 .05243 L .62859 .05243 L .63115 .05243 L .63354 .05243 L .63479 .05243 L Mistroke .63549 .05243 L .63613 .04866 L .63683 .04866 L .63759 .04866 L .63897 .04866 L .64398 .04866 L .66294 .04866 L .68427 .04866 L .69434 .04866 L .69876 .04866 L .70126 .04866 L .70249 .04866 L .7036 .04866 L .70477 .04557 L .70588 .04557 L .70831 .04557 L .71329 .04557 L .72377 .04557 L .74275 .04557 L .75241 .04557 L .76268 .04557 L .76689 .04557 L .76911 .04557 L .77031 .04557 L .77144 .04557 L .77268 .043 L .77334 .043 L .77404 .043 L .77642 .043 L .7811 .043 L .80103 .043 L .81152 .043 L .82262 .043 L .83253 .043 L .83525 .043 L .83675 .043 L .83817 .043 L .83949 .043 L .84023 .04082 L .84092 .04082 L .84344 .04082 L .86262 .04082 L .88147 .04082 L .89138 .04082 L .90182 .04082 L .9044 .04082 L .90582 .04082 L .90716 .04082 L .90792 .04082 L .90875 .03896 L Mistroke .9095 .03896 L .91019 .03896 L .91301 .03896 L .92329 .03896 L .94348 .03896 L .97619 .03896 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]HGAYHf4PAg9QL6QYHgoooooako0000E_ooool001_ooooo00?o0000ooooooooool0O?oo oolKo`0006_ooooo000Kooooo`03o`000?oooooooooo07cooooo00?o0000ooooooooool00_ooool; o`0007Kooooo000Kooooo`;o0000JooooolGo`00087ooooo000Kooooo`03o`000?oooooooooo06[o oooo00?o0000ooooool000002_l0002;ooooo`006oooool00ol0003oooooooooo`1GoooooaGo0000 U_ooool001_ooooo00?o0000ooooooooool0Eoooool00ol0003oooooooooo`05ooooo`Go0000W_oo ool001_ooooo00?o0000ooooooooool0Eoooool00ol0003oooooooooo`05o`000:?ooooo000Koooo o`;o0000A_oooolEo`000:Sooooo000Kooooo`03o`000?oooooooooo04Gooooo00?o0000oooooooo ool02?ooool5o`000:gooooo0002ooooo`;o00001?ooool01?l0003oooooooooooooool5o`0000;o oooo0ol00005ooooo`03o`000?oooooooooo04Gooooo00?o0000ooooooooool01?ooool4o`000;;o oooo00001Ooooooo0000oooooooooooo000000Sooooo00Ko0000oooooooooooo0000ooooool00003 ooooo`03o`000?oooooooooo00;ooooo00?o0000ooooooooool0AOooool01?l0003ooooooooooooo ool3o`000;Kooooo00001Ooooooo0000oooooooooooo000000Wooooo00?o0000ooooooooool01Ooo ool00ol0003oooooooooo`02ooooo`03o`000?oooooooooo04Gooooo1?l0002iooooo`0000Gooooo o`000?ooooooooooo`00000:ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool00_oo ool2o`0003Cooooo4ol0002looooo`0000Goooooo`000?ooooooooooo`000007ooooo`06o`000?oo ooooooooooooool0003ooooo1?l00005ooooo`03o`000?oooooooooo03?ooooo00?o0000oooooooo ool02oooool2o`000;oooooo00001Ooooooo0000oooooooooooo000000Oooooo00Oo0000oooooooo ooooooooo`000?oooooo000000Sooooo00?o0000ooooooooool0ooooo`006oooool00ol0003oooooooooo`0Q ooooo`03o`000?oooooooooo00gooooo00?o0000ooooooooool0c_ooool001_ooooo0_l0000Roooo o`03o`000?oooooooooo00_ooooo0_l0003Aooooo`006oooool00ol0003oooooooooo`0Qooooo`03 o`000?oooooooooo00[ooooo00?o0000ooooooooool0dOooool001_ooooo00?o0000ooooooooool0 8Oooool00ol0003oooooooooo`08ooooo`;o0000e?ooool001_ooooo00?o0000ooooooooool08Ooo ool00ol0003oooooooooo`07ooooo`03o`000?oooooooooo0=Cooooo000Kooooo`;o00008_ooool0 0ol0003oooooooooo`06ooooo`03o`000?oooooooooo0=Gooooo000Kooooo`03o`000?oooooooooo 027ooooo00?o0000ooooooooool01Oooool00ol0003oooooooooo`3Fooooo`006oooool00ol0003o ooooooooo`0Qooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool0eoooool001_ooooo 00?o0000ooooooooool08Oooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo0=Sooooo 000Kooooo`03o`000?oooooooooo027ooooo00?o0000ooooooooool00_ooool00ol0003ooooooooo o`3Iooooo`006oooool2o`0002;ooooo00Go0000ooooooooooooooooo`00003Looooo`006oooool0 0ol0003oooooooooo`0Qooooo`04o`000?ooooooooooo`000=gooooo0008ooooo`;o00001?ooool0 0ol0003oooooooooo`02ooooo`?o00001Oooool00ol0003oooooooooo`0Qooooo`03o`000?oooooo 00000=kooooo0007ooooo`04o`000?ooooooooooo`0000Oooooo00Go0000ooooooooooooooooo`00 0004ooooo`03o`000?oooooooooo027ooooo0_l0003Oooooo`001oooool01?l0003oooooooooool0 000;ooooo`03o`000?oooooooooo00;ooooo0_l0000@oooooaCo0000goooool000Oooooo00Co0000 oooooooooooo00002oooool00ol0003oooooooooo`02ooooo`03o`000?oooooooooo00oooooo00?o 0000ooooooooool03oooool00ol0003oooooooooo`3Nooooo`001oooool01?l0003oooooooooool0 0007ooooo`Co00001Oooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo00kooooo00?o 0000ooooooooool0goooool000Oooooo00Co0000oooooooooooo00001oooool00ol0003ooooooooo o`06ooooo`03o`000?oooooooooo00oooooo00?o0000ooooooooool03Oooool00ol0003ooooooooo o`3Pooooo`002?ooool2o`0000Sooooo1Ol00004ooooo`03o`000?oooooooooo00oooooo00?o0000 ooooooooool03Oooool00ol0003oooooooooo`3Pooooo`006oooool2o`00013ooooo00?o0000oooo ooooool03?ooool00ol0003oooooooooo`3Qooooo`006oooool00ol0003oooooooooo`0?ooooo`03 o`000?oooooooooo00_ooooo00?o0000ooooooooool0h_ooool001_ooooo00?o0000ooooooooool0 3oooool00ol0003oooooooooo`0;ooooo`03o`000?oooooooooo0>;ooooo000Kooooo`03o`000?oo oooooooo00oooooo00?o0000ooooooooool02_ooool00ol0003oooooooooo`3Sooooo`006oooool2 o`00013ooooo00?o0000ooooooooool02_ooool00ol0003oooooooooo`3Sooooo`006oooool00ol0 003oooooooooo`0?ooooo`03o`000?oooooooooo00Wooooo00?o0000ooooooooool0i?ooool001_o oooo00?o0000ooooooooool03oooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo0>Co oooo000Kooooo`03o`000?oooooooooo00oooooo00?o0000ooooooooool02?ooool00ol0003ooooo ooooo`3Uooooo`006oooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo00Sooooo00?o 0000ooooooooool0iOooool001_ooooo0_l0000@ooooo`03o`000?oooooooooo00Oooooo00?o0000 ooooooooool0i_ooool001_ooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`07oooo o`03o`000?oooooooooo0>Kooooo000Kooooo`03o`000?oooooooooo00oooooo00?o0000oooooooo ool01_ooool00ol0003oooooooooo`3Wooooo`006oooool00ol0003oooooooooo`0?ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool0ioooool001_ooooo0_l0000@ooooo`03o`000?oo oooooooo00Gooooo00?o0000ooooooooool0j?ooool001_ooooo00?o0000ooooooooool03oooool0 0ol0003oooooooooo`05ooooo`03o`000?oooooooooo0>Sooooo0002ooooo`;o00001?ooool00ol0 003oooooooooo`03ooooo`03o`000?oooooooooo00;ooooo0ol00005ooooo`03o`000?oooooooooo 00oooooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`3Yooooo`0000Goooooo`000?oo ooooooooo`000009ooooo`05o`000?ooooooooooooooool000000oooool00ol0003oooooooooo`02 ooooo`03o`000?oooooooooo00oooooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`3Y ooooo`0000Goooooo`000?ooooooooooo`00000:ooooo`03o`000?oooooooooo00Cooooo00?o0000 ooooooooool00_ooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo00?ooooo00?o0000 ooooooooool0j_ooool00005ooooool0003oooooooooool000002_ooool00ol0003oooooooooo`04 ooooo`03o`000?oooooooooo00;ooooo0_l0000@ooooo`03o`000?oooooooooo00?ooooo00?o0000 ooooooooool0j_ooool00005ooooool0003oooooooooool000002oooool00ol0003oooooo`000003 o`0000Gooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`02ooooo`03o`000?oooooo oooo0>_ooooo00001Ooooooo0000oooooooooooo000000Oooooo00Oo0000ooooooooooooooooo`00 0?oooooo000000Sooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`02ooooo`03o`00 0?oooooooooo0>_ooooo0002ooooo`;o00002?ooool5o`000003ooooool0003o000000?o00001?oo ool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo00;ooooo00?o0000ooooooooool0jooo ool001_ooooo0_l0000@ooooo`05o`000?ooooooooooooooool00000k_ooool001_ooooo00?o0000 ooooooooool03oooool01Ol0003ooooooooooooooooo00000>kooooo000Kooooo`03o`000?oooooo oooo00oooooo00Go0000ooooooooooooooooo`00003^ooooo`006oooool00ol0003oooooooooo`0? ooooo`04o`000?ooooooooooo`000>oooooo000Kooooo`03o`000?oooooooooo00oooooo00Co0000 oooooooooooo0000koooool001_ooooo0_l0000@ooooo`04o`000?ooooooooooo`000>oooooo000K ooooo`03o`000?oooooooooo00oooooo00Co0000oooooooooooo0000koooool001_ooooo00?o0000 ooooooooool03oooool00ol0003oooooo`00003`ooooo`006oooool00ol0003oooooooooo`0?oooo o`03o`000?oooooo00000?3ooooo000Kooooo`;o00004?ooool00ol0003oooooo`00003`ooooo`00 6oooool00ol0003oooooooooo`0?ooooo`03o`000?oooooo00000?3ooooo000Kooooo`03o`000?oo oooooooo00oooooo0_l0003aooooo`006oooool00ol0003oooooooooo`0?ooooo`;o0000lOooool0 01_ooooo00?o0000ooooooooool03oooool2o`000?7ooooo000Kooooo`;o00004?ooool2o`000?7o oooo000Kooooo`03o`000?oooooooooo00oooooo0_l0003aooooo`004oooool3o`0000Gooooo00?o 0000ooooooooool03oooool00ol0003oooooooooo`3`ooooo`005?ooool00ol0003oooooooooo`04 ooooo`03o`000?oooooooooo00oooooo00?o0000ooooooooool0l?ooool001Cooooo00?o0000oooo ooooool01?oooolCo`000?;ooooo000Dooooo`03o`000?oooooooooo00Cooooo00?o0000oooooooo ool03oooool00ol0003oooooooooo`3`ooooo`005?ooool00ol0003oooooooooo`04ooooo`03o`00 0?oooooooooo00kooooo00?o0000ooooooooool0lOooool001?ooooo0_l00006ooooo`03o`000?oo oooooooo00kooooo00?o0000ooooooooool0lOooool001Cooooo00?o0000ooooooooool01?ooool0 0ol0003oooooooooo`0>ooooo`03o`000?oooooooooo0?7ooooo000Kooooo`;o00003oooool00ol0 003oooooooooo`3aooooo`006oooool00ol0003oooooooooo`0>ooooo`03o`000?oooooooooo0?7o oooo000Kooooo`03o`000?oooooooooo00gooooo00?o0000ooooooooool0l_ooool001_ooooo00?o 0000ooooooooool03Oooool00ol0003oooooooooo`3booooo`006oooool2o`0000kooooo00?o0000 ooooooooool0l_ooool001_ooooo00?o0000ooooooooool03Oooool00ol0003oooooooooo`3boooo o`006oooool00ol0003oooooooooo`0=ooooo`03o`000?oooooooooo0?;ooooo000Kooooo`03o`00 0?oooooooooo00cooooo00?o0000ooooooooool0loooool001_ooooo00?o0000ooooooooool03?oo ool00ol0003oooooooooo`3cooooo`006oooool2o`0000gooooo00?o0000ooooooooool0loooool0 01_ooooo00?o0000ooooooooool03?ooool00ol0003oooooooooo`3cooooo`006oooool00ol0003o ooooooooo`0"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-1.5101, -0.148248, \ 0.0552619, 0.0110764}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{\({fL[x], f[x], fR[x]}\), ",", \({x, leftEnd, howMany\ delta}\), "\n", StyleBox[",", FontColor->GrayLevel[0.500008]], StyleBox[\(AxesOrigin -> {leftEnd, 0}\), FontColor->GrayLevel[0.500008]]}], "]"}]], "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 0.0680272 0.0147151 0.528542 [ [.15986 .00222 -3 -9 ] [.15986 .00222 3 0 ] [.29592 .00222 -3 -9 ] [.29592 .00222 3 0 ] [.43197 .00222 -3 -9 ] [.43197 .00222 3 0 ] [.56803 .00222 -3 -9 ] [.56803 .00222 3 0 ] [.70408 .00222 -6 -9 ] [.70408 .00222 6 0 ] [.84014 .00222 -6 -9 ] [.84014 .00222 6 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.01131 .12042 -18 -4.5 ] [.01131 .12042 0 4.5 ] [.01131 .22613 -18 -4.5 ] [.01131 .22613 0 4.5 ] [.01131 .33184 -18 -4.5 ] [.01131 .33184 0 4.5 ] [.01131 .43755 -18 -4.5 ] [.01131 .43755 0 4.5 ] [.01131 .54326 -6 -4.5 ] [.01131 .54326 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15986 .01472 m .15986 .02097 L s [(2)] .15986 .00222 0 1 Mshowa .29592 .01472 m .29592 .02097 L s [(4)] .29592 .00222 0 1 Mshowa .43197 .01472 m .43197 .02097 L s [(6)] .43197 .00222 0 1 Mshowa .56803 .01472 m .56803 .02097 L s [(8)] .56803 .00222 0 1 Mshowa .70408 .01472 m .70408 .02097 L s [(10)] .70408 .00222 0 1 Mshowa .84014 .01472 m .84014 .02097 L s [(12)] .84014 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(14)] .97619 .00222 0 1 Mshowa .125 Mabswid .05782 .01472 m .05782 .01847 L s .09184 .01472 m .09184 .01847 L s .12585 .01472 m .12585 .01847 L s .19388 .01472 m .19388 .01847 L s .22789 .01472 m .22789 .01847 L s .2619 .01472 m .2619 .01847 L s .32993 .01472 m .32993 .01847 L s .36395 .01472 m .36395 .01847 L s .39796 .01472 m .39796 .01847 L s .46599 .01472 m .46599 .01847 L s .5 .01472 m .5 .01847 L s .53401 .01472 m .53401 .01847 L s .60204 .01472 m .60204 .01847 L s .63605 .01472 m .63605 .01847 L s .67007 .01472 m .67007 .01847 L s .7381 .01472 m .7381 .01847 L s .77211 .01472 m .77211 .01847 L s .80612 .01472 m .80612 .01847 L s .87415 .01472 m .87415 .01847 L s .90816 .01472 m .90816 .01847 L s .94218 .01472 m .94218 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .12042 m .03006 .12042 L s [(0.2)] .01131 .12042 1 0 Mshowa .02381 .22613 m .03006 .22613 L s [(0.4)] .01131 .22613 1 0 Mshowa .02381 .33184 m .03006 .33184 L s [(0.6)] .01131 .33184 1 0 Mshowa .02381 .43755 m .03006 .43755 L s [(0.8)] .01131 .43755 1 0 Mshowa .02381 .54326 m .03006 .54326 L s [(1)] .01131 .54326 1 0 Mshowa .125 Mabswid .02381 .04114 m .02756 .04114 L s .02381 .06757 m .02756 .06757 L s .02381 .094 m .02756 .094 L s .02381 .14685 m .02756 .14685 L s .02381 .17328 m .02756 .17328 L s .02381 .1997 m .02756 .1997 L s .02381 .25256 m .02756 .25256 L s .02381 .27899 m .02756 .27899 L s .02381 .30541 m .02756 .30541 L s .02381 .35827 m .02756 .35827 L s .02381 .38469 m .02756 .38469 L s .02381 .41112 m .02756 .41112 L s .02381 .46398 m .02756 .46398 L s .02381 .4904 m .02756 .4904 L s .02381 .51683 m .02756 .51683 L s .02381 .56968 m .02756 .56968 L s .02381 .59611 m .02756 .59611 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 .09184 .54326 m .09259 .54326 L .09396 .54326 L .10458 .54326 L .12341 .54326 L .13412 .54326 L .14415 .54326 L .15371 .54326 L .15646 .54326 L .15782 .54326 L .15908 .54326 L .16021 .27899 L .16143 .27899 L .16399 .27899 L .18502 .27899 L .20499 .27899 L .2155 .27899 L .22124 .27899 L .22404 .27899 L .22527 .27899 L .2266 .27899 L .22788 .27899 L .22907 .1909 L .2302 .1909 L .2314 .1909 L .23655 .1909 L .24747 .1909 L .26667 .1909 L .27604 .1909 L .28614 .1909 L .29078 .1909 L .29332 .1909 L .29455 .1909 L .29567 .1909 L .29671 .14685 L .29769 .14685 L .29985 .14685 L .30442 .14685 L .34288 .14685 L .35315 .14685 L .35817 .14685 L .36037 .14685 L .36153 .14685 L .36276 .14685 L .36405 .12042 L .36524 .12042 L .36759 .12042 L .37278 .12042 L .3838 .12042 L .40382 .12042 L Mistroke .41434 .12042 L .42008 .12042 L .42544 .12042 L .42791 .12042 L .43025 .12042 L .43155 .12042 L .43228 .10281 L .43295 .10281 L .43541 .10281 L .44634 .10281 L .46556 .10281 L .48426 .10281 L .48938 .10281 L .49207 .10281 L .4949 .10281 L .49739 .10281 L .49807 .10281 L .4988 .10281 L .50011 .09022 L .50139 .09022 L .50261 .09022 L .50487 .09022 L .54339 .09022 L .55369 .09022 L .55872 .09022 L .56331 .09022 L .5645 .09022 L .56579 .09022 L .56702 .09022 L .56815 .08078 L .56934 .08078 L .57066 .08078 L .57334 .08078 L .58436 .08078 L .60531 .08078 L .61449 .08078 L .62453 .08078 L .62925 .08078 L .63183 .08078 L .63311 .08078 L .63428 .08078 L .63539 .08078 L .63656 .07344 L .63774 .07344 L .63903 .07344 L .64336 .07344 L .66319 .07344 L .68424 .07344 L .69423 .07344 L .69909 .07344 L Mistroke .70121 .07344 L .70232 .07344 L .7035 .07344 L .70473 .06757 L .70587 .06757 L .7081 .06757 L .71301 .06757 L .72339 .06757 L .74229 .06757 L .75178 .06757 L .76194 .06757 L .76687 .06757 L .76929 .06757 L .77036 .06757 L .77154 .06757 L .77259 .06276 L .77357 .06276 L .77573 .06276 L .78028 .06276 L .81899 .06276 L .82938 .06276 L .83444 .06276 L .83665 .06276 L .83781 .06276 L .83904 .06276 L .84035 .05876 L .84155 .05876 L .84392 .05876 L .84913 .05876 L .86015 .05876 L .87996 .05876 L .89806 .05876 L .90283 .05876 L .90536 .05876 L .90674 .05876 L .90804 .05876 L .90928 .05537 L .90998 .05537 L .91062 .05537 L .91296 .05537 L .91752 .05537 L .93841 .05537 L .97619 .05537 L Mfstroke .08352 .61803 m .09312 .53345 L .10458 .45987 L .11478 .40993 L .12409 .37326 L .145 .31139 L .16409 .27103 L .18485 .23798 L .20462 .21357 L .22563 .19287 L .26338 .1648 L .30359 .14323 L .34227 .12762 L .38341 .1147 L .42304 .10478 L .46115 .09693 L .50171 .08995 L .54075 .08427 L .58225 .0791 L .62223 .0748 L .6607 .07117 L .70162 .06776 L .74102 .06485 L .77891 .06233 L .81925 .05992 L .85807 .05781 L .89935 .05578 L .93911 .054 L .97619 .05247 L s .02381 .54326 m .04262 .54326 L .06244 .54326 L .07216 .54326 L .08255 .54326 L .08562 .54326 L .08852 .54326 L .08979 .54326 L .09113 .54326 L .09183 .54326 L .0926 .27899 L .0933 .27899 L .09396 .27899 L .10458 .27899 L .12312 .27899 L .14335 .27899 L .14866 .27899 L .15431 .27899 L .15706 .27899 L .15841 .27899 L .15965 .27899 L .16078 .1909 L .16197 .1909 L .16449 .1909 L .18458 .1909 L .20444 .1909 L .21311 .1909 L .22255 .1909 L .22507 .1909 L .22645 .1909 L .22775 .1909 L .22885 .14685 L .23004 .14685 L .23257 .14685 L .24206 .14685 L .26297 .14685 L .28301 .14685 L .28788 .14685 L .29056 .14685 L .29309 .14685 L .29452 .14685 L .29533 .14685 L .29608 .12042 L .2974 .12042 L .2988 .12042 L .30411 .12042 L .342 .12042 L .35198 .12042 L .35689 .12042 L .35928 .12042 L Mistroke .36145 .12042 L .36275 .12042 L .36398 .10281 L .36527 .10281 L .36667 .10281 L .37236 .10281 L .38234 .10281 L .40192 .10281 L .41229 .10281 L .418 .10281 L .42339 .10281 L .42853 .10281 L .42993 .10281 L .4307 .10281 L .43143 .10281 L .4327 .09022 L .43338 .09022 L .4341 .09022 L .44386 .09022 L .46293 .09022 L .48301 .09022 L .4931 .09022 L .49587 .09022 L .49739 .09022 L .49813 .09022 L .49882 .09022 L .49947 .09022 L .50015 .08078 L .50084 .08078 L .5016 .08078 L .50413 .08078 L .52525 .08078 L .54452 .08078 L .55407 .08078 L .55911 .08078 L .56188 .08078 L .56447 .08078 L .56672 .08078 L .56798 .08078 L .56914 .07344 L .57034 .07344 L .57165 .07344 L .5743 .07344 L .58339 .07344 L .60462 .07344 L .62392 .07344 L .62859 .07344 L .63115 .07344 L .63354 .07344 L .63479 .07344 L Mistroke .63549 .07344 L .63613 .06757 L .63683 .06757 L .63759 .06757 L .63897 .06757 L .64398 .06757 L .66294 .06757 L .68427 .06757 L .69434 .06757 L .69876 .06757 L .70126 .06757 L .70249 .06757 L .7036 .06757 L .70477 .06276 L .70588 .06276 L .70831 .06276 L .71329 .06276 L .72377 .06276 L .74275 .06276 L .75241 .06276 L .76268 .06276 L .76689 .06276 L .76911 .06276 L .77031 .06276 L .77144 .06276 L .77268 .05876 L .77334 .05876 L .77404 .05876 L .77642 .05876 L .7811 .05876 L .80103 .05876 L .81152 .05876 L .82262 .05876 L .83253 .05876 L .83525 .05876 L .83675 .05876 L .83817 .05876 L .83949 .05876 L .84023 .05537 L .84092 .05537 L .84344 .05537 L .86262 .05537 L .88147 .05537 L .89138 .05537 L .90182 .05537 L .9044 .05537 L .90582 .05537 L .90716 .05537 L .90792 .05537 L .90875 .05247 L Mistroke .9095 .05247 L .91019 .05247 L .91301 .05247 L .92329 .05247 L .94348 .05247 L .97619 .05247 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]HGAYHf4PAg9QL6QYHgOooool00ol0003ooooo ooooo`0Pooooo`Go00008?ooool01Ol0003ooooooooooooooooo0000023ooooo00Go0000oooooooo ooooooooo`00000Oooooo`03o`000?oooooooooo00;ooooo00Co0000oooooooooooo00007?ooool0 0ol0003oooooooooo`03ooooo`03o`000?oooooooooo01cooooo00Co0000oooooooooooooooo1Ol0 0003ooooo`00>_ooool00ol0003oooooooooo`0Oooooo`04o`000?ooooooooooo`00027ooooo1?l0 000Rooooo`?o00008?ooool00ol0003oooooooooo`02ooooo`04o`000?ooooooooooo`0001cooooo 00?o0000ooooooooool01?ooool00ol0003oooooooooo`0Kooooo`05o`000?ooooooooooooooool0 00000_ooool00ol0003oooooooooo`02ooooo`00=oooool01Ol0003ooooooooooooooooo0000027o oooo00?o0000ooooool000008Oooool00ol0003oooooooooo`0Rooooo`05o`000?oooooooooooooo ool000007oooool00ol0003oooooooooo`02ooooo`04o`000?ooooooooooo`0001cooooo00Go0000 ooooooooooooooooo`000003ooooo`03o`000?oooooooooo01[ooooo00?o0000ooooooooool00_oo ool00ol0003oooooo`000004ooooo`00=oooool01Ol0003ooooooooooooooooo000002;ooooo0_l0 000Rooooo`03o`000?oooooooooo027ooooo00Go0000ooooooooooooooooo`00000Nooooo`;o0000 1?ooool01?l0003oooooooooool0000Kooooo`;o00000oooool01Ol0003ooooooooooooooooo0000 01_ooooo0_l00005ooooo`;o00001?ooool003Sooooo0ol0000Tooooo`03o`000?oooooooooo027o oooo0_l0000Rooooo`?o00008?ooool00ol0003oooooooooo`03ooooo`;o00007Oooool00ol0003o ooooooooo`02ooooo`?o00007Oooool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo00;o oooo000Eooooo`03o`000?oooooooooo0?oooooo2Oooool001Gooooo00?o0000ooooooooool0oooo ool9ooooo`005Oooool00ol0003oooooooooo`3oooooo`Wooooo000Eooooo`03o`000?oooooooooo 0?oooooo2Oooool000koooooool0000Co`0000005Oooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01oooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`07ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Oooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01oooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`07ooooo`03o`00 0?oooooooooo00Kooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Oooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Oooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`00 0?oooooooooo00Gooooo000Eooooo`03o`000?oooooooooo02;ooooo00?o0000ooooooooool08_oo ool00ol0003oooooooooo`0Rooooo`03o`000?oooooooooo02;ooooo00?o0000ooooooooool08_oo ool00ol0003oooooooooo`0Rooooo`03o`000?oooooooooo02;ooooo00?o0000ooooooooool01Ooo ool001Gooooo00?o0000ooooooooool0ooooool9ooooo`005Oooool00ol0003oooooooooo`3ooooo o`Wooooo000Eooooo`03o`000?oooooooooo0?oooooo2Oooool001Gooooo00?o0000ooooooooool0 ooooool9ooooo`005Oooool2o`000?oooooo2_ooool001Gooooo00?o0000ooooooooool0ooooool9 ooooo`005Oooool00ol0003oooooooooo`3oooooo`Wooooo000Eooooo`03o`000?oooooooooo0>ko oooo4ol00007ooooo`005Oooool00ol0003oooooooooo`3KooooobKo00001oooool001Gooooo00?o 0000ooooooooool0bOoooolUo`0001[ooooo000Eooooo`03o`000?oooooooooo0;Kooooo9_l0000/ ooooo`005Oooool00ol0003oooooooooo`2fooooo`03o`000?oooooooooo00;ooooo2_l00004oooo o`03o`000?oooooooooo03cooooo000Eooooo`;o0000YOoooolUo`0003oooooo000Eooooo`03o`00 0?oooooooooo097ooooo9_l0001Aooooo`005Oooool00ol0003oooooooooo`2Aooooo`03o`000?oo oooooooo00Oooooo2_l0001Sooooo`005Oooool00ol0003oooooooooo`1oooooobGo0000I?ooool0 01Gooooo00?o0000ooooooooool0Ooooool00ol0003oooooooooo`05ooooo`Wo000000?oooooo`00 0?ooool0MOooool001Gooooo00?o0000ooooooooool0O_ooool01?l0003oooooooooooooool5o`00 00[ooooo00?o0000ooooooooool0M?ooool001Gooooo00?o0000ooooooooool0K?oooolVo`0007Ko oooo000Eooooo`;o0000KOooool00ol0003oooooooooo`08ooooo`Go00000_ooool00ol0003ooooo ooooo`27ooooo`005Oooool00ol0003oooooooooo`1/ooooo`03o`000?oooooooooo00?ooooo1Ol0 0007ooooo`03o`000?oooooooooo08Oooooo000Eooooo`03o`000?oooooooooo05Wooooo9_l00029 ooooo`005Oooool00ol0003oooooooooo`1Iooooo`03o`000?oooooooooo00_ooooo1_l0002Koooo o`000_ooool2o`0000Cooooo00Co0000oooooooooooooooo1Ol00004ooooo`03o`000?oooooooooo 05Wooooo00?o0000ooooooooool01_ooool5o`0000Gooooo00?o0000ooooooooool0VOooool00005 ooooool0003oooooooooool000002?ooool01?l0003oooooooooool00004ooooo`03o`000?oooooo oooo05Wooooo00?o0000ooooooooool00_ooool4o`0000[ooooo00?o0000ooooooooool0VOooool0 0005ooooool0003oooooooooool000002Oooool00ol0003oooooooooo`04ooooo`03o`000?oooooo oooo05Wooooo00?o0000ooooool000000_l0000>ooooo`03o`000?oooooooooo09Wooooo00001Ooo oooo0000oooooooooooo000000[ooooo00?o0000ooooooooool00oooool3o`0004Oooooo9_l0002K ooooo`0000Goooooo`000?ooooooooooo`000007ooooo`05o`000?ooooooooooooooool000001?oo ool00ol0003oooooooooo`17ooooo`03o`000?oooooooooo00_ooooo0ol000000ooooooo0000oooo o`2]ooooo`0000Goooooo`000?ooooooooooo`000007ooooo`05o`000?ooooooooooooooool00000 1?ooool00ol0003oooooooooo`17ooooo`03o`000?oooooooooo00Wooooo0_l00004ooooo`03o`00 0?oooooooooo0:cooooo0002ooooo`;o00002Oooool3o`0000Gooooo00?o0000ooooooooool0Aooo ool00ol0003oooooooooo`06ooooo`?o00001_ooool00ol0003oooooooooo`2/ooooo`005Oooool0 0ol0003oooooooooo`17ooooo`03o`000?oooooooooo00?ooooo0ol00009ooooo`03o`000?oooooo oooo0:cooooo000Eooooo`03o`000?oooooooooo04Oooooo00?o0000ooooooooool00ol0000ooooo`?o0000d_ooool001Gooooo0_l0000Sooooo`03o`000?oooooooooo00gooooo00Co 0000oooooooooooo0000d_ooool001Gooooo00?o0000ooooooooool08_ooool00ol0003ooooooooo o`0ooooo`03o`000?oooooooooo0=7ooooo000Eooooo`03o`000?oooooooooo02;o oooo00?o0000ooooool000003oooool00ol0003oooooooooo`3Aooooo`005Oooool00ol0003ooooo ooooo`0Rooooo`;o00004?ooool00ol0003oooooooooo`3Aooooo`005Oooool00ol0003ooooooooo o`0Rooooo`;o00004?ooool00ol0003oooooooooo`3Aooooo`005Oooool2o`00017ooooo9Ol0003C ooooo`005Oooool00ol0003oooooooooo`0@ooooo`03o`000?oooooooooo00oooooo00?o0000oooo ooooool0hoooool001Gooooo00?o0000ooooooooool04?ooool00ol0003oooooooooo`0>ooooo`;o 0000iOooool001Gooooo00?o0000ooooooooool04?ooool00ol0003oooooooooo`0>ooooo`;o0000 iOooool001Gooooo00?o0000ooooooooool04?ooool00ol0003oooooooooo`0=ooooo`03o`000?oo oooo00000>Gooooo000Eooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool03Oooool0 0ol0003oooooo`00003Uooooo`005Oooool00ol0003oooooooooo`0@ooooo`03o`000?oooooooooo 00gooooo00?o0000ooooool00000iOooool001Gooooo0_l0000Aooooo`03o`000?oooooooooo00co oooo00Co0000oooooooooooo0000iOooool001Gooooo00?o0000ooooooooool04?ooool00ol0003o ooooooooo`0Gooooo000Eooooo`03o`000?oooooooooo013o oooo00?o0000ooooooooool02oooool01Ol0003ooooooooooooooooo00000>Gooooo000Eooooo`03 o`000?oooooooooo013ooooo00?o0000ooooooooool02oooool01Ol0003ooooooooooooooooo0000 0>Gooooo000Eooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool02_ooool00ol0003o ooooooooo`02ooooo`03o`000?oooooooooo0>?ooooo0002ooooo`;o00001?ooool00ol0003ooooo ooooo`02ooooo`?o00001Oooool00ol0003oooooooooo`0@ooooo`03o`000?oooooooooo00[ooooo 00?o0000ooooooooool00_ooool00ol0003oooooooooo`3Sooooo`0000Goooooo`000?oooooooooo o`000007ooooo`05o`000?ooooooooooooooool000001?ooool00ol0003oooooooooo`0@ooooo`03 o`000?oooooooooo00[ooooo00?o0000ooooooooool00_ooool00ol0003oooooooooo`3Sooooo`00 00Goooooo`000?ooooooooooo`000007ooooo`05o`000?ooooooooooooooool000001?ooool3o`00 013ooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo 0>?ooooo00001Ooooooo0000oooooooooooo000000Oooooo1?l00005ooooo`03o`000?oooooooooo 013ooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo 0>?ooooo00001Ooooooo0000oooooooooooo000000Oooooo00?o0000ooooooooool01_ooool00ol0 003oooooooooo`0@ooooo`03o`000?oooooooooo00Wooooo00?o0000ooooooooool00oooool00ol0 003oooooooooo`3Sooooo`0000Goooooo`000?ooooooooooo`000008ooooo`03o`000?oooooooooo 00Gooooo00?o0000ooooooooool04?ooool00ol0003oooooooooo`08ooooo`03o`000?oooooooooo 00Cooooo00?o0000ooooooooool0hoooool000;ooooo0_l0000:ooooo`;o00001Oooool00ol0003o ooooooooo`0@ooooo`03o`000?oooooooooo00Sooooo00?o0000ooooooooool01?ooool00ol0003o ooooooooo`3Sooooo`005Oooool00ol0003oooooooooo`0@ooooo`03o`000?oooooooooo00Sooooo 00?o0000ooooooooool01?ooool00ol0003oooooooooo`3Sooooo`005Oooool00ol0003ooooooooo o`0@ooooo`03o`000?oooooooooo00Oooooo00?o0000ooooooooool01Oooool00ol0003ooooooooo o`3Sooooo`005Oooool00ol0003oooooooooo`0@ooooo`03o`000?oooooooooo00Oooooo00?o0000 ooooooooool01Oooool00ol0003oooooooooo`3Sooooo`005Oooool2o`00017ooooo00?o0000oooo ooooool01oooool00ol0003oooooooooo`05ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`03 o`000?oooooooooo013ooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03 o`000?oooooooooo0>?ooooo000Eooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool0 1_ooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`03o`000?oo oooooooo013ooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`000?oo oooooooo0>?ooooo000Eooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool01Oooool0 0ol0003oooooooooo`07ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`03o`000?oooooooooo 013ooooo00?o0000ooooooooool01Oooool00ol0003oooooooooo`07ooooo`03o`000?oooooooooo 0>?ooooo000Eooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool01Oooool00ol0003o ooooooooo`07ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`;o00004Oooool00ol0003ooooo ooooo`04ooooo`03o`000?oooooooooo00Sooooo00?o0000ooooooooool0hoooool001Gooooo00?o 0000ooooooooool04?ooool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo00Sooooo00?o 0000ooooooooool0hoooool001Gooooo00?o0000ooooooooool04?ooool00ol0003oooooooooo`04 ooooo`03o`000?oooooooooo00Sooooo00?o0000ooooooooool0hoooool001Gooooo00?o0000oooo ooooool04?ooool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo00Sooooo00?o0000oooo ooooool0hoooool001Gooooo00?o0000ooooooooool04?ooool00ol0003oooooooooo`04ooooo`03 o`000?oooooooooo00Sooooo00?o0000ooooooooool0hoooool001Gooooo00?o0000ooooooooool0 4?ooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00Wooooo00?o0000ooooooooool0 hoooool001Gooooo00?o0000ooooooooool04?ooool00ol0003oooooooooo`03ooooo`03o`000?oo oooooooo00Wooooo00?o0000ooooooooool0hoooool001Gooooo0_l0000Aooooo`03o`000?oooooo oooo00?ooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`3Sooooo`005Oooool00ol0 003oooooooooo`0?ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool02Oooool00ol0 003oooooooooo`3Sooooo`005Oooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo00Co oooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`3Sooooo`005Oooool00ol0003ooooo ooooo`0?ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool02_ooool00ol0003ooooo ooooo`3Sooooo`005Oooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo00?ooooo00?o 0000ooooooooool02_ooool00ol0003oooooooooo`3Sooooo`000_ooool2o`0000Cooooo00?o0000 ooooooooool00_ooool3o`0000Gooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`03 ooooo`03o`000?oooooooooo00[ooooo00?o0000ooooooooool0hoooool00005ooooool0003ooooo ooooool000001oooool01Ol0003ooooooooooooooooo000000Cooooo00?o0000ooooooooool03ooo ool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00[ooooo00?o0000ooooooooool0hooo ool00005ooooool0003oooooooooool000001oooool01Ol0003ooooooooooooooooo000000Cooooo 0ol0000?ooooo`03o`000?oooooooooo00;ooooo00?o0000ooooooooool02oooool00ol0003ooooo ooooo`3Sooooo`0000Goooooo`000?ooooooooooo`000008ooooo`?o00001Oooool00ol0003ooooo ooooo`0?ooooo`03o`000?oooooooooo00;ooooo00?o0000ooooooooool02oooool00ol0003ooooo ooooo`3Sooooo`0000Goooooo`000?ooooooooooo`000007ooooo`05o`000?ooooooooooooooool0 00001?ooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo00;ooooo00?o0000oooooooo ool02oooool00ol0003oooooooooo`3Sooooo`0000Goooooo`000?ooooooooooo`000007ooooo`05 o`000?ooooooooooooooool000001?ooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo 00;ooooo00?o0000ooooooooool02oooool00ol0003oooooooooo`3Sooooo`000_ooool2o`0000Wo oooo0ol00005ooooo`03o`000?oooooooooo00oooooo00?o0000ooooooooool00_ooool00ol0003o ooooooooo`0;ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`03o`000?oooooooooo00oooooo 00Go0000ooooooooooooooooo`00000>ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`03o`00 0?oooooooooo00oooooo00Go0000ooooooooooooooooo`00000>ooooo`03o`000?oooooooooo0>?o oooo000Eooooo`;o00004?ooool01Ol0003ooooooooooooooooo000000kooooo00?o0000oooooooo ool0hoooool001Gooooo00?o0000ooooooooool03oooool01Ol0003ooooooooooooooooo000000ko oooo00?o0000ooooooooool0hoooool001Gooooo00?o0000ooooooooool03oooool01Ol0003ooooo oooooooooooo000000kooooo00?o0000ooooooooool0hoooool001Gooooo00?o0000ooooooooool0 3oooool01?l0003oooooooooool0000?ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`03o`00 0?oooooooooo00oooooo00Co0000oooooooooooo00003oooool00ol0003oooooooooo`3Sooooo`00 5Oooool00ol0003oooooooooo`0?ooooo`04o`000?ooooooooooo`0000oooooo00?o0000oooooooo ool0hoooool001Gooooo00?o0000ooooooooool03oooool01?l0003oooooooooool0000?ooooo`03 o`000?oooooooooo0>?ooooo000Eooooo`03o`000?oooooooooo00oooooo00Co0000oooooooooooo 00003oooool00ol0003oooooooooo`3Sooooo`005Oooool2o`00013ooooo00Co0000oooooooooooo 00003oooool00ol0003oooooooooo`3Sooooo`005Oooool00ol0003oooooooooo`0?ooooo`04o`00 0?ooooooooooo`0000oooooo00?o0000ooooooooool0hoooool001Gooooo00?o0000ooooooooool0 3oooool00ol0003oooooo`00000@ooooo`03o`000?oooooooooo0>?ooooo000Eooooo`03o`000?oo oooooooo00oooooo00?o0000ooooool000004?ooool00ol0003oooooooooo`3Sooooo`005Oooool0 0ol0003oooooooooo`0?ooooo`03o`000?oooooo0000013ooooo00?o0000ooooooooool0hoooool0 01Gooooo00?o0000ooooooooool03oooool00ol0003oooooo`00000@ooooo`03o`000?oooooooooo 0>?ooooo000Eooooo`03o`000?oooooooooo00oooooo00?o0000ooooool000004?ooool00ol0003o ooooooooo`3Sooooo`005Oooool2o`00013ooooo00?o0000ooooool000004?ooool00ol0003ooooo ooooo`3Sooooo`005Oooool00ol0003oooooooooo`0?ooooo`03o`000?oooooo0000013ooooo00?o 0000ooooooooool0hoooool001Gooooo00?o0000ooooooooool03oooool2o`00017ooooo00?o0000 ooooooooool0hoooool001Gooooo00?o0000ooooooooool03oooool2o`00017ooooo00?o0000oooo ooooool0hoooool000gooooo0ol00005ooooo`03o`000?oooooooooo00oooooo0_l0000Aooooo`03 o`000?oooooooooo0>?ooooo000>ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool0 3oooool2o`00017ooooo00?o0000ooooooooool0hoooool000kooooo00?o0000ooooooooool01?oo ool00ol0003oooooooooo`0?ooooo`;o00004Oooool00ol0003oooooooooo`3Sooooo`003_ooool0 0ol0003oooooooooo`04ooooobKo0000iOooool000kooooo00?o0000ooooooooool01?ooool00ol0 003oooooooooo`0@ooooo`03o`000?oooooooooo0?Gooooo000=ooooo`;o00001_ooool00ol0003o ooooooooo`0?ooooo`03o`000?oooooooooo0?Kooooo000>ooooo`03o`000?oooooooooo00Cooooo 00?o0000ooooooooool03oooool00ol0003oooooooooo`3fooooo`005Oooool00ol0003ooooooooo o`0?ooooo`03o`000?oooooooooo0?Kooooo000Eooooo`03o`000?oooooooooo00oooooo00?o0000 ooooooooool0m_ooool001Gooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`3foooo o`005Oooool2o`00013ooooo00?o0000ooooooooool0m_ooool001Gooooo00?o0000ooooooooool0 3oooool00ol0003oooooooooo`3fooooo`005Oooool00ol0003oooooooooo`0>ooooo`03o`000?oo oooooooo0?Oooooo000Eooooo`03o`000?oooooooooo00kooooo00?o0000ooooooooool0moooool0 01Gooooo00?o0000ooooooooool03_ooool00ol0003oooooooooo`3gooooo`005Oooool00ol0003o ooooooooo`0>ooooo`03o`000?oooooooooo0?Oooooo000Eooooo`03o`000?oooooooooo00kooooo 00?o0000ooooooooool0moooool001Gooooo0_l0000?ooooo`03o`000?oooooooooo0?Oooooo000E ooooo`03o`000?oooooooooo00kooooo00?o0000ooooooooool0moooool001Gooooo00?o0000oooo ooooool03_ooool00ol0003oooooooooo`3gooooo`005Oooool00ol0003oooooooooo`0=ooooo`03 o`000?oooooooooo0?Sooooo000Eooooo`03o`000?oooooooooo00gooooo00?o0000ooooooooool0 n?ooool001Gooooo00?o0000ooooooooool03Oooool00ol0003oooooooooo`3hooooo`005Oooool0 0ol0003oooooooooo`0=ooooo`03o`000?oooooooooo0?Sooooo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-1.15634, -0.087587, \ 0.0540293, 0.00695397}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Closed]], Cell[BoxData[ \(<< Graphics`FilledPlot`\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FilledPlot", "[", RowBox[{\({fL[x], f[x], fR[x]}\), ",", \({x, leftEnd, howMany\ delta}\), "\n", StyleBox[",", FontColor->GrayLevel[0.500008]], StyleBox[\(AxesOrigin -> {leftEnd, 0}\), FontColor->GrayLevel[0.500008]], "\n", StyleBox["\t", FontColor->GrayLevel[0.500008]], StyleBox[",", FontColor->GrayLevel[0.500008]], StyleBox[\(PlotRange -> {0, 1}\), FontColor->GrayLevel[0.500008]], StyleBox["\n", FontColor->GrayLevel[0.500008]], StyleBox["\t", FontColor->GrayLevel[0.500008]], StyleBox[",", FontColor->GrayLevel[0.500008]], StyleBox[\(Fills\ -> \ {{{1, 2}, Hue[0]}, \n\ {{2, \ 3}, Hue[ .3]}}\), FontColor->GrayLevel[0.500008]], StyleBox["\n", FontColor->GrayLevel[0.500008]], StyleBox["\t", FontColor->GrayLevel[0.500008]], StyleBox[",", FontColor->GrayLevel[0.500008]], StyleBox[\(Curves\ -> \ Front\), FontColor->GrayLevel[0.500008]]}], "]"}]], "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 1 0 0.618034 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % Start of sub-graphic p 0 0 1 0.618034 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0680272 0 0.618034 [ [.15986 -0.0125 -3 -9 ] [.15986 -0.0125 3 0 ] [.29592 -0.0125 -3 -9 ] [.29592 -0.0125 3 0 ] [.43197 -0.0125 -3 -9 ] [.43197 -0.0125 3 0 ] [.56803 -0.0125 -3 -9 ] [.56803 -0.0125 3 0 ] [.70408 -0.0125 -6 -9 ] [.70408 -0.0125 6 0 ] [.84014 -0.0125 -6 -9 ] [.84014 -0.0125 6 0 ] [.97619 -0.0125 -6 -9 ] [.97619 -0.0125 6 0 ] [.01131 .12361 -18 -4.5 ] [.01131 .12361 0 4.5 ] [.01131 .24721 -18 -4.5 ] [.01131 .24721 0 4.5 ] [.01131 .37082 -18 -4.5 ] [.01131 .37082 0 4.5 ] [.01131 .49443 -18 -4.5 ] [.01131 .49443 0 4.5 ] [.01131 .61803 -6 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15986 0 m .15986 .00625 L s [(2)] .15986 -0.0125 0 1 Mshowa .29592 0 m .29592 .00625 L s [(4)] .29592 -0.0125 0 1 Mshowa .43197 0 m .43197 .00625 L s [(6)] .43197 -0.0125 0 1 Mshowa .56803 0 m .56803 .00625 L s [(8)] .56803 -0.0125 0 1 Mshowa .70408 0 m .70408 .00625 L s [(10)] .70408 -0.0125 0 1 Mshowa .84014 0 m .84014 .00625 L s [(12)] .84014 -0.0125 0 1 Mshowa .97619 0 m .97619 .00625 L s [(14)] .97619 -0.0125 0 1 Mshowa .125 Mabswid .05782 0 m .05782 .00375 L s .09184 0 m .09184 .00375 L s .12585 0 m .12585 .00375 L s .19388 0 m .19388 .00375 L s .22789 0 m .22789 .00375 L s .2619 0 m .2619 .00375 L s .32993 0 m .32993 .00375 L s .36395 0 m .36395 .00375 L s .39796 0 m .39796 .00375 L s .46599 0 m .46599 .00375 L s .5 0 m .5 .00375 L s .53401 0 m .53401 .00375 L s .60204 0 m .60204 .00375 L s .63605 0 m .63605 .00375 L s .67007 0 m .67007 .00375 L s .7381 0 m .7381 .00375 L s .77211 0 m .77211 .00375 L s .80612 0 m .80612 .00375 L s .87415 0 m .87415 .00375 L s .90816 0 m .90816 .00375 L s .94218 0 m .94218 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .12361 m .03006 .12361 L s [(0.2)] .01131 .12361 1 0 Mshowa .02381 .24721 m .03006 .24721 L s [(0.4)] .01131 .24721 1 0 Mshowa .02381 .37082 m .03006 .37082 L s [(0.6)] .01131 .37082 1 0 Mshowa .02381 .49443 m .03006 .49443 L s [(0.8)] .01131 .49443 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(1)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0309 m .02756 .0309 L s .02381 .0618 m .02756 .0618 L s .02381 .09271 m .02756 .09271 L s .02381 .15451 m .02756 .15451 L s .02381 .18541 m .02756 .18541 L s .02381 .21631 m .02756 .21631 L s .02381 .27812 m .02756 .27812 L s .02381 .30902 m .02756 .30902 L s .02381 .33992 m .02756 .33992 L s .02381 .40172 m .02756 .40172 L s .02381 .43262 m .02756 .43262 L s .02381 .46353 m .02756 .46353 L s .02381 .52533 m .02756 .52533 L s .02381 .55623 m .02756 .55623 L s .02381 .58713 m .02756 .58713 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 1 0 0 r .09184 .61803 m .09259 .61803 L .09396 .61803 L .10458 .61803 L .12341 .61803 L .13412 .61803 L .14415 .61803 L .15371 .61803 L .15646 .61803 L .15782 .61803 L .15908 .61803 L .16021 .30902 L .16143 .30902 L .16399 .30902 L .18502 .30902 L .20499 .30902 L .2155 .30902 L .22124 .30902 L .22404 .30902 L .22527 .30902 L .2266 .30902 L .22788 .30902 L .22907 .20601 L .2302 .20601 L .2314 .20601 L .23655 .20601 L .24747 .20601 L .26667 .20601 L .27604 .20601 L .28614 .20601 L .29078 .20601 L .29332 .20601 L .29455 .20601 L .29567 .20601 L .29671 .15451 L .29769 .15451 L .29985 .15451 L .30442 .15451 L .34288 .15451 L .35315 .15451 L .35817 .15451 L .36037 .15451 L .36153 .15451 L .36276 .15451 L .36405 .12361 L .36524 .12361 L .36759 .12361 L .37278 .12361 L .3838 .12361 L .40382 .12361 L .41434 .12361 L .42008 .12361 L .42544 .12361 L .42791 .12361 L .43025 .12361 L .43155 .12361 L .43228 .10301 L .43295 .10301 L .43541 .10301 L .44634 .10301 L .46556 .10301 L .48426 .10301 L .48938 .10301 L .49207 .10301 L .4949 .10301 L .49739 .10301 L .49807 .10301 L .4988 .10301 L .50011 .08829 L .50139 .08829 L .50261 .08829 L .50487 .08829 L .54339 .08829 L .55369 .08829 L .55872 .08829 L .56331 .08829 L .5645 .08829 L .56579 .08829 L .56702 .08829 L .56815 .07725 L .56934 .07725 L .57066 .07725 L .57334 .07725 L .58436 .07725 L .60531 .07725 L .61449 .07725 L .62453 .07725 L .62925 .07725 L .63183 .07725 L .63311 .07725 L .63428 .07725 L .63539 .07725 L .63656 .06867 L .63774 .06867 L .63903 .06867 L .64336 .06867 L .66319 .06867 L .68424 .06867 L .69423 .06867 L .69909 .06867 L .70121 .06867 L .70232 .06867 L .7035 .06867 L .70473 .0618 L .70587 .0618 L .7081 .0618 L .71301 .0618 L .72339 .0618 L .74229 .0618 L .75178 .0618 L .76194 .0618 L .76687 .0618 L .76929 .0618 L .77036 .0618 L .77154 .0618 L .77259 .05618 L .77357 .05618 L .77573 .05618 L .78028 .05618 L .81899 .05618 L .82938 .05618 L .83444 .05618 L .83665 .05618 L .83781 .05618 L .83904 .05618 L .84035 .0515 L .84155 .0515 L .84392 .0515 L .84913 .0515 L .86015 .0515 L .87996 .0515 L .89806 .0515 L .90283 .0515 L .90536 .0515 L .90674 .0515 L .90804 .0515 L .90928 .04754 L .90998 .04754 L .91062 .04754 L .91296 .04754 L .91752 .04754 L .93841 .04754 L .97619 .04754 L .97619 .04415 L .93911 .04593 L .89935 .04802 L .85807 .0504 L .81925 .05286 L .77891 .05568 L .74102 .05862 L .70162 .06203 L .6607 .06601 L .62223 .07026 L .58225 .07529 L .54075 .08133 L .50171 .08798 L .46115 .09613 L .42304 .10531 L .38341 .11692 L .34227 .13202 L .30359 .15027 L .26338 .17549 L .22563 .20832 L .20462 .23252 L .18485 .26107 L .16409 .29971 L .145 .34691 L .12409 .41926 L .11478 .46214 L .10458 .52053 L .09312 .60657 L .09184 .61977 L F .2 1 0 r .02381 1.05949e+06 m .02499 35.7618 L .02605 18.7254 L .02729 12.0818 L .02846 9.04737 L .02954 7.34204 L .03053 6.25377 L .03163 5.37869 L .03279 4.68389 L .03395 4.14633 L .0352 3.69069 L .03746 3.07904 L .03884 2.79649 L .04016 2.57213 L .04262 2.23541 L .045 1.98437 L .04753 1.7722 L .0521 1.48627 L .05489 1.35265 L .05752 1.24703 L .06244 1.08821 L .06757 .96074 L .07299 .85494 L .08269 .7141 L .09312 .60657 L .10458 .52053 L .11478 .46214 L .12409 .41926 L .145 .34691 L .16409 .29971 L .18485 .26107 L .20462 .23252 L .22563 .20832 L .26338 .17549 L .30359 .15027 L .34227 .13202 L .38341 .11692 L .42304 .10531 L .46115 .09613 L .50171 .08798 L .54075 .08133 L .58225 .07529 L .62223 .07026 L .6607 .06601 L .70162 .06203 L .74102 .05862 L .77891 .05568 L .81925 .05286 L .85807 .0504 L .89935 .04802 L .93911 .04593 L .97619 .04415 L .97619 .04415 L .94348 .04415 L .92329 .04415 L .91301 .04415 L .91019 .04415 L .9095 .04415 L .90875 .04415 L .90792 .04754 L .90716 .04754 L .90582 .04754 L .9044 .04754 L .90182 .04754 L .89138 .04754 L .88147 .04754 L .86262 .04754 L .84344 .04754 L .84092 .04754 L .84023 .04754 L .83949 .0515 L .83817 .0515 L .83675 .0515 L .83525 .0515 L .83253 .0515 L .82262 .0515 L .81152 .0515 L .80103 .0515 L .7811 .0515 L .77642 .0515 L .77404 .0515 L .77334 .0515 L .77268 .0515 L .77144 .05618 L .77031 .05618 L .76911 .05618 L .76689 .05618 L .76268 .05618 L .75241 .05618 L .74275 .05618 L .72377 .05618 L .71329 .05618 L .70831 .05618 L .70588 .05618 L .70477 .05618 L .7036 .0618 L .70249 .0618 L .70126 .0618 L .69876 .0618 L .69434 .0618 L .68427 .0618 L .66294 .0618 L .64398 .0618 L .63897 .0618 L .63759 .0618 L .63683 .0618 L .63613 .0618 L .63549 .06867 L .63479 .06867 L .63354 .06867 L .63115 .06867 L .62859 .06867 L .62392 .06867 L .60462 .06867 L .58339 .06867 L .5743 .06867 L .57165 .06867 L .57034 .06867 L .56914 .06867 L .56798 .07725 L .56672 .07725 L .56447 .07725 L .56188 .07725 L .55911 .07725 L .55407 .07725 L .54452 .07725 L .52525 .07725 L .50413 .07725 L .5016 .07725 L .50084 .07725 L .50015 .07725 L .49947 .08829 L .49882 .08829 L .49813 .08829 L .49739 .08829 L .49587 .08829 L .4931 .08829 L .48301 .08829 L .46293 .08829 L .44386 .08829 L .4341 .08829 L .43338 .08829 L .4327 .08829 L .43143 .10301 L .4307 .10301 L .42993 .10301 L .42853 .10301 L .42339 .10301 L .418 .10301 L .41229 .10301 L .40192 .10301 L .38234 .10301 L .37236 .10301 L .36667 .10301 L .36527 .10301 L .36398 .10301 L .36275 .12361 L .36145 .12361 L .35928 .12361 L .35689 .12361 L .35198 .12361 L .342 .12361 L .30411 .12361 L .2988 .12361 L .2974 .12361 L .29608 .12361 L .29533 .15451 L .29452 .15451 L .29309 .15451 L .29056 .15451 L .28788 .15451 L .28301 .15451 L .26297 .15451 L .24206 .15451 L .23257 .15451 L .23004 .15451 L .22885 .15451 L .22775 .20601 L .22645 .20601 L .22507 .20601 L .22255 .20601 L .21311 .20601 L .20444 .20601 L .18458 .20601 L .16449 .20601 L .16197 .20601 L .16078 .20601 L .15965 .30902 L .15841 .30902 L .15706 .30902 L .15431 .30902 L .14866 .30902 L .14335 .30902 L .12312 .30902 L .10458 .30902 L .09396 .30902 L .0933 .30902 L .0926 .30902 L .09183 .61803 L .09113 .61803 L .08979 .61803 L .08852 .61803 L .08562 .61803 L .08255 .61803 L .07216 .61803 L .06244 .61803 L .04262 .61803 L .02381 .61803 L F 0 g .5 Mabswid .09184 .61803 m .09259 .61803 L .09396 .61803 L .10458 .61803 L .12341 .61803 L .13412 .61803 L .14415 .61803 L .15371 .61803 L .15646 .61803 L .15782 .61803 L .15908 .61803 L .16021 .30902 L .16143 .30902 L .16399 .30902 L .18502 .30902 L .20499 .30902 L .2155 .30902 L .22124 .30902 L .22404 .30902 L .22527 .30902 L .2266 .30902 L .22788 .30902 L .22907 .20601 L .2302 .20601 L .2314 .20601 L .23655 .20601 L .24747 .20601 L .26667 .20601 L .27604 .20601 L .28614 .20601 L .29078 .20601 L .29332 .20601 L .29455 .20601 L .29567 .20601 L .29671 .15451 L .29769 .15451 L .29985 .15451 L .30442 .15451 L .34288 .15451 L .35315 .15451 L .35817 .15451 L .36037 .15451 L .36153 .15451 L .36276 .15451 L .36405 .12361 L .36524 .12361 L .36759 .12361 L .37278 .12361 L .3838 .12361 L .40382 .12361 L Mistroke .41434 .12361 L .42008 .12361 L .42544 .12361 L .42791 .12361 L .43025 .12361 L .43155 .12361 L .43228 .10301 L .43295 .10301 L .43541 .10301 L .44634 .10301 L .46556 .10301 L .48426 .10301 L .48938 .10301 L .49207 .10301 L .4949 .10301 L .49739 .10301 L .49807 .10301 L .4988 .10301 L .50011 .08829 L .50139 .08829 L .50261 .08829 L .50487 .08829 L .54339 .08829 L .55369 .08829 L .55872 .08829 L .56331 .08829 L .5645 .08829 L .56579 .08829 L .56702 .08829 L .56815 .07725 L .56934 .07725 L .57066 .07725 L .57334 .07725 L .58436 .07725 L .60531 .07725 L .61449 .07725 L .62453 .07725 L .62925 .07725 L .63183 .07725 L .63311 .07725 L .63428 .07725 L .63539 .07725 L .63656 .06867 L .63774 .06867 L .63903 .06867 L .64336 .06867 L .66319 .06867 L .68424 .06867 L .69423 .06867 L .69909 .06867 L Mistroke .70121 .06867 L .70232 .06867 L .7035 .06867 L .70473 .0618 L .70587 .0618 L .7081 .0618 L .71301 .0618 L .72339 .0618 L .74229 .0618 L .75178 .0618 L .76194 .0618 L .76687 .0618 L .76929 .0618 L .77036 .0618 L .77154 .0618 L .77259 .05618 L .77357 .05618 L .77573 .05618 L .78028 .05618 L .81899 .05618 L .82938 .05618 L .83444 .05618 L .83665 .05618 L .83781 .05618 L .83904 .05618 L .84035 .0515 L .84155 .0515 L .84392 .0515 L .84913 .0515 L .86015 .0515 L .87996 .0515 L .89806 .0515 L .90283 .0515 L .90536 .0515 L .90674 .0515 L .90804 .0515 L .90928 .04754 L .90998 .04754 L .91062 .04754 L .91296 .04754 L .91752 .04754 L .93841 .04754 L .97619 .04754 L Mfstroke .09201 .61803 m .09312 .60657 L .10458 .52053 L .11478 .46214 L .12409 .41926 L .145 .34691 L .16409 .29971 L .18485 .26107 L .20462 .23252 L .22563 .20832 L .26338 .17549 L .30359 .15027 L .34227 .13202 L .38341 .11692 L .42304 .10531 L .46115 .09613 L .50171 .08798 L .54075 .08133 L .58225 .07529 L .62223 .07026 L .6607 .06601 L .70162 .06203 L .74102 .05862 L .77891 .05568 L .81925 .05286 L .85807 .0504 L .89935 .04802 L .93911 .04593 L .97619 .04415 L s .02381 .61803 m .04262 .61803 L .06244 .61803 L .07216 .61803 L .08255 .61803 L .08562 .61803 L .08852 .61803 L .08979 .61803 L .09113 .61803 L .09183 .61803 L .0926 .30902 L .0933 .30902 L .09396 .30902 L .10458 .30902 L .12312 .30902 L .14335 .30902 L .14866 .30902 L .15431 .30902 L .15706 .30902 L .15841 .30902 L .15965 .30902 L .16078 .20601 L .16197 .20601 L .16449 .20601 L .18458 .20601 L .20444 .20601 L .21311 .20601 L .22255 .20601 L .22507 .20601 L .22645 .20601 L .22775 .20601 L .22885 .15451 L .23004 .15451 L .23257 .15451 L .24206 .15451 L .26297 .15451 L .28301 .15451 L .28788 .15451 L .29056 .15451 L .29309 .15451 L .29452 .15451 L .29533 .15451 L .29608 .12361 L .2974 .12361 L .2988 .12361 L .30411 .12361 L .342 .12361 L .35198 .12361 L .35689 .12361 L .35928 .12361 L Mistroke .36145 .12361 L .36275 .12361 L .36398 .10301 L .36527 .10301 L .36667 .10301 L .37236 .10301 L .38234 .10301 L .40192 .10301 L .41229 .10301 L .418 .10301 L .42339 .10301 L .42853 .10301 L .42993 .10301 L .4307 .10301 L .43143 .10301 L .4327 .08829 L .43338 .08829 L .4341 .08829 L .44386 .08829 L .46293 .08829 L .48301 .08829 L .4931 .08829 L .49587 .08829 L .49739 .08829 L .49813 .08829 L .49882 .08829 L .49947 .08829 L .50015 .07725 L .50084 .07725 L .5016 .07725 L .50413 .07725 L .52525 .07725 L .54452 .07725 L .55407 .07725 L .55911 .07725 L .56188 .07725 L .56447 .07725 L .56672 .07725 L .56798 .07725 L .56914 .06867 L .57034 .06867 L .57165 .06867 L .5743 .06867 L .58339 .06867 L .60462 .06867 L .62392 .06867 L .62859 .06867 L .63115 .06867 L .63354 .06867 L .63479 .06867 L Mistroke .63549 .06867 L .63613 .0618 L .63683 .0618 L .63759 .0618 L .63897 .0618 L .64398 .0618 L .66294 .0618 L .68427 .0618 L .69434 .0618 L .69876 .0618 L .70126 .0618 L .70249 .0618 L .7036 .0618 L .70477 .05618 L .70588 .05618 L .70831 .05618 L .71329 .05618 L .72377 .05618 L .74275 .05618 L .75241 .05618 L .76268 .05618 L .76689 .05618 L .76911 .05618 L .77031 .05618 L .77144 .05618 L .77268 .0515 L .77334 .0515 L .77404 .0515 L .77642 .0515 L .7811 .0515 L .80103 .0515 L .81152 .0515 L .82262 .0515 L .83253 .0515 L .83525 .0515 L .83675 .0515 L .83817 .0515 L .83949 .0515 L .84023 .04754 L .84092 .04754 L .84344 .04754 L .86262 .04754 L .88147 .04754 L .89138 .04754 L .90182 .04754 L .9044 .04754 L .90582 .04754 L .90716 .04754 L .90792 .04754 L .90875 .04415 L Mistroke .9095 .04415 L .91019 .04415 L .91301 .04415 L .92329 .04415 L .94348 .04415 L .97619 .04415 L Mfstroke MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0 0 1 0.618034 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0680272 0 0.618034 [ [.15986 -0.0125 -3 -9 ] [.15986 -0.0125 3 0 ] [.29592 -0.0125 -3 -9 ] [.29592 -0.0125 3 0 ] [.43197 -0.0125 -3 -9 ] [.43197 -0.0125 3 0 ] [.56803 -0.0125 -3 -9 ] [.56803 -0.0125 3 0 ] [.70408 -0.0125 -6 -9 ] [.70408 -0.0125 6 0 ] [.84014 -0.0125 -6 -9 ] [.84014 -0.0125 6 0 ] [.97619 -0.0125 -6 -9 ] [.97619 -0.0125 6 0 ] [.01131 .12361 -18 -4.5 ] [.01131 .12361 0 4.5 ] [.01131 .24721 -18 -4.5 ] [.01131 .24721 0 4.5 ] [.01131 .37082 -18 -4.5 ] [.01131 .37082 0 4.5 ] [.01131 .49443 -18 -4.5 ] [.01131 .49443 0 4.5 ] [.01131 .61803 -6 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15986 0 m .15986 .00625 L s [(2)] .15986 -0.0125 0 1 Mshowa .29592 0 m .29592 .00625 L s [(4)] .29592 -0.0125 0 1 Mshowa .43197 0 m .43197 .00625 L s [(6)] .43197 -0.0125 0 1 Mshowa .56803 0 m .56803 .00625 L s [(8)] .56803 -0.0125 0 1 Mshowa .70408 0 m .70408 .00625 L s [(10)] .70408 -0.0125 0 1 Mshowa .84014 0 m .84014 .00625 L s [(12)] .84014 -0.0125 0 1 Mshowa .97619 0 m .97619 .00625 L s [(14)] .97619 -0.0125 0 1 Mshowa .125 Mabswid .05782 0 m .05782 .00375 L s .09184 0 m .09184 .00375 L s .12585 0 m .12585 .00375 L s .19388 0 m .19388 .00375 L s .22789 0 m .22789 .00375 L s .2619 0 m .2619 .00375 L s .32993 0 m .32993 .00375 L s .36395 0 m .36395 .00375 L s .39796 0 m .39796 .00375 L s .46599 0 m .46599 .00375 L s .5 0 m .5 .00375 L s .53401 0 m .53401 .00375 L s .60204 0 m .60204 .00375 L s .63605 0 m .63605 .00375 L s .67007 0 m .67007 .00375 L s .7381 0 m .7381 .00375 L s .77211 0 m .77211 .00375 L s .80612 0 m .80612 .00375 L s .87415 0 m .87415 .00375 L s .90816 0 m .90816 .00375 L s .94218 0 m .94218 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .12361 m .03006 .12361 L s [(0.2)] .01131 .12361 1 0 Mshowa .02381 .24721 m .03006 .24721 L s [(0.4)] .01131 .24721 1 0 Mshowa .02381 .37082 m .03006 .37082 L s [(0.6)] .01131 .37082 1 0 Mshowa .02381 .49443 m .03006 .49443 L s [(0.8)] .01131 .49443 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(1)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0309 m .02756 .0309 L s .02381 .0618 m .02756 .0618 L s .02381 .09271 m .02756 .09271 L s .02381 .15451 m .02756 .15451 L s .02381 .18541 m .02756 .18541 L s .02381 .21631 m .02756 .21631 L s .02381 .27812 m .02756 .27812 L s .02381 .30902 m .02756 .30902 L s .02381 .33992 m .02756 .33992 L s .02381 .40172 m .02756 .40172 L s .02381 .43262 m .02756 .43262 L s .02381 .46353 m .02756 .46353 L s .02381 .52533 m .02756 .52533 L s .02381 .55623 m .02756 .55623 L s .02381 .58713 m .02756 .58713 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 MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooool5o`00027ooooo0ol0000Oooooo`?o00008?ooool3o`0001gooooo0ol00004oooo o`;o00006oooool3o`0000;ooooo1Ol0000Iooooo`?o00001?ooool3o`0000Wooooo000looooo`04 o`000?ooooooooooo`0002;ooooo00?o0000ooooooooool07Oooool01Ol0003ooooooooooooooooo 000001kooooo00Go0000ooooooooooooooooo`00000Mooooo`03o`000?oooooooooo00;ooooo00Co 0000oooooooooooo00006oooool00ol0003oooooooooo`02ooooo`04o`000?ooooooooooo`0001[o oooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`08ooooo`00?Oooool00ol0003ooooo ooooo`0Oooooo`Go00007_ooool01Ol0003ooooooooooooooooo000001kooooo00Go0000oooooooo ooooooooo`00000Mooooo`03o`000?oooooooooo00;ooooo00Co0000oooooooooooo00006oooool0 0ol0003oooooooooo`03ooooo`03o`000?oooooooooo01[ooooo00Co0000oooooooooooooooo1Ol0 0009ooooo`00?_ooool00ol0003oooooooooo`0Nooooo`04o`000?ooooooooooo`0001oooooo1?l0 000Pooooo`?o00007_ooool00ol0003oooooooooo`02ooooo`04o`000?ooooooooooo`0001_ooooo 00?o0000ooooooooool01?ooool00ol0003oooooooooo`0Iooooo`05o`000?ooooooooooooooool0 00000_ooool00ol0003oooooooooo`08ooooo`00>oooool01Ol0003ooooooooooooooooo0000023o oooo00?o0000ooooool000007oooool00ol0003oooooooooo`0Pooooo`05o`000?oooooooooooooo ool000007Oooool00ol0003oooooooooo`02ooooo`04o`000?ooooooooooo`0001_ooooo00Go0000 ooooooooooooooooo`000003ooooo`03o`000?oooooooooo01Sooooo00?o0000ooooooooool00_oo ool00ol0003oooooo`00000:ooooo`00>oooool01Ol0003ooooooooooooooooo0000027ooooo0_l0 000Pooooo`03o`000?oooooooooo01oooooo00Go0000ooooooooooooooooo`00000Looooo`;o0000 1?ooool01?l0003oooooooooool0000Jooooo`;o00000oooool01Ol0003ooooooooooooooooo0000 01Wooooo0_l00005ooooo`;o00002_ooool003cooooo0ol0000Sooooo`03o`000?oooooooooo01oo oooo0_l0000Pooooo`?o00007_ooool00ol0003oooooooooo`03ooooo`;o00007?ooool00ol0003o ooooooooo`02ooooo`?o00006oooool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo00So oooo003oooooob7ooooo003oooooob7ooooo003oooooob7ooooo003oooooob7ooooo000Eoooooooo 00001Ol00007ooooo`006oooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo00Kooooo 00?o0000ooooooooool01_ooool00ol0003oooooooooo`05ooooo`03o`000?oooooooooo00Kooooo 00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo00Kooooo 00?o0000ooooooooool01Oooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo00Kooooo 00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo00Kooooo 00?o0000ooooooooool01Oooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo00Kooooo 00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo00Gooooo 00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo00Kooooo 00?o0000ooooooooool01_ooool00ol0003oooooooooo`05ooooo`03o`000?oooooooooo00Kooooo 00?o0000ooooooooool01_ooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo00_ooooo 000Kooooo`03o`000?oooooooooo0?oooooo0oooool001_ooooo00?o0000ooooooooool0ooooool3 ooooo`006oooool00ol0003oooooooooo`3oooooo`?ooooo000Kooooo`03o`000?oooooooooo0?oo oooo0oooool001_ooooo00?o0000ooooooooool0ooooool3ooooo`006oooool00ol0003ooooooooo o`3oooooo`?ooooo000Kooooo`;o0000ooooool4ooooo`006oooool00ol0003oooooooooo`3ooooo o`?ooooo000Kooooo`03o`000?oooooooooo0?oooooo0oooool001_ooooo00?o0000ooooooooool0 h_oooolCo`0000gooooo000Kooooo`03o`000?oooooooooo0=7ooooo9?l0000=ooooo`006oooool0 0ol0003oooooooooo`2oooooobCo00007oooool001_ooooo00?o0000ooooooooool0[_oooolSo`00 037ooooo000Kooooo`03o`000?oooooooooo0:kooooo00Co0000oc?o0?lco`3ooc?o0003o`000?oooooooooo0=oooooo000Kooooo`03o`000?oooooooooo 00oooooo00?o0000oc?o0?lco`003Olco`02o`000>7ooooo000Kooooo`03o`000?oooooooooo00oo oooo00?o0000oc?o0?lco`003Olco`02o`000>7ooooo000Kooooo`03o`000?oooooooooo00oooooo 00?o0000oc?o0?lco`003?lco`000ol0003oo`00o`00003Qooooo`006oooool00ol0003ooooooooo o`0?ooooo`03o`000?lco`3o7ooooo000Koooo o`03o`000?oooooooooo00oooooo00?o0000oc?o0?lco`002olco`001?l0003oo`00ool00?l0003Q ooooo`006oooool2o`00013ooooo00?o0000oc?o0?lco`002olco`001?l0003oo`00ool00?l0003Q ooooo`006oooool00ol0003oooooooooo`0?ooooo`03o`000?lco`3o