{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 " " 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Diagnostic" 7 9 1 {CSTYLE "" -1 -1 "" 0 1 64 128 64 1 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output " 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 454 "R:=`R`:\nxphug :=[ diff(theta(t),t) = piec ewise(y(t)>0, (v(t)^2 - cos(theta(t)))/v(t), 0),\n diff(v(t), t) = piecewise(y(t)>0, -sin(theta(t)) - R*v(t)^2 , 0),\n \+ diff(x(t),t) = piecewise(y(t)>0, v(t)*cos(theta(t)), \+ 0),\n diff(y(t),t) = piecewise(y(t)>0, v(t)*sin(theta (t)), 0),\n diff(T(t),t) = piecewise(y(t)>0, \+ 1, 0)];\nphug := [xphug[1], xphug[2]];" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&xphugG7'/-%%diffG6$-%&thetaG6#%\"t GF--%*PIECEWISEG6$7$*&,&*$)-%\"vGF,\"\"#\"\"\"F9-%$cosG6#F*!\"\"F9F6F= 2\"\"!-%\"yGF,7$F?%*otherwiseG/-F(6$F6F--F/6$7$,&-%$sinGFFB/-F(6$-%\"xGF,F--F/6$7$*&F6F9F:F9F>FB/-F(6$F@F--F/6$7$*&F6F9F KF9F>FB/-F(6$-%\"TGF,F--F/6$7$F9F>FB" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%%phugG7$/-%%diffG6$-%&thetaG6#%\"tGF--%*PIECEWISEG6$7$*&,&*$)-%\"v GF,\"\"#\"\"\"F9-%$cosG6#F*!\"\"F9F6F=2\"\"!-%\"yGF,7$F?%*otherwiseG/- F(6$F6F--F/6$7$,&-%$sinGFFB" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 27 "with(plots): with(DEtools):" }}{PARA 7 "" 1 " " {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "\nR:=0.2;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG$\"\"#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v0G$\"#:!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "sol :=dsolve( \{op(xphug), theta(0)=0, x(0)=0, y(0)=2, T(0)=0, v(0)=1.5\}, \n [theta(t), v(t), x(t), y(t), T(t)], numeric);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$solGf*6#%(rkf45_xG6.%\"iG%/comp_soln_dataG%(o deprocG%&icvecG%(LR_caseG%\"YG%$valG%)outpointG%#ptG%*stop_procG%+stop _arrayG%&cplexG6#%aoCopyright~(c)~2000~by~the~University~of~Waterloo.~ All~rights~reserved.GE\\s\"Q(complex6\"%&falseGC2@$-%'memberG6$9$7$Q4l eft_comp_soln_dataF9Q5right_comp_soln_dataF9O\"\"!@$2%'DigitsG-%&trunc G6#-%'evalhfG6#FH>FHFI>8+-%&evalfG6#F@@$4-%%typeG6$FQ.%(numericG@%-F>6 $FQ7%Q&startF9Q%leftF9Q&rightF9O$FEFEO-.9!FT>8&f*6&%\"NG%\"tG%\"YG%#YP GF96#%`o[Y[1]~=~theta(t),~Y[2]~=~v(t),~Y[3]~=~x(t),~Y[4]~=~y(t),~Y[5]~ =~T(t)]GF9C'>&9'6#\"\"\"-%*piecewiseG6%2F^o&9&6#\"\"%*&,&*$)&Fhp6#\"\" #FaqFbpFbp*&$FbpFEFbp-%$cosG6#&FhpFapFbp!\"\"FbpF_qFhqF^o>&F`pF`q-Fdp6 %Ffp,&-%$sinGFfq$FhqFE*&$FaqFhqFbpF^qFbpFhqF^o>&F`p6#\"\"$-Fdp6%Ffp*&F _qFbpFdqFbpF^o>&F`pFip-Fdp6%Ffp*&F_qFbpF^rFbpF^o>&F`p6#\"\"&-Fdp6%Ffp$ FbpFEF^oF9F9F9>8'=F96#;FbpFbsE\\[l&FbpF^oFaq$\"#:FhqFfrF^oFjp$FaqFEFbs F^o>8-FE>8.FE>8)-%$mapG6$%$rhsG-%&parseG6#-%#opG6$Ffr-%%evalG6#Fdo>8/- Fbo6#F8@'/FQF^oO7$/FhoFQ-%$seqG6$/&Fdt6#8$-FS6#&FgsF`v/Fav;Fbp-%%nopsG 6#Fdt1F^oFQ>8(FC>F\\wFB>8%-Fbo6#F\\w@%4-FX6$7#F_w7#.%%listGC%Z%>F_w-%; dsolve/numeric/SC/IVPsolveG6)Fdo;F^oFQFgsF`tFbtFcu/%'scprocGF:F9C&@$/F cu%%trueGYF9>FcuFfx>F_wF]x>FduFfx>8*&&F_wFer6#&F_wF`q>F`wF_wC$>F\\yF]y @$53/F\\wFC2F\\yFQ3/F\\wFB2FQF\\yC&@$5/&F_w6#\"\")Fbp2\"#5F`zC$>F\\yF] y@%FgyY6$QQcannot~evaluate~the~solution~further~right~of~%1F9-&FSFaz6# F\\yY6$QPcannot~evaluate~the~solution~further~left~of~%1F9F[[lZ%>F_w-% Fc uFfx>F_wFc[l>FduFfx>F`wF_w>F\\yF]y@&FgyC$@$33/%:_Env_smart_dsolve_nume ricGFfx2F^oF\\y2-Fbo6#F\\oF\\y>Fg\\lF\\y@$Fhy@)/&F`wFazFbpY6$Qcocannot ~evaluate~the~solution~further~right~of~%1,~probably~a~singularityF9F[ [l/F]]lFaqY6$Qcqcannot~evaluate~the~solution~further~right~of~%1,~maxf un~limit~exceeded~(see~?dsolve,maxfun~for~details)F9F[[l2FdzF]]lC$@$0% 7_Env_dsolve_nowarnstopGFfx-%(WARNINGG6#-_%,StringToolsG%.FormatMessag eG6%Qhocannot~evaluate~the~solution~further~right~of~%1,~stop~conditio n~#%2~violatedF9F[[l,&F]]lFbpFdzFhq>FQF\\yYFizFjyC$@$33Fc\\l2F\\yF^o2F \\y-Fbo6#F[o>F\\_lF\\y@$F[z@)F\\]lY6$Qbocannot~evaluate~the~solution~f urther~left~of~%1,~probably~a~singularityF9F[[lFa]lY6$Qbqcannot~evalua te~the~solution~further~left~of~%1,~maxfun~limit~exceeded~(see~?dsolve ,maxfun~for~details)F9F[[lFe]lC$@$Fh]l-F[^l6#-F^^l6%Qgocannot~evaluate ~the~solution~further~left~of~%1,~stop~condition~#%2~violatedF9F[[lFc^ l>FQF\\yYF_[l>F\\y-%9dsolve/numeric/SC/IVPvalG6$F_wFQ7$Fju-F\\v6$/F_v& F\\yF`vFevF9F9F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sol(20); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7(/%\"tG$\"#?\"\"!/-%&thetaG6#F%$! 3`l+uk6\"=0#!#=/-%\"vGF,$\"3Ge2WB^I-5!# \+ " 0 "" {MPLTEXT 1 0 127 "sol_5:=dsolve( \{op(xphug), theta(0)=0, x(0)= 0, y(0)=2, T(0)=0, v(0)=.5\}, \n [theta(t), v(t), x(t), y(t), T (t)], numeric);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sol_5Gf*6#%(rkf4 5_xG6.%\"iG%/comp_soln_dataG%(odeprocG%&icvecG%(LR_caseG%\"YG%$valG%)o utpointG%#ptG%*stop_procG%+stop_arrayG%&cplexG6#%aoCopyright~(c)~2000~ by~the~University~of~Waterloo.~All~rights~reserved.GE\\s\"Q(complex6\" %&falseGC2@$-%'memberG6$9$7$Q4left_comp_soln_dataF9Q5right_comp_soln_d ataF9O\"\"!@$2%'DigitsG-%&truncG6#-%'evalhfG6#FH>FHFI>8+-%&evalfG6#F@@ $4-%%typeG6$FQ.%(numericG@%-F>6$FQ7%Q&startF9Q%leftF9Q&rightF9O$FEFEO- .9!FT>8&f*6&%\"NG%\"tG%\"YG%#YPGF96#%`o[Y[1]~=~theta(t),~Y[2]~=~v(t),~ Y[3]~=~x(t),~Y[4]~=~y(t),~Y[5]~=~T(t)]GF9C'>&9'6#\"\"\"-%*piecewiseG6% 2F^o&9&6#\"\"%*&,&*$)&Fhp6#\"\"#FaqFbpFbp*&$FbpFEFbp-%$cosG6#&FhpFapFb p!\"\"FbpF_qFhqF^o>&F`pF`q-Fdp6%Ffp,&-%$sinGFfq$FhqFE*&$FaqFhqFbpF^qFb pFhqF^o>&F`p6#\"\"$-Fdp6%Ffp*&F_qFbpFdqFbpF^o>&F`pFip-Fdp6%Ffp*&F_qFbp F^rFbpF^o>&F`p6#\"\"&-Fdp6%Ffp$FbpFEF^oF9F9F9>8'=F96#;FbpFbsE\\[l&FbpF ^oFaq$FbsFhqFfrF^oFjp$FaqFEFbsF^o>8-FE>8.FE>8)-%$mapG6$%$rhsG-%&parseG 6#-%#opG6$Ffr-%%evalG6#Fdo>8/-Fbo6#F8@'/FQF^oO7$/FhoFQ-%$seqG6$/&Fct6# 8$-FS6#&FgsF_v/F`v;Fbp-%%nopsG6#Fct1F^oFQ>8(FC>F[wFB>8%-Fbo6#F[w@%4-FX 6$7#F^w7#.%%listGC%Z%>F^w-%;dsolve/numeric/SC/IVPsolveG6)Fdo;F^oFQFgsF _tFatFbu/%'scprocGF:F9C&@$/Fbu%%trueGYF9>FbuFex>F^wF\\x>FcuFex>8*&&F^w Fer6#&F^wF`q>F_wF^wC$>F[yF\\y@$53/F[wFC2F[yFQ3/F[wFB2FQF[yC&@$5/&F^w6# \"\")Fbp2\"#5F_zC$>F[yF\\y@%FfyY6$QQcannot~evaluate~the~solution~furth er~right~of~%1F9-&FSF`z6#F[yY6$QPcannot~evaluate~the~solution~further~ left~of~%1F9FjzZ%>F^w-%FbuFex>F^wFb[l>FcuFex>F_wF^w>F[yF\\y@&FfyC$@$33/% :_Env_smart_dsolve_numericGFex2F^oF[y2-Fbo6#F\\oF[y>Ff\\lF[y@$Fgy@)/&F _wF`zFbpY6$Qcocannot~evaluate~the~solution~further~right~of~%1,~probab ly~a~singularityF9Fjz/F\\]lFaqY6$Qcqcannot~evaluate~the~solution~furth er~right~of~%1,~maxfun~limit~exceeded~(see~?dsolve,maxfun~for~details) F9Fjz2FczF\\]lC$@$0%7_Env_dsolve_nowarnstopGFex-%(WARNINGG6#-_%,String ToolsG%.FormatMessageG6%Qhocannot~evaluate~the~solution~further~right~ of~%1,~stop~condition~#%2~violatedF9Fjz,&F\\]lFbpFczFhq>FQF[yYFhzFiyC$ @$33Fb\\l2F[yF^o2F[y-Fbo6#F[o>F[_lF[y@$Fjy@)F[]lY6$Qbocannot~evaluate~ the~solution~further~left~of~%1,~probably~a~singularityF9FjzF`]lY6$Qbq cannot~evaluate~the~solution~further~left~of~%1,~maxfun~limit~exceeded ~(see~?dsolve,maxfun~for~details)F9FjzFd]lC$@$Fg]l-Fj]l6#-F]^l6%Qgocan not~evaluate~the~solution~further~left~of~%1,~stop~condition~#%2~viola tedF9FjzFb^l>FQF[yYF^[l>F[y-%9dsolve/numeric/SC/IVPvalG6$F^wFQ7$Fiu-F[ v6$/F^v&F[yF_vFdvF9F9F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " sol_5(20);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7(/%\"tG$\"#?\"\"!/-%&th etaG6#F%$!3n!HJLJ>0P\"!#=/-%\"vGF,$\"3Pz2!G1#pl)*F//-%\"xGF,$\"3#y!3S8 ^6(\\(!# " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 177 "bise ct := proc(f, interval)\nxlo := interval[1];\nxhi := interval[2];\nmid := (xlo + xhi)/2;\n\nif ( f(mid) < 0 ) then\n xlo := mid;\nelse\n \+ xhi := mid;\nfi;\n\nreturn([xlo,xhi]);\nend;" }{TEXT -1 0 "" }}{PARA 7 "" 1 "" {TEXT -1 66 "Warning, `xlo` is implicitly declared local to \+ procedure `bisect`\n" }}{PARA 7 "" 1 "" {TEXT -1 66 "Warning, `xhi` is implicitly declared local to procedure `bisect`\n" }}{PARA 7 "" 1 "" {TEXT -1 66 "Warning, `mid` is implicitly declared local to procedure \+ `bisect`\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'bisectGf*6$%\"fG%)int ervalG6%%$xloG%$xhiG%$midG6\"F-C'>8$&9%6#\"\"\">8%&F26#\"\"#>8&,&F0#F4 F9*&F=F4F6F4F4@%2-9$6#F;\"\"!>F0F;>F6F;O7$F0F6F-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "bisect( x-> x^3, [-1, 3]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7$!\"\"\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "trace(bisect);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'b isectG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "bisect( x-> x^3, \+ [-1, 3]);" }}{PARA 9 "" 1 "" {TEXT -1 81 "\{--> enter bisect, args = p roc (x) options operator, arrow; x^3 end proc, [-1, 3]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xloG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% $xhiG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$midG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xhiG\"\"\"" }}{PARA 9 "" 1 "" {TEXT -1 45 "<-- exit bisect (now at top level) = [-1, 1]\}" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7$!\"\"\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "bisect( x-> x^3, [-1, 1]);" }}{PARA 9 "" 1 "" {TEXT -1 81 "\{- -> enter bisect, args = proc (x) options operator, arrow; x^3 end proc , [-1, 1]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xloG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xhiG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$midG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xhiG\"\"!" }} {PARA 9 "" 1 "" {TEXT -1 45 "<-- exit bisect (now at top level) = [-1, 0]\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$!\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 224 "bisect := proc(f, interval)\nxlo : = interval[1];\nxhi := interval[2];\nwhile( xhi - xlo > 0.001 ) do\n \+ mid := (xlo + xhi)/2;\n if ( f(mid) < 0 ) then\n xlo := mid;\n e lse\n xhi := mid;\n fi; \nod;\n\nreturn([xlo,xhi]);\nend;" }} {PARA 7 "" 1 "" {TEXT -1 66 "Warning, `xlo` is implicitly declared loc al to procedure `bisect`\n" }}{PARA 7 "" 1 "" {TEXT -1 66 "Warning, `x hi` is implicitly declared local to procedure `bisect`\n" }}{PARA 7 " " 1 "" {TEXT -1 66 "Warning, `mid` is implicitly declared local to pro cedure `bisect`\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'bisectGf*6$%\" fG%)intervalG6%%$xloG%$xhiG%$midG6\"F-C&>8$&9%6#\"\"\">8%&F26#\"\"#?(F -F4F4F-2$F4!\"$,&F6F4F0!\"\"C$>8&,&F0#F4F9*&FDF4F6F4F4@%2-9$6#FB\"\"!> F0FB>F6FBO7$F0F6F-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "b isect( x-> x^2 - 2, [1, 2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$#\"$ \"=\"$G\"#\"%\\9\"%C5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "tr ace(bisect);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'bisectG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "bisect( x-> x^2 - 2, [1, 2]);" }} {PARA 9 "" 1 "" {TEXT -1 82 "\{--> enter bisect, args = proc (x) optio ns operator, arrow; x^2-2 end proc, [1, 2]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xloG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xhi G\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$midG#\"\"$\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xhiG#\"\"$\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$midG#\"\"&\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %$xloG#\"\"&\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$midG#\"#6\"\") " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xloG#\"#6\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$midG#\"#B\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$xhiG#\"#B\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$midG#\"#X\"#K " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xloG#\"#X\"#K" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$midG#\"#\"*\"#k" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$xhiG#\"#\"*\"#k" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$midG#\"$\"= \"$G\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xloG#\"$\"=\"$G\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$midG#\"$j$\"$c#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$xhiG#\"$j$\"$c#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%$midG#\"$D(\"$7&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xhiG#\"$D(\" $7&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$midG#\"%\\9\"%C5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xhiG#\"%\\9\"%C5" }}{PARA 9 "" 1 "" {TEXT -1 58 "<-- exit bisect (now at top level) = [181/128, 1449/1024] \}" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$#\"$\"=\"$G\"#\"%\\9\"%C5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "untrace(bisect);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'bisectG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "bisect(x->x^2 - 2, [1.1, 2.2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+%)*3UT\"!\"*$\"+%4YZT\"F&" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 235 "bisect := proc(f, interval, epsilon)\nxlo := \+ interval[1];\nxhi := interval[2];\nwhile( xhi - xlo > epsilon ) do\n \+ mid := (xlo + xhi)/2;\n if ( f(mid) < 0 ) then\n xlo := mid;\n e lse\n xhi := mid;\n fi; \nod;\n\nreturn([xlo,xhi]);\nend;" }} {PARA 7 "" 1 "" {TEXT -1 66 "Warning, `xlo` is implicitly declared loc al to procedure `bisect`\n" }}{PARA 7 "" 1 "" {TEXT -1 66 "Warning, `x hi` is implicitly declared local to procedure `bisect`\n" }}{PARA 7 " " 1 "" {TEXT -1 66 "Warning, `mid` is implicitly declared local to pro cedure `bisect`\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'bisectGf*6%%\" fG%)intervalG%(epsilonG6%%$xloG%$xhiG%$midG6\"F.C&>8$&9%6#\"\"\">8%&F3 6#\"\"#?(F.F5F5F.29&,&F7F5F1!\"\"C$>8&,&F1#F5F:*&FDF5F7F5F5@%2-9$6#FB \"\"!>F1FB>F7FBO7$F1F7F.F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "bisect( x-> x^2 - 2, [1.1, 2.2], 0.0000001);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7$$\"+3N@99!\"*$\"+tN@99F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "22 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }