{VERSION 5 0 "IBM INTEL NT" "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 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 " Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } } {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 104 " Define your parametric c urves x(t), y(t) as described in the text, then piece them together as follows;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 78 "xt:=t->piecewise(t<0, 0, t>0 and t<2,t+t^2+1,t>2 an d t<3, -t+t^2+t^3,t>3, 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#xtGf *6#%\"tG6\"6$%)operatorG%&arrowGF(-%*piecewiseG6*29$\"\"!F132F1F02F0\" \"#,(F0\"\"\"*$)F0F5F7F7F7F732F5F02F0\"\"$,(F0!\"\"F8F7*$)F0F=F7F72F=F 0F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "yt:=t->piecewi se(t<0, 0,t>0 and t<2,8*t^2-5*t^3, t>2 and t<3,7 - t ,t>3,0) ;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ytGf*6#%\"tG6\"6$%)operatorG%&arrow GF(-%*piecewiseG6*29$\"\"!F132F1F02F0\"\"#,&*&\"\")\"\"\")F0F5F9F9*&\" \"&F9)F0\"\"$F9!\"\"32F5F02F0F>,&\"\"(F9F0F?2F>F0F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot([xt(t),yt(t),t=0..3]);\n" }} {PARA 13 "" 1 "" {GLPLOT2D 488 488 488 {PLOTDATA 2 "6%-%'CURVESG6$7ap7 $$\"\"!F)F(7$$\"3zb1qpO5/5!#<$\"3Sp(4BE]GL\"!#@7$$\"3DB,*fuS#35F-$\"3c Bqh))yu<`F07$$\"3S-%o)G7T75F-$\"3#y'))z88U$>\"!#?7$$\"3,$\\N$=^h;5F-$ \"3Kl\"\\piwh6#F;7$$\"3[4h.4UZwL5F-$ \"3'>^:)ziKx$)F;7$$\"3UP%p7()[90\"F-$\"3!4ti;'yBl=!#>7$$\"3%)))y'e]n'p 5F-$\"3i%GT&Hj-\"G$FP7$$\"3duQlfdk-6F-$\"3-Zact+cJmFP7$$\"3U!z&>MECP6F -$\"3%>?&[u`\"\\5\"!#=7$$\"3yN7I/G(4A\"F-$\"3[/lf9yo_CFjn7$$\"3*)p\"=( )4GNJ\"F-$\"3RXRT(p](RUFjn7$$\"3ddY.f=)QT\"F-$\"3e:(e****HxO'Fjn7$$\"3 CaczH[E9:F-$\"3wO6(HpUIe)Fjn7$$\"3xP&p^9]ci\"F-$\"3'>XP,Lw`5\"F-7$$\"3 9*y\"o\">7)[F-7$$\"3%p$=Irzfb@F-$\"3s0uN.\\(*[@F- 7$$\"3z%eI]#G@8BF-$\"3Q')fc&RS;R#F-7$$\"3g2jx>-!*zCF-$\"3o)pxXlsyg#F-7 $$\"3#\\bwCrA&[EF-$\"39HY&zSlDy#F-7$$\"3\\C7w-4W3GF-$\"3hyG!37$H1HF-7$ $\"3,2q)z#[e1HF-$\"3A-0TvavhHF-7$$\"3*R>pcF9q+$F-$\"3G(yc:+)H-IF-7$$\" 3'>s)*4MzQ4$F-$\"3W^$3'H$4T-$F-7$$\"3U_ffoXQ#=$F-$\"3I%oZC]xO.$F-7$$\" 3IB#3x!3S(G$F-$\"3TR^U(zo%GIF-7$$\"3s&)>\\'QOYR$F-$\"3NbCDH8j/IF-7$$\" 3#4n6Ru49\\$F-$\"3#\\'R&4W)4nHF-7$$\"3wVCK4?#**e$F-$\"36.XNZ9L8HF-7$$ \"3N6H\\[M=7QF-$\"3n<-!*=eoMFF-7$$\"3'4()z0Y6;.%F-$\"3_\\#f;@T5[#F-7$$ \"3GDSnm]loUF-$\"382ez,v!=7#F-7$$\"3O83)[F:O\\%F-$\"3'4km\"p%4,q\"F-7$ $\"3O!4ww6zSu%F-$\"3P6Mu\"F-7$$\" 3M'=(yN62jcF-$!3*)QbRBD,<&)HF#F-7$$\"3i s\\A<[\")[fF-$!3!p*p%)4FH`GF-7$$\"3mYR!3F/J4'F-$!3eJi4dc`qMF-7$$\"3lcz 0f;fMiF-$!303%e!>Oy.TF-7$$\"3!G`#emz#zP'F-$!3E%eZ;mBLx%F-7$$\"3&Qj&ybY CRlF-$!3MBG;#3x-c&F-7$$\"3rey5^2%Gq'F-$!3i%\\u#yj;%R'F-7$$\"37oa(f,#3x nF-$!3!=[9(zoR%y'F-7$$\"3'Hj6)oLy^oF-$!3SdLAP)QW=(F-7$$\"3YDz@ylI*)oF- $!3o#)[`A=<)Q(F-7$$\"3&fN;'4[%p#pF-$!3yV6]CpR%f(F-7$$\"3[BEceq!e%pF-$! 3#R?Y!3\"[%)p(F-7$$\"3=Ep+j!)pkpF-$!3qTYLFs7.yF-7$$\"3GR3a[V:upF-$!3)4 n%)Rx-d&yF-7$$\"39j#\\H#yh$)pF-$!3f3I*y\"fV3zF-7$$\"39&>Ki[)3$*pF-$!3E n/]joKhzF-7$$\"3cii)o+q2+\"!#;$\"3?+++&y'[**\\F-7$$\"3MZ%G4#Q6]5Fd]l$ \"3I++DO$)4n\\F-7$$\"3@UWwfp%45\"Fd]l$\"3R++]())4Z$\\F-7$$\"3/0xSoI$p> \"Fd]l$\"39+]i!R7g([F-7$$\"3W5y8o\")o28Fd]l$\"3$)****\\A0%=\"[F-7$$\"3 kHA9ehe<9Fd]l$\"3?+]i&zf9v%F-7$$\"35K^%Rm+&Q:Fd]l$\"3]**\\7QXM)o%F-7$$ \"3u`VR*RFGm\"Fd]l$\"3d++]PyjEYF-7$$\"3))4AcISh*z\"Fd]l$\"39+]iSm.iXF- 7$$\"3C4HSbS\"z$>Fd]l$\"3E+++5!=)*\\%F-7$$\"3#zqa0c`h3#Fd]l$\"3(****\\ PZ!>OWF-7$$\"3<4()3k`6SAFd]l$\"3#)**\\i0)*3tVF-7$$\"3W'Ry1l@yQ#Fd]l$\" 3')*****\\%o5:VF-7$$\"3An#z?_/Yc#Fd]l$\"3#****\\(G=l[UF-7$$\"3HTMn\\1k HFFd]l$\"3++++qO@*=%F-7$$\"3z3jQ^y%H\"HFd]l$\"3$***\\i&>Se7%F-7$$\"3`y OcwrR.IFd]l$\"39+++X>^&4%F-7$$\"3#G8@gRLc4$Fd]l$\"3]**\\P%p$=lSF-7$$\" 3;bcQju$f9$Fd]l$\"31]7yqx))[SF-7$$\"3/*=/b&[w'>$Fd]l$\"3v*\\(=Z=fKSF-7 $$\"3w-Av4cPAKFd]l$\"3fC1R&)QWCSF-7$$\"3y5f()o\"=\"[KFd]l$\"3K]PfBfH;S F-7$$\"3#***=pw*Q5E$Fd]l$\"3H7`pU>A7SF-7$$\"3K5xVdG*RF$Fd]l$\"3;vozhz9 3SF-7$$\"3e=v$G@#[!G$Fd]l$\"3:cwMr461SF-7$$\"3)Rk$o^)zpG$Fd]l$\"3-Q%)* 3)R2/SF-7$$\"3'\\PZ!zd[$H$Fd]l$\"3,>#\\/*p.-SF-F'-%'COLOURG6&%$RGBG$\" #5!\"\"F(F(-%+AXESLABELSG6$Q!6\"Fcfl-%%VIEWG6$%(DEFAULTGFhfl" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 148 " Make sure your curves join together sm oothly!! (not like the one here). You can check by zooming in to the p oints where they join (plot the curve " }}{PARA 0 "" 0 "" {TEXT -1 83 "only for t values around where they join; in the example here these t imes are t=2)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "4 1 0" 83 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }