{VERSION 4 0 "IBM INTEL NT" "4.0" } {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 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{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 "Heading 1 " -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 " Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 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 P lot" -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 {SECT 0 {PARA 3 "" 0 "" {TEXT -1 44 "Piecewise defined functio ns and their graphs" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with( plots):" }{TEXT -1 54 " This package is needed for the display command below." }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "wi th(plottools):" }{TEXT -1 63 " This package is needed for the disk and circle commands below." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 " f:=x->piecewise(x<=0,0, x>0 and x<=1, x^2, x>1 and x<=2, 3-x, x>2,1+2* (x-2)); \n" }{TEXT -1 40 "Define a function in a piecewise manner." }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowG F(-%*piecewiseG6*19$\"\"!F132F1F01F0\"\"\"*$)F0\"\"#F532F5F01F0F8,&\" \"$F5F0!\"\"2F8F0,&!\"$F5*&F8F5F0F5F5F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }{TEXT -1 85 " This is how to see the formul a for f. Maple has a strange way of listing the cases!" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%*PIECEWISEG6&7$\"\"!1%\"xGF'7$*$)F)\"\"#\"\"\" 32,$F)!\"\"F'1,&F)F.F.F2F'7$,&\"\"$F.F)F232F1F21,&F)F.F-F2F'7$,&!\"$F. *&F-F.F)F.F.2F-F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "r:=0.03 ; " }{TEXT -1 98 "Radius for open and closed circles in the plot. Thi s needs to be chosen case by case, and if the " }{TEXT 258 2 "x " } {TEXT -1 4 "and " }{TEXT 259 1 "y" }{TEXT -1 62 " axes have different \+ scales, the circles will become ellipses!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG$\"\"$!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "p1:=plot(f,-2..3,discont=true,color=black,thickness=3):" } {TEXT -1 37 "Note that you do not need the letter " }{TEXT 257 1 "x" } {TEXT -1 6 " here." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "p2:=d isk([1,1],r,color=white,thickness=2):" }{TEXT -1 66 " A white disk. 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