{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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Tim es" 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 "Bullet Item" 0 15 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 3 3 0 0 0 0 0 0 15 2 }} {SECT 0 {EXCHG {PARA 15 "" 0 "" {TEXT -1 15 "Line Equations:" }}{PARA 0 "" 0 "" {TEXT -1 76 "You should try the exercises on 'line equations ' that are listed on the web." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot(3*x-2, x=-5..5, y=-10..10);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot(-2*x^2+1, x=-5..5);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(abs(x), x=-5..5);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 257 4 "Note" }{TEXT -1 40 ": You should r emember the graph of y = " }{XPPEDIT 18 0 "abs(x);" "6#-%$absG6#%\"xG " }{TEXT -1 2 ". " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot( \{abs(x), abs(x+1), abs(x)-2\}, " }{TEXT -1 0 "" }{MPLTEXT 1 0 29 "x=- 5..5,y=-2..2,thickness=3);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 4 "Note" }{TEXT -1 55 ". For the graphs above, do you know w hich one is which?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "with( plots): implicitplot(x^2+y^2 =1, x =-2..2, y=-2..2,\n scaling=cons trained); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "animate(x^2+a , x=-5..5, a=-3..3, color=red);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 4 "Note" }{TEXT -1 83 ". Do you see that the animation above is go ing from bottom to top? Do you know why?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "with(plots):\nanimate((x^3+a), x=-5..5, a=-30..30, co lor=black, thickness=3);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "animate((x+a)^2, x=-20..20, a=-3..3, color=black);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "plot(\{ sqrt(x-2),2*sqrt(x-2),(1/2)*sqrt(x-2)\},x=0..4,y=0..4,thickness=3); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:=x->(x+2)^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "g:=x->2*(x+2)^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "h:=x->(1/2)*(x+2)^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(\{f,g,h\},-4..2,-8..8, thickness=3);\n" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Do you know which one is which? Co mpare f(0), g(0) and h(0)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f(0); g(0); h(0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f: =x->-(x-2)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "g:=x->-2*( x-2)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "h:=x->(-1/2)*(x- 2)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "plot(\{f,g,h\},0.. 4,-10..4, thickness=3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " f(3);g(3);h(3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f:=x->sin(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "g:=x->f(2*x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(f(x),x=0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(g(x),x=0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(\{f(x),g(x)\},x=0..2*Pi,thickness=2);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{MARK "0 1 0" 76 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }