{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 "" -1 256 "" 1 24 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "T imes" 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 Plot" -1 256 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 "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT 256 14 "Tangent Planes" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 0 "" }{TEXT 259 10 "Example 1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "z:=(x,y,z)->3*x*y-x^3-y^3;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "G:=plot3d(z(x,y,z),x=-3..3,y =-3..3,axes=framed):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "w:= (x,y,z)->3*x*y-x^3-y^3-z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "implicitplot3d(w(x,y,z)=0,x=-3..3,y=-3..3,z=-10..10,axes=framed,nu mpoints=5000,labels=[x,y,z]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "p:=(x,y,z)->z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "P:= implicitplot3d(p(x,y,z)=0,x=-1..1,y=-1..1,z=0..1,color=blue):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "S:=implicitplot3d(w(x,y,z)=0 ,x=-3..3,y=-3..3,z=-10..10,axes=framed,numpoints=5000,labels=[x,y,z]): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "display3d([S,P],axes=fr amed,labels=[x,y,z]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "P2 :=implicitplot3d(p(x,y,z)=1,x=0..2,y=0..2,z=0..1,color=red):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "display3d([S,P2],orientation =[9,63]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "n1:=arrow([1,1 ,1],[0,0,6], color=blue,width=.03): \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "display3d([S,P2,n1],orientation=[-60,72]);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 257 10 "Example 2:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 38 "w2:=(x,y,z)->-x*y*exp(-(x^2+y^2)/2)-z;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "implicitplot3d(w2(x,y,z)=0, x=-4..4,y=-4..4,z=-.4..0.4,axes=framed,numpoints=7000,orientation=[73, 57]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "S2:=implicitplot3 d(w2(x,y,z)=0,x=-4..4,y=-4..4,z=-.4..0.4,axes=framed,numpoints=7000,or ientation=[73,57]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "P3:= implicitplot3d(p(x,y,z)=-exp(-1),x=0..2,y=0..2,z=-.4..0.4,color=yellow ):" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "P4:=im plicitplot3d(p(x,y,z)=-exp(-1),x=-2..0,y=-2..0,z=-.4..0.4,color=blue): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "P5:=implicitplot3d(p(x, y,z)=exp(-1),x=0..2,y=-2..0,z=-.4..0.4,color=green):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "P6:=implicitplot3d(p(x,y,z)=exp(-1),x=-2. .0,y=0..2,z=-.4..0.4,color=red):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "display3d([S2,P3,P4,P5,P6]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "26" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }