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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 14 "Tangent Planes" }}{PARA 
19 "" 0 "" {TEXT -1 16 "Warren Weckesser" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 59 "The Maple worksheet shows a few ex
amples of tangent planes." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name cha
ngecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 13 "f := x^4+y^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*$)%
\"xG\"\"%\"\"\"F**$)%\"yG\"\"#F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "plot3d(f,x=0..2,y=0..4,axes=boxed);" }}{PARA 13 "" 1 
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0 "" 0 "" {TEXT -1 20 "Now zoom in a bit..." }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 84 "p1 := plot3d(f,x=0.75..1.25,y=1.75..2.25,axes=boxe
d,title=\"Tangent Plane at (1,2)\"):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "p2 := plot3d(L,x=0.75..1.25,y=1.75..2.25,color=green)
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AAAAC401C000000000002-%&COLORG6&%$RGBG$\"\"!F=$\"*++++\"!\")F<-%*AXESS
TYLEG6#%$BOXG-%+AXESLABELSG6&%\"xG%\"yGQ!F4-%%FONTG6#%(DEFAULTG-%&TITL
EG6#Q7Tangent~Plane~at~(1,2)F4" 1 2 0 1 10 0 2 1 1 2 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 18 "Another example..." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "g := x*exp(y)+x^2*y+1;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"gG,(*&%\"xG\"\"\"-%$expG6#%\"yGF(F(*&)F'\"\"#F(F,F(F(F(F(" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "K := mtaylor(g,\{x=1,y=0\}
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\"yGF'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "p1 := plot3
d(g,x=0..2,y=-1..1,axes=boxed):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 54 "p2 := plot3d(K,x=0..2,y=-1..1,axes=boxed,color=green):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "display(\{p1,p2\});" }}
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