TangentPlanes

# TangentPlanes - .1.25,y=1.75....

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Tangent Planes Warren Weckesser The Maple worksheet shows a few examples of tangent planes. > with(plots): Warning, the name changecoords has been redefined > f := x^4+y^2; := f + x 4 y 2 > plot3d(f,x=0. .2,y=0. .4,axes=boxed); Use the Maple function "mtaylor" to find the equation of the tangent plane. .. > L := mtaylor(g,{x=1,y=2},2); := L - + + 7 4 x 4 y > p1 := plot3d(f,x=0. .2,y=0. .4,axes=boxed,title="Tangent Plane at (1,2)"): > p2 := plot3d(L,x=0. .2,y=0. .4,color=green): > display({p1,p2});

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Now zoom in a bit. .. > p1 := plot3d(f,x=0.75.

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Unformatted text preview: .1.25,y=1.75. .2.25,axes=boxed,title="Tangent Plane at (1,2)"): > p2 := plot3d(L,x=0.75. .1.25,y=1.75. .2.25,color=green): > display({p1,p2}); Another example. .. > g := x*exp(y)+x^2*y+1; := g + + x e y x 2 y 1 > K := mtaylor(g,{x=1,y=0},2); := K + + x 2 y 1 > p1 := plot3d(g,x=0. .2,y=-1. .1,axes=boxed): > p2 := plot3d(K,x=0. .2,y=-1. .1,axes=boxed,color=green): > display({p1,p2}); Note that the graph is saddle-like, so the tangent plane cuts the graph along two curves. >...
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## This note was uploaded on 02/11/2012 for the course MTH 141, 142, taught by Professor Mcallister during the Spring '08 term at SUNY Empire State.

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TangentPlanes - .1.25,y=1.75....

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