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200pj3 - in your estimate 2 Find a three dimensional unit...

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Math 200 Fall, 2006 Project #3 Instructions: Use your knowledge of Maple commands to obtain your solutions. Include explanations of how you obtain your answers, and illustrate your work with graphs whenever appropriate. Try to answer questions in a clear, direct, and e ffi cient way. 1. Consider the function f ( x, y ) = ln( x - 3 y ). (a) Find the equation of the tangent plane of f ( x, y ) at the point (7 , 2). (b) Make a Maple plot showing the graph of f ( x, y ) and the tangent plane at (7 , 2). (c) Use the linear approximation to estimate f (6 . 9 , 2 . 06). Compute the absolute error
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Unformatted text preview: in your estimate. 2. Find a three dimensional unit vector that is normal to the graph of z = x 2-y 2 + cos(sin( x )) at the point ( π, 1 , π 2 ). 3. Consider the level surface xyz = 6 at the point (1 , 2 , 3). (a) Find the equation for the tangent plane. (b) Find the parametric equation for the normal line. (c) Make a Maple plot showing the level surface, the tangent plane, and the normal line. Choose the domain and the viewpoint so that you get a good view of all three objects....
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