a3 - Math 237 Assignment 3 Due: Friday, Jan 28th *1. Find...

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Unformatted text preview: Math 237 Assignment 3 Due: Friday, Jan 28th *1. Find the first and second partial derivatives of a) f (x, y ) = |2x2 − y |. b) g (x, y ) = xex+cos y . *2. Let f (x, y ) = xy . x2 +y 2 a) Find the equation of the tangent plane of f at (2, 1, 2/5). b) Approximate f (1.9, 1.1). *3. Let f (x, y ) = x4 y 2 x2 + y 2 1 +1 if (x, y ) = (0, 0) if (x, y ) = (0, 0). a) Determine fx (0, 0) and fy (0, 0). b) Determine fx (x, y ) for all (x, y ) = (0, 0). c) Determine if fx is continuous at (0, 0). 4. Find fx (0, 0) and fy (0, 0) for f (x, y ) = x3 −y 3 x2 +y 2 1 +1 if (x, y ) = (0, 0) if (x, y ) = (0, 0). 5. a) Find a function f (x, y ) such that f (x, y ) is continuous at (0, 0), but fx (0, 0) and fy (0, 0) both do not exist. Justify your answer. b) Find a function g (x, y ) such that gx (0, 0) and gy (0, 0) both exist at (0, 0), but g (x, y ) is not continuous at (0, 0). Justify your answer. NOTE: Only * questions will be graded ...
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This note was uploaded on 12/05/2011 for the course MATH 237 taught by Professor Wolczuk during the Winter '08 term at Waterloo.

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