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

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Math 237 Assignment 3 Due: Friday, Jan 28th * 1. Find the first and second partial derivatives of a) f ( x, y ) = | 2 x 2 - y | . b) g ( x, y ) = xe x +cos y . * 2. Let f ( x, y ) = xy x 2 + 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 ) = ( x 4 y 2 x 2 + y 2 + 1 if ( x, y ) 6 = (0 , 0) 1 if ( x, y ) = (0 , 0) . a) Determine f x (0 , 0) and f y (0 , 0). b) Determine f x ( x, y ) for all ( x, y ) 6 = (0 , 0). c) Determine if f x is continuous at (0 , 0). 4. Find f x (0 , 0) and f y (0 , 0) for f ( x, y ) = ( x 3 - y 3 x 2 + y 2 + 1 if ( x, y ) 6 = (0 , 0) 1 if ( x, y ) = (0 , 0) . 5.
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