a3 - ) = (0 , 0) . 4. Invent a function f : R 2 R such that...

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Math 237 Assignment 3 Due: Friday, Oct 9th 1. Use the linear approximation to approximate arctan(0 . 99(1 . 01) 3 ). 2. Let f ( x, y, z ) = xyz x + y + z . Use the linear approximation to approximate f ( - 1 . 04 , - 1 . 98 , 3 . 97). 3. For each of the following functions f : R 2 R , determine if f is differentiable at (0 , 0). a) f ( x, y ) = ± x 4 - y 4 x 2 + y 2 , if ( x, y ) 6 = (0 , 0) 0 , if ( x, y ) = (0 , 0) . b) f ( x, y ) = ± y 3 x 2 + y 2 , if ( x, y ) 6 = (0 , 0) 0 , if ( x, y ) = (0 , 0) . c) f ( x, y ) = ± xy x 2 + y 2 + 1 , if ( x, y ) 6 = (0 , 0) 1 , if ( x, y
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Unformatted text preview: ) = (0 , 0) . 4. Invent a function f : R 2 R such that f x (1 , 1) and f y (1 , 1) both exist, but f is not dierentiable at (1 , 1). Prove your function satises the conditions. 5. Prove that if f satises | f ( x, y ) | x 2 + y 2 for all ( x, y ) R 2 , then f is dierentiable at (0 , 0)....
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This note was uploaded on 10/12/2010 for the course MATH 237 taught by Professor Wolczuk during the Fall '08 term at Waterloo.

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