a4 - . 4. Let f : R 2 R and dene g ( x, y ) = f (sin y, cos...

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Math 237 Assignment 4 Due: Friday, Oct 15th 1. Determine all points where the function is differentiable. a) f ( x, y ) = ± x 3 + y 3 x 2 + y 2 , if ( x, y ) 6 = (0 , 0) 0 , if ( x, y ) = (0 , 0) . b) g ( x, y ) = | x | 1 / 2 . 2. Prove that if all of the second partial derivative of f are continuous at ( a, b ), then f is continuous at ( a, b ). 3. Let f, g : R R where f and g are twice differentiable. Show that u ( x, t ) = f ( x - at ) + g ( x + at ) is a solution of the wave equation: u tt = a 2 u xx
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Unformatted text preview: . 4. Let f : R 2 R and dene g ( x, y ) = f (sin y, cos x ). Find g xx and g yy . State any assumptions you needed to make. 5. Let f ( x, y ) = | x | r | y | s , where r and s are positive numbers. a) For what values of r and s is f dierentiable at (0 , 0)? b) For what values of r and s is f dierentiable on R 2 ?...
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This note was uploaded on 12/10/2010 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.

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