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Unformatted text preview: z = ln( x 2 + y ) at (2 ,3 , ). 7. Let f ( x, y ) = p ( x 2 + y 2 ). Use Taylors Theorem to show that for x 1, y 1  R 1 , (1 , 1) ( x, y )  23 / 2 ( x1) 2 + ( y1) 2 8. Determine if each of the following limits exist. Evaluate the limits that exist. a) lim ( x,y ) (0 , 0) x 2 y 4 x 4 + y 8 . b) lim ( x,y ) (0 , 0)2 x 2 + x 2 y 22 y 2 x 2 + y 2 . 9. Let f ( x, y ) = x 7 / 3 y 2 / 3 x 2 + y 2 , ( x, y ) 6 = (0 , 0) , ( x, y ) = (0 , 0) . a) Determine if f ( x, y ) is continuous at (0 , 0). b) Determine all points where f is dierentiable. c) Based on your answer in part b), what can you conclude about the continuity of both f x and f y at (0 , 0)? d) Find the directional derivative of f at (0 , 0) in the direction of the vector (1 , 1)....
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This note was uploaded on 06/28/2011 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.
 Spring '08
 WOLCZUK
 Math

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