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Unformatted text preview: D u f ( a, b ) of f at ( a, b ) in the direction of the unit vector u . b) Find the rate of change of f at the point (1 , 2) in the direction of the vector (1 ,3). c) In what direction from (2 , 1) does f change most rapidly and what is the maximum rate of change. 7. Determine if each of the following limits exist. Evaluate the limits that exist. a) lim ( x,y ) (0 , 0) x 2xyy 2 x 2 + y 2 . b) lim ( x,y ) (0 , 0) x 2  x    y   x  +  y  . 8. Consider the function f ( x, y ) = x 4 / 3 y x 2 + y 2 , ( x, y ) 6 = (0 , 0) , ( x, y ) = (0 , 0) . a) Where is f dierentiable on its domain? b) Based on your answer in part a), what can you conclude about the continuity of both f x and f y at (0 , 0)?...
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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.
 Spring '08
 WOLCZUK
 Approximation, Linear Approximation

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