a2f08 - ASSIGNMENT # 2 1. Let f ( x, y ) = 5 x 3 y . (a)...

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ASSIGNMENT # 2 1. Let 5 3 ) , ( y x y x f = . (a) Show that the partial derivatives ) 0 , 0 ( x and ) 0 , 0 ( y exist, and evaluate them. (b) Prove that f is not differentiable at . ) 0 , 0 ( 2. Consider the function xy y x f 2 ) , ( = . In what directions at the point (1, 2) is the directional derivative of f equal to 4? 3. Suppose that the temperature at each point of a metal plate is given by the function . Find the path followed by a heat seeking particle that originates at . Give the answer in rectangular coordinates. 2 2 1 ) , ( y x y x T + = ) 1 , 2 ( Verify that the path of the particle is perpendicular to each of the level curves of T . 4. The function is differentiable on R xy x y x f = 3 ) , ( 2 . Let ) 2 , 1 ( , ) 1 , 0 ( = = b a . Find a point c on the line segment joining a and b such that ) ( ) ( ) ( ) ( a b c a b = f f f . 5. (a) Prove that the function 2 2 ) , ( y x xy y x f + = is differentiable at each point in its domain. (b) Suppose that
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This note was uploaded on 10/21/2010 for the course MATHEMATIC MAT237Y1 taught by Professor Romauldstanczak during the Fall '09 term at University of Toronto.

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a2f08 - ASSIGNMENT # 2 1. Let f ( x, y ) = 5 x 3 y . (a)...

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