237t1 - 1. Supposethatthefunction f : R 2 R...

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1. Suppose that the function   R R f 2 :  is differentiable and  2 3 : R R g  is defined by           ) , ( ) , , ( yz xz z y x = g . (a) [4 marks]   Let  ) , , ( ) , ( z y x v u g = . Find  D  and   ) , ( ) , ( z x v u . (b) [6 marks]  If  ) , ( ) , )( ( yz xz f y x f w = = g , then  k z w z y w y x w x = - + , where  k  is a                        constant. Determine the value of   k . 2

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2.  (a)  [7 marks]  In the neighborhood of the point   ) 2 , 1 , 1 (   the equation   xyz z y x 5 3 3 3 = + +                                      defines    as a function of    and   y , that is  ) , ( y x f z = . Find the directional                                   derivative  f u  (or  z u  in another notation) at the point  ) 1 , 1 ( 0 P   in the direction                                   of the vector from  0 P  to  ) 5 , 4 ( 1 P                                 (b)
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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- Toronto.

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237t1 - 1. Supposethatthefunction f : R 2 R...

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