Fall 2006 - Hall's Class - Practice Exam 1

Fall 2006 - Hall's Class - Practice Exam 1 - Math 20E...

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Unformatted text preview: Math 20E Practice Exam 1 Solutions October 15, 2006 1. Let f ( x,y ) = ( x 2 y,e- 2 xy , 2 x- y ). (a) (10 points) Compute the derivative matrix D f(x,y). D f ( x,y ) = f 1 x f 1 y f 2 x f 2 y f 3 x f 3 y (pg. 135) = 2 xy x 2- 2 ye- 2 xy- 2 xe 2 xy- 2 ( x- y ) 2 2 ( x- y ) 2 (b) (10 points) Suppose g : R 2 R 2 satisfies g (1 , 1) = (0 , 2), and D g (1 , 1) = 2 1- 1 3 . Compute D ( f g )(1 , 1) . We use the form of the Chain Rule provided on the exam reference sheet. D ( f g )(1 , 1) = D f (0 , 2) D g (1 , 1) = 2(0)(2) 2- 2(2) e- 2(0)(2)- 2(0) e 2(0)(2)- 2 (0- 2) 2 2 (0- 2) 2 2 1- 1 3 = - 4- 1 2 1 2 2 1- 1 3 = - 8- 4- 3 2 1 1 2. The height h in kilometers of a mountain is given by h ( x,y ) = 2- x 2- 1 4 y 2 , where x and y are the east-west and north-south distances from the top of the mountain in kilometers, respectively....
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This note was uploaded on 04/30/2008 for the course MATH 20E taught by Professor Enright during the Fall '07 term at UCSD.

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Fall 2006 - Hall's Class - Practice Exam 1 - Math 20E...

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