finalsample

# finalsample - Math 252 Fall 2010 Sample Problems for the...

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Math 252 Fall 2010 Sample Problems for the Final Exam 1. Let f ( x, y ) = arctan ³ y x ´ . a) Determine the linear approximation to f based at ¡ 3 , 1 ¢ . b) Make use of the result of part a) in order to approximate f (1 . 8 , 0 . 8) (you need not simplify). (Problem 3, Section 2.5). 2. Let f ( x, y )= p x 2 + y 2 . a) Determine the di f erential of f . b) Make use of the di f erential of f in order to approximate f (12 . 1 , 4 . 9) . (Problem 6, Section 2.5). 3. Let f ( x, y )= e x 2 y 2 . a) Compute the gradient of f. b) Compute the directional derivative of f at (2 , 1) in the direction of the vector v = ( 1 , 3) . (Problem 3, Section 2.7). 4. Let f ( x, y )= x 2 3 xy +5 x 2 y +6 y 2 +8 . Determine the nature of the critical points of f (maximum, minimum, or saddle point). (Problem 5, Section 2.8). 5. Let f ( x, y )=3 x 4 y. Make use of Lagrange multipliers to determine the maximum and minimum values of f on the set D = { ( x, y ): x 2 + y 2 =9 . (Problem 2, Section 2.9).

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## This note was uploaded on 12/13/2010 for the course MATH 252 taught by Professor Bologna during the Spring '03 term at San Diego State.

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finalsample - Math 252 Fall 2010 Sample Problems for the...

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