Mth122Test1Sample

# Mth122Test1Sample - x inches, y inches, and z inches, must...

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Math 122 Spring 2009 Name: | {z } by writing my name I swear by the honor code Test 1 Sample You must show all the work clearly to get full credit. Good luck! 1. (6 pts) Given f ( x,y ) = p x 2 - y 3 + z 2 . Find ∂f ∂x , ∂f ∂y and 2 f ∂x∂y . 2. (4 pts )Given f (0 , 1) = 2, ∂f ∂x (0 , 1) = - 2, ∂f ∂x (0 , 1) = 4. Approximate f (0 . 2 , 1) and f (0 , 1 . 2). 3. (8 pts ) Let f ( x,y ) = x 5 + y 5 - 5 x - 80 y . Find the critical points and and use the second-derivative test to determine the nature of these points. 4. (6 pts ) According to U.S. postal regulations, a rectangular package whose three side lengths measure

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Unformatted text preview: x inches, y inches, and z inches, must satisfy that 2 x + 2 y + z cannot exceed 84. Suppose we want to make a package with maximum surface. Write down the objective function and constraint function for this problem and SET UP (DONOT SOLVE) the Lagrange multipliers equations. 1 2 5. Evaluate the following integrals. a) (6 pts ) R x √ x 2-16 dx b) (6 pts ) R ln(5 y + 1) dy c) (7 pts ) R 1 1 (2 x +1) 3 dx d) (7 pts ) R 2 ze-z dz...
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## This note was uploaded on 02/20/2009 for the course MTH 122 taught by Professor Buettgens during the Spring '08 term at SUNY Buffalo.

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Mth122Test1Sample - x inches, y inches, and z inches, must...

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