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ex2_pra - MA 174: Multivariable Calculus EXAM II (practice)...

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Unformatted text preview: MA 174: Multivariable Calculus EXAM II (practice) NAME INSTRUCTOR NO CALCULATORS, BOOKS, OR PAPERS ARE ALLOWED. Use the back of the test pages for scrap paper. Points awarded 1. (5 pts) 9. (5 pts) 2. (5 pts) 9. (5 pts) 3. (5 pts) 9. (5 pts) 4. (5 pts) 9. (5 pts) 5. (5 pts) 9. (5 pts) 6. (5 pts) 9. (5 pts) Total Points: 1 1. Suppose z = f ( x, y ) , where x = e t and y = t 2 + 3 t + 2 . Given that ∂z ∂x = 2 xy 2- y and ∂z ∂y = 2 x 2 y- x , find dz dt when t = 0 . A. 3 B. 6 C. 15 D. 9 E.- 1 2. Find the directional derivative of the function f ( x, y, z ) = x 2 y 2 z 6 at the point (1 , 1 , 1) in the direction of the vector h 2 , 1 ,- 2 i . A.- 6 B.- 2 C. D. 2 E. 6 3. Find the direction in which the function z = x 2 + 3 xy- 1 2 y 2 is increasing most rapidly at (- 1 ,- 1) . A. 3 i B. 5 ~ i + 2 ~ j- ~ k C.- 5 ~ i- 2 ~ j D. 2 ~ i- 5 ~ j E. √ 29 2 4. If xz 3- xyz = 4 , find ∂z ∂x ....
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This note was uploaded on 04/23/2011 for the course MA 173 taught by Professor Staff during the Spring '08 term at Purdue.

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ex2_pra - MA 174: Multivariable Calculus EXAM II (practice)...

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