ex2_pra

# ex2_pra - MA 174 Multivariable Calculus EXAM II(practice...

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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

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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 2 , 1 , - 2 . 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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