MATH 2630 Final Exam Practice Problems

2 e 3 ma 261 final exam fall 2001 name page 611 z 9

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Unformatted text preview: 58 9 17 B. 2 C. 6 A. D. 10 129 E. 8 8y 8. If the directional derivative of f (x, y ) = at (2, 1) in the direction of a￿ + 3￿ is equal i j x to zero, then a equals A. 6 B. 4 C. 5 D. −2 E. −3 MA 261 FINAL EXAM Fall 2001 Name: Page 6/11 ∂z 9. Suppose z = f (x, y ) where x = t2 uv and y = u + tv 2 . Given that (4, 3) = 4 and ∂x ∂z ∂z (4, 3) = −1 compute when (t, u, v ) = (2, 1, 1). ∂y ∂t A. 6 B. 7 C. 12 D. 15 E. 16 10. The area of the image of the square [0, 1] × [0, 1] under the map T (u, v ) = (u2 + v, 2v ) is A. 4 B. 6 C. 2 D. 1 E. 3 MA 261 FINAL EXAM Fall 2001 Name: Page 7/11 11. Find a and b such that ￿ 0 1 ￿ 1 f (x, y ) dy dx = x2 ￿ 0 1 ￿ b f (x, y ) dx dy a A. a = 1, b = x2 √ B. a = y, b = 1 √ C. a = 1, b = y √ D. a = y, b = 1 √ E. a = 0, b = y 12. Use polar coordinates to compute the double integral ￿ 1 0 ￿ √ 0 1−x2 sin ￿ π2 (x + y 2 ) 2 ￿ dy dx π 2 1 B. 2 π C. 3 π D. 4 √ π E. 2 A. MA 261 FINAL EXAM Fall 2001 Name: Page 8/11 = 13. The volume of the solid bounded from above by the sphere x2 + y 2 + z 2￿ 4 an...
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This note was uploaded on 10/09/2013 for the course MATH 2630 taught by Professor Staff during the Fall '08 term at Auburn University.

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