MATH 2630 Final Exam Practice Problems

# 2 1 0 b 2 0 c 0 2 1 0 e 0 0 2 2 0 0 2 r2 r2 2

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Unformatted text preview: d below ￿ √ 1￿2 π 2 is by the cone z = √ x +y tan 3 = 3 3 π A. 3 5π B. 2 π C. 2 π D. 4 8π E. 3 14. The volume of the solid bounded from below by z = x2 + y 2 and from above by x2 + y 2 + z 2 = 2 is given, in cylindrical coordinates, by A. 2 ￿ π ￿1 0 B. 2 ￿π ￿ 0 C. 0 2 ￿ π ￿1 0 E. 0 0 2 ￿ π ￿2 0 0 2 ￿−r2 r2 √ 2 ￿−r2 2 2 ￿ π ￿2 0 D. 0 √ √ r2 √ 2 ￿−r2 r2 √ 2 ￿−r2 r dzdrdθ r dzdrdθ r dzdrdθ r dzdrdθ 0 √ 2 ￿−r2 0 r 2 dzdrdθ MA 261 FINAL EXAM 2 Fall 2001 2 Name: 15. If C is the circle x + y = 2 oriented counterclockwise, then Page 9/11 ￿ C −x2 y dx + y 2 x dy is A. 0 B. 2π √ 42 C. π 3 D. 4π E. 8π 16. If ∇f (x, y ) = (2x + y 2 − 3x2 y )￿ + (2xy − x3 + 3y 2 )￿ and f (0, 0) = 1, then f (1, 1) is i j A. 5 B. 4 C. 3 D. 0 E. −1 MA 261 FINAL EXAM Fall 2001 Name: Page 10/11 17. If S is the portion of the paraboloid z = 1 − x2 − y 2 , with￿z ≥ 0, oriented by the ￿ ￿ ￿n upward unit normal ￿ and F (x, y, z ) = x￿ + y ￿ + z ￿ , then n i j k F · ￿ dS is S A. 0 π B. 2 C. π 3π D. 2 E. 2π 18. If C is the curve given by ￿(t) = t￿ + t2 ￿ + t4 ￿ , 0 ≤ t ≤ 1, then r i k j ￿ (x2 − y )dx + (y 2 − z )dy + (z 2 − x)dz is C A. B. C. D. E. 19 12 11 9 0 −7 15 −5 11 MA 261 FINAL EXAM Fall 2001 Name: 2 Page 11/11 2 1 /2 19. If S is the portion of the cone z = 2(x + y ) with 0 ≤ z ≤ 2, then A. B. C. D. E. √ ￿￿ S 25 π 3 √ 45 π 3 √ 85 π 3 √ 16 5 π 3 √ 32 5 π 3 20. Let S be the sphere x2 + y 2 + z 2 = 1 with outward ￿ ￿ orientation. If ￿n ￿ F · ￿ dS is F (x, y, z ) = (x + yz )￿ + (y + zx)￿ + (z + xy )￿ then i j k S A. 0 2 B. π 3 C. 2π 4π D. 3 E. 4π zdS is...
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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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