Final Exam

# Final Exam - MATH 253.504506 Final Exam, version A 12/13/99...

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MATH 253.504–506 An unsupported answer Final Exam, version A is a wrong answer! 12/13/99 This test has 2 pages, 13 problems, and 175 points. Conversion from spherical to Cartesian coordinates: x = ρ sin φ cos θ y = ρ sin φ sin θ z = ρ cos φ dV = ρ 2 sin φdρdθdφ 1. (10 pts.) Find the equation of the plane tangent to the surface xy 2 z 3 = 2 at the point (2 , 1 , 1). 2. (10 pts.) Evaluate the line integral R C ydx - xdy on the semicircle x 2 + y 2 =4 , y 0, from the point (2 , 0) to ( - 2 , 0). 3. (15 pts.) Reverse the order of integration to write Z 3 1 Z - 2 x +8 6 /x φ ( x, y ) dy dx as an iterated integral in the order dx dy . (You won’t be evaluating an integral in this problem.) 4. (10 pts.) Write a parameterization for the part of the cylinder x 2 + z 2 = 4, which lies between the planes y = - 1and x +2 y + z = 8. Be sure to specify the parameter domain. 5. (15 pts.) Using the divergence theorem, compute RR S ( ~ F · ~n ) dS ,where S

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## This note was uploaded on 03/26/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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Final Exam - MATH 253.504506 Final Exam, version A 12/13/99...

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