Name ID Number TA Section Time MTH 234 Exam 4 Practice December 7 2010 50 minutes Sects 16 1 16 5 16 7 16 8 1 No calculators or any other devices allowed If any question is not clear ask for clarification No credit will be given for illegible solutions If you present different answers for the same problem the worst answer will be graded Show all your work Box your answers 20 points Find the potential function for F D 2x 1 x2 E for y 0 y y2 2 20 I points Use the Green Theorem in the plane to show that line integral given by 2 xy dx x2 y 2x dy around any square depends only on the area of the square C and not on its location in the plane 3 20 points Write an integral which gives the surface area of the surface cut from the hemisphere x2 y 2 z 2 6 with z 0 by the cylinder x 1 2 y 2 1 Your final answer should be written in cylindrical coordinates Do not evaluate the integral 4 20 points Use the Stokes Theorem to compute the line integral of the vector field F hx2 y 1 zi along the path C given by the intersection of the cylinder x2 y 2 4 and the hemisphere x2 y 2 z 2 16 with z 0 counterclockwise when viewed from above 5 20 p points Use the Divergence Theorem to find the outward flux of the field F x2 y 2 z 2 hx y zi across the boundary of the region D 1 6 x2 y 2 z 2 6 2 Pts 1 20 2 20 3 20 4 20 5 20 100 Score
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