212_Practicetest2

212_Practicetest2 - Test 2 Math 212 Spring 2008 Practice...

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Test 2: Math 212 Spring 2008 Practice Exam This is a practice exam for Math 212 Exam 2, Spring 2008. It is LONGER than the in class and take home exam will be, but should give you a good idea for the standard types of problems and diﬃculty level that will be on the exam. Problems like these will constitute roughly 80% of the exam. The rest of the exam will consist of types of problems that you have not seen before. Let me know if you see any typos!! Problem 1 Evaluate Z 1 0 Z 1 y e - x 2 / 2 dxdy Problem 2 Let f ( x,y ) = 1 3 x 3 + y 2 + 3 and let D be the triangle with vertices (0 , 0) , (1 , 0) , and (1 , 1). Let S be the surface given by the graph of f ( x,y ) over D . (a) Find a parametrization for S . (b) Compute ZZ S 4 x 2 dS 1

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Problem 3 For this problem: Let S be the disk ± ( x,y, 5) | x 2 + y 2 1 ² oriented so that the positive side of S is up. Let C be the oriented line from (2 , 2 , 2) to (0 , 0 , 0). Also let f ( x,y,z ) = xy 2 z 3 , F ( x,y,z ) = - y ˆ i + x ˆ j, G ( x,y,z
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212_Practicetest2 - Test 2 Math 212 Spring 2008 Practice...

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