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exam1review

# exam1review - Practice exam for calc IV Summer 2007 Exam 1...

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Practice exam for calc IV, Summer 2007 Exam 1 Exam 1 will consist of roughly 100 points of similar problems to those below. No notes, texts or calculators will be allowed on the exam. You will be provided with a formula sheet. Answers to these problems will appear in a few days. 1. (15 points) a) Compute 1 - 3 2 - x 2 2 x - 1 x 2 dydx . b) Sketch the region in R 2 over which the above integral is computed. c) Write the above integral as a sum of one or more integrals in dxdy order. You are not asked to compute the result! 2. (15 points) In this problem you will compute R ( x - y 2 ) 100 dA where R is the region in R 2 bounded by y = 0 , y = 1 , y = x, and y = x - 1. a) Sketch the region in R in the plane. b) Guess a transformation T from ( u, v ) to ( x, y ) which will greatly simplify the integral. Hint: finding the inverse transformation T - 1 is often easier c) Sketch the region in ( u, v ) space which corresponds to R in ( x, y ) space. d) Compute the Jacobian of T .
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