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# exam2solutions - Midterm 2 of Math 254.01(Au10 November 8...

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Midterm 2 of Math 254.01 (Au10) November 8, 2010 The Ohio State University 12:30pm-1:18pm Including the cover sheet, this exam consists of six (6) pages and six (6) problems and is worth a total of 102 points. The point value of each problem is indicated. To obtain full credit, you must have the correct answers along with relevant supporting work to jus- tify them. Partial credit will be given based on the work that is shown. However, answers without sufficient supporting work will receive no credit. Also, you must complete the exam in 48 minutes. Good luck! Name: Kwa, Kiam Heong Signature: OSU Internet Username: Problem # Score Problem # Score 1 4 (20 pts) (16 pts) 2 5 (24 pts) (16 pts) 3 6 (12 pts) (14 pts)

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1. Let f ( x, y ) be a continuous function. For each of the following iterated integrals, sketch and shade the region of integration and change the order of integration. (a) (10) R e 2 e R ln x 1 f ( x, y ) dy dx Solution: R 2 1 R e 2 e y f ( x, y ) dx dy . (b) (10) R 27 8 R 3 3 y f ( x, y ) dx dy Solution: R 3 2 R x 3 8 f ( x, y ) dy dx .
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