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# exam_4 sample solutions - Fourth Preliminary Exam Math 213...

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Unformatted text preview: Fourth Preliminary Exam Math 213 — Spring 2008 Name : Solutions This exam has 5 questions on 11 pages, for a total of 50 points. You have 50 minutes to answer all questions. This is closed book, closed notes exam. Use of calculators and other electronic devices is not permitted. Question Points Score 1 9 2 14 3 10 4 12 5 5 Total: 50 Multiple Choice No partial credit! 1. Circle the correct answer for each question. (a) (3 points) British mathematician and physicist George Green (7/14/1793–5/31/1841): A. Was born on July 14, 1793. B. Died on May 31, 1841. C. Was a British mathematician and physicist. D. All of the above! D (but the other three are also correct). (b) (3 points) An integration factor for the differential equation y 17 dx + x 17 dy = 0 is: A. I = x 17 + y 17 B. I = x- 17 y- 17 C. I = 17 ln( x )- 17 ln( y ) D. None of the above B: Multiplying through, we obtain x- 17 dx + y- 17 dy = 0, which is separable and hence exact. (c) (3 points) The area of the region R bounded by the positively oriented simple closed curve C is given by: A. Z C y 2 dx + x 2 dx B. Z C x 3 dy- 2 y 3 dx C. Z C y dx D. None of the above B: P =- 2 y/ 3 and Q = x/ 3 so Q x- P y = 1 / 3+2 / 3 = 1. Therefore, by Green’s Theorem, the line integral is equal to RR R 1 dA , which is the area of R . Page 2 Medium Answer Show your work! 2. First-Order Differential Equations (a) (4 points) Find the general solution of y = x 2- y 2 xy ....
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exam_4 sample solutions - Fourth Preliminary Exam Math 213...

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