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Unformatted text preview: Second Preliminary Exam Math 213 Spring 2008 Name : Solutions This exam has 6 questions on 7 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 12 2 6 3 10 4 8 5 8 6 6 Total: 50 Multiple Choice No partial credit! 1. Circle the correct answer for each question. (a) (4 points) French mathematician Alexis Claude de Clairault (5/3/1713 5/17/1765): A. Was born on May 3, 1713. B. Died on May 17, 1765. C. Was a French mathematician. D. All of the above! D (but the other three are also correct). (b) (4 points) Let C be the curve parametrized by r ( t ) = h 3 cos( t ) ,, 3 sin( t ) i for 0 t , then Z C ds equals: A. 2 B. 3 C. 6 D. None of the above B: The curve is a semicircle of radius 3, so its length Z C ds is 3 . (c) (4 points) If C is the piece of the hyperbola xy = from (1 / 2 , 2 ) to (2 ,/ 2), then Z C e x sin( y ) dx + e x cos( y ) dy equals: A. e 2 B. e C. 2 D. None of the above A: ( e x sin( y )) = h e x sin( y ) ,e x cos( y ) i , so the integral is e 2 sin( / 2)- e 1 / 2 sin(2 ) = e 2 by the Fundamental Theorem for Line Integrals....
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