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exam_3 sample solutions - Third Preliminary Exam Math 213...

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Third Preliminary Exam Math 213 — Spring 2008 Name : 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 12 3 8 4 8 5 5 6 5 Total: 50

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Multiple Choice No partial credit! 1. Circle the correct answer for each question. (a) (3 points) Italian mathematician Guido Fubini (1/19/1879 – 6/6/1943): A. Was born on January 19, 1879 B. Died on June 6, 1943 C. Was an Italian mathematician. D. All of the above! D (but the other three are also correct). (b) (3 points) Let D be the disc of radius 1 centered at the origin in the xy -plane. Then RR D x 2 y dA is A. 0 B. 2 π C. 4 π D. None of the above A: The function f ( x, y ) = x 2 y has odd symmetry with respect to x (i.e. f ( x, - y ) = - f ( x, y )) and D is also symmetric about the y -axis. (c) (3 points) Consider the change of variables x = cos( u )+sin( v ), y = cos( v )+sin( u ). Then ( x, y ) ( u, v ) is A. sin( u ) cos( v ) - cos( u ) sin( v ) B. sin( u ) sin( v ) - cos( u ) cos( v ) C. cos( u ) sin( v ) - sin( u ) cos( v ) D. None of the above.
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