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Spring '06 Exam 3

Spring '06 Exam 3 - Math 13 Tufts University Department of...

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Tufts University Math 13 Department of Mathematics April 10, 2006 Exam 3 (100 points) noon – 1:20 p.m. Except in the true-false questions, show all your work. Simplify and box your answers. No calculators, notes, or books are allowed. You are required to sign your bluebook. With your signature you are pledging that you have neither given nor received assistance on the exam. Students found violating this pledge will receive an F in the course. 1. (10 points) For each statement, write True if it is always true and False if it is not always true. Write your answers on the inside front cover of the bluebook. No explanation is necessary. a) Let D be the plane region bounded on the left by x 2 + y 2 = 4 and on the right by the y -axis. The integral integraltextintegraltext D x 2 y + x 3 y 5 dA = 0 by symmetry. b) Let E be the solid bounded above by z = 4 and below by z = x 2 + y 2 . The triple integral integraltextintegraltextintegraltext E (cos x ) y 2 z dV = 0 by symmetry.
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