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Unformatted text preview: Tufts University Math 12 Department of Mathematics May 5, 2006 Final Exam 8:3010:30 am Instructions: Final course grades will be available to you 24 hours after they have been posted on SIS. No calculators, notes or books allowed. Remember to sign your blue book. With your signature you are pledging that you have neither given nor received assistance on this exam. Part I. On the first page of your bluebook, put answers only to the following problem. No partial credit is available. 1. (7 points total) a) (3 points) Give the three cube roots of 8 i in polar form. b) (1 point) Plot the cube roots of 8 i in the complex plane. c) (3 points) Find the complex number z satisfying z + iz = 2 i . Express your answer in the form z = a + bi . Part II. For the problems in this part you must show your work in the blue book, giving full justification . Cross out any work you do not want graded. 2. (18 points) Evaluate a) Z t 2 ln t dt b) Z 1 x 2 ( x 1)( x + 1) dx c) Z sin 2 (3 ) d 3. (10 points) Justify your answers to the following questions by citing and performing the appropriate3....
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This test prep was uploaded on 03/26/2008 for the course MATH 12 taught by Professor Garant during the Spring '08 term at Tufts.
 Spring '08
 GARANT
 Math

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