MAC 2312 Exam 2 - MAC 2312 Exam 2 Solutions July 7 2011 Name |{z By writing my name I swear by the honor code Read all of the following information

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Unformatted text preview: MAC 2312 Exam 2 Solutions July 7, 2011 Name: | {z } By writing my name, I swear by the honor code. Read all of the following information before starting the exam: • Show all work, clearly and in order, if you want to get full credit. I reserve the right to take off points if I cannot see how you arrived at your answer (even if your final answer is correct). • Circle or otherwise indicate your final answers. • This test has 5 problems and is worth 50 points, plus one bonus problem at the end. It is your responsibility to make sure that you have all of the pages! • Since time is limited, it is crucial that you think before you compute. • You must state any theorems or tests that you use. All hypotheses must be verified. • Good luck! 1. Evaluate the integral. Z 2 x 2- x + 1 x 3 + x dx Solution: The integrand is a proper rational function, so we use partial fractions. 2 x 2- x + 1 x 3 + x = 2 x 2- x + 1 x ( x 2 + 1) = A x + Bx + C x 2 + 1 Multiplying both sides by x ( x 2 + 1) yields 2 x 2- x + 1 = A ( x 2 + 1) + ( Bx + C ) x. Plugging in x = 0 gives that A = 1. Then, expanding and equating coefficients gives B = 1 and C =- 1. Thus, Z 2 x 2- x + 1 x 3 + x dx = Z dx x + Z x- 1 x 2 + 1 dx = ln | x | + Z x x 2 + 1 dx- Z dx x...
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This note was uploaded on 10/13/2011 for the course MAC 2312 taught by Professor Bonner during the Summer '08 term at University of Florida.

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MAC 2312 Exam 2 - MAC 2312 Exam 2 Solutions July 7 2011 Name |{z By writing my name I swear by the honor code Read all of the following information

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