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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.
 Summer '08
 Bonner
 Calculus

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