Exam 2 Solutions 2011

in the numerators then youd need to solve for the

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Unformatted text preview: x 1 − x 3 dx 1 1 = ln(|x|) − ln(|x + 3|) + C x+3 3 3 Page 4 (4) x3 + 1 into “partial fractions”, you’d need to write it as a sum of fractions + 1) with unknowns A, B , C , . . . in the numerators, then you’d need to solve for the unknowns A, B , C , . . . . What is this sum of fractions? Just set it up, using the unknowns A, B , etc. but do not solve for the unknowns. 9. (5 points) To decompose x2 (x2 Solution: Cx + D A B x3 + 1 = + 2+ 2 2 (x2 + 1) x x x x +1 3 10. (10 points) Show how to approximate 1 2xdx using a midpoint estimate with 4 rectangles. Be sure to sketch the picture to show what you are doing. You don’t need to actually add up all the numbers, just get it to the point where I could punch your answer into a calculator and let the calculator compute the answer. (Yes I know you could give me the exact integral, but I’m not asking for that.) Solution: y 6 5 4 3 2 1 0.5 1.0 1.5 2.0 2.5 3.0 x midpoint rule approximation = (0.5)((2)(1.25) + (2)(1.75) + (2)(2.25) + (2)(2.75)) Page 5...
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This document was uploaded on 03/05/2014 for the course MAT 193 at CSU Dominguez Hills.

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