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Exam3AReview - Practice Problems for Math 133 Exam 3 1 Work...

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Unformatted text preview: Practice Problems for Math 133 Exam 3 1. Work out the following integrals using partial fractions. (a) integraldisplay 4 x 2 + 6 dx x 3 + 3 x = ln ( x 2 ( x 2 + 3) ) + C (b) integraldisplay x 2 + x dx ( x- 1)( x 2 + 1) = ln( x- 1) + arctan x + C (c) integraldisplay x 2 + x- 10 dx (2 x- 3)( x 2 + 4) = 1 2 ln x 2 + 4 2 x- 3 + arctan x 2 + C (d) integraldisplay x 5 + 9 x 3- 9 x 2- 9 dx ( x 3 + 9 x ) = x 3 3- ln bracketleftbig x ( x 2 + 9) 4 bracketrightbig + C (e) integraldisplay dx ( x 3 + x 2 + x ) =- 1 2 ln x 2 + x + 1 x 2- √ 3 3 arctan 2 x + 1 √ 3 + C (f) integraldisplay 1 5 x dx ( x + 2)( x 2 + 1) = ln 8 9 + π 4 = 0 . 667 ... (g) integraldisplay 1 (4 x 2 + 2 x ) dx ( x 2 + 1)( x + 1) 2 = π 4 + 1 2- ln 2 = 0 . 592 ... 2. Work out the following improper integrals. Show all limits and justify your responses using the Comparison Test (CT) and Limit Comparision Test (LCT). (a) integraldisplay 2 dx √ 4- x 2 = π 2 (b) integraldisplay 12 2 x dx ( x 2- 16) 2 / 3 = 9 · 16 2 / 3 (c) integraldisplay...
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This note was uploaded on 05/12/2008 for the course MATH 133 taught by Professor Wei during the Spring '07 term at Michigan State University.

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Exam3AReview - Practice Problems for Math 133 Exam 3 1 Work...

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