152pretestsols - ∑-1 n n n 2 D-1 n n n 2 6→ ∑-1 n ln...

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Question 1 Choose the best integration technique for each integral. Integral u - substitution integration by parts trigonometric substitution integration by fractional parts u = . . . , du = . . . u = . . . , v 0 = . . . x = . . . , dx = . . . general terms R x ln ( x ) dx u = ln ( x ) , v 0 = x R 1 x 2 - 7 x + 10 dx A / ( x - 2 ) + B / ( x - 5 ) R 1 4 - x 2 dx x = 2 sin θ , dx = 2 cos θ d θ A / ( x - 2 ) + B / ( x + 2 ) R 1 ( 9 x 2 - 1 ) 5/2 dx x = 1/3 sec θ , dx = 1/3 sec θ tan θ d θ R 5 xe x 2 dx u = x 2 , du = 2 x dx R 1 x ( x + 1 ) dx A / x + B / ( x + 1 ) R 3 x + 2 x 2 - 2 x + 1 dx A / ( x - 1 ) + B / ( x - 1 ) 2 R 3 x sin ( x 2 ) dx u = x 2 , du = 2 x dx R x cos ( x ) dx u = x , v 0 = cos x R x 2 e x dx u = x 2 , v 0 = e x R e x 2 x dx u = x , du = dx /2 x R 2 x 4 + x 2 dx u = 4 + x 2 , du = 2 x dx
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Question 2 Choose the best convergence test for each infinite series. Don’t forget to state whether the series converges or diverges! Series C / D divergence test alt. series test integral test comparison test limit comparison ratio test root test a n 6→ 0 b n > 0, 0 technique a n <> b n | a n b n | → . . . | a n + 1 a n | → . . . n p | a n | → . . . 2 n 4 n + 6 - n C 2
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Unformatted text preview: ∑ (-1 ) n n n + 2 D (-1 ) n n n + 2 6→ ∑ (-1 ) n ln ( n ) n 2 C ln ( n ) n 2 → ∑ ( n 3 n + 1 ) n C ( n 3 n + 1 ) n n → 1 3 ∑ ne-n 2 C u-sub ∑ 2 n 3 n 4 + 4 n 2 C 2 n 3 n 4 + 4 n 2 < 2 3 n 3 ∑ (-1 ) n cos ( π n ) D (-1 ) n cos ( π n ) 6→ ∑ (-1 ) n 5 n n ! C 5 n n ! → ∑ 1 n ln ( n ) D u-sub ∑ (-1 ) n 1 n ln ( n ) C 1 n ln ( n ) → ∑ ( 1 2 + 1 n )-n D ( 1 2 + 1 n )-n 6→ ( 1 2 + 1 n )-n n → 2 ∑ 1 ( 2 n ) ! C ( 2 n ) ! ( 2 ( n + 1 )) ! → ∑ 1 √ n 3-3 C n 3/2 √ n 3-3 → 1...
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