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review-t2-web

# review-t2-web - Review for Test 2 In 1-2 nd the partial...

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Review for Test 2 In 1-2 find the partial fraction decomposition. Be sure to find the values of A, B, and C, etc. There is nothing to be integrated. 1. x ( x - 2)( x - 3) 2 = 2 x - 2 + B x - 3 + 3 ( x - 3) 2 Put x = 4. Then 2 = 1 + B + 3. So B = - 2. Write final answer. 2. x ( x - 1)( x 2 - x + 1) = 1 x - 1 + Bx + C x 2 - x + 1 Put x = 0: 0 = - 1 + C . C = 1. Put x = 2: 2 3 = 1 + 2 B + 1 3 . B = - 1. Write answer. 3. Find each integral. (a) Z 5 x + 4 x 2 + 4 x + 10 dx (b) Z 5 x + 4 ( x 2 + 4 x + 10) 2 dx Complete square in each denominator. Put t = x +2. So x = t - 2 and dx = dt . (a) Z 5( t - 2) + 4 t 2 + 6 dt = 5 2 ln( x 2 + 4 x + 10) - 6 arctan x + 2 6 + C (b) 5 Z t dt ( t 2 + 6) 2 - 6 Z dt (6 + t 2 ) 2 Use the power rule for the first integral. Use formula 5 on the handout for Sec. 7.3 for the second integral. 4. Do 53, 55, and 56 in Exercises 7.8 Review for Sections 11.1, 11.2, and 11.3. In 1–15, find the limit if a n has a limit and show work. Otherwise, explain why a n has no limit at all. 1. lim n cos n n 2 + 4 0 ≤ | a n | ≤ n n 2 + 4 = b n . 0 0 & b n 0. So | a n | → 0 by Sq Th. Hence a n 0 by Th 11.1.6. 2. lim n cos 2 n e n 0 < a n n e n = b n 0 0; b n 0 since x k e ax 0 as x → ∞ . Hence a n 0 by Sq Th.

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3. lim sin 3 n 4. lim cos 3 n 5. lim n sin 1 n = lim x →∞ sin 1 x 1 x = 1 by Red Box 2 page 190. 6. lim n sin 3 n 7. lim n cos
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