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Final Review S10

Final exam page 12 of 15 may 8 2010 15 determine if

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Unformatted text preview: Final Exam, Page 12 of 15 May 8, 2010 15. Determine if each of the following series converges or diverges. If it converges, find its sum . (a) (4 pts) ∞ X n =0 6 n- 2(3 n ) 10 n (b) (4 pts) ∞ X n =0 1 n + 3- 1 n + 4 (c) (4 pts) 3- 3 4 + 3 16- 3 64 + 3 256 + ... Final Exam, Page 13 of 15 May 8, 2010 16. Determine if each of the following series converges or diverges. For each series, state which test you use . (Note this problem continues on the next page.) (a) (4 pts) ∞ X n =1 1 cos( πn ) (b) (4 pts) ∞ X n =1 n ( n 2 + 4) 5 / 2 (c) (4 pts) ∞ X n =1 7 n e- 1 Question 16 continues ... Final Exam, Page 14 of 15 May 8, 2010 (d) (4 pts) ∞ X n =1 6 n 5 n- 1 17. Find the interval of convergence for each of the following series. (a) (3 pts) ∞ X n =1 3 n x n n 2 (b) (3 pts) ∞ X n =1 e n ( x- 5) n n ! Final Exam, Page 15 of 15 May 8, 2010 18. (5 pts) Find Taylor series for f ( x ) = xe x +1 centered at x = 0. State the interval of convergence. 19. (6 pts) Use an appropriate Taylor series to find Z x cos( t 2 ) dt . Express your answer as a summation (that is, with a Σ)....
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Final Exam Page 12 of 15 May 8 2010 15 Determine if each of...

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