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Unformatted text preview: X n =1 2 + (1) n n √ n 5. ∞ X n =1 n ! 100 n 6. ∞ X n =1 (1) n arctan n n 2 7. Suppose that the series ∞ X n =0 c n ( x2) n converges when x = 4 and diverges when x =1. Determine if the following series converge or diverge. You do not need to justify your answers and no partial credit is possible. a. ∞ X n =0 c n (1) n b. ∞ X n =0 4 n c n c. ∞ X n =0 2 n c n d. ∞ X n =0 nc n 8. If f ( x ) = ∞ X n =1 ( x + 1) n n 4 n , ﬁnd the intervals of convergence for f ( x ) and f ( x ). 9. Find power series centered at a = 0 equal to the following functions. Be sure to state where (i.e. for what values of x ) these series representations are valid. a. a ( x ) = 1 x + 10 b. b ( x ) = x x 2 + 10 c. c ( x ) = ln ( x 2 + 10) 10. Find the Taylor series for f ( x ) = x 43 x 2 + 1 at the point a = 1. Calculus II, Exam 3 Work Page...
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 Fall '09
 Calculus, Taylor Series, Mathematical analysis, A Closed Book, following series converge

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