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Unformatted text preview: Test. ∞ X n =123 (1) n n 3 e n Problem 3. (20 points) a) Find the interval of convergence of the following series: ∞ X k =1 kx k 2 k Problem 4. (20 points) We want to approximate e 1 3 using Taylor polynomials. a) (12 points) Using the remainder bound, ﬁnd an n so that the error is at most .01 if we use the n th Taylor polynomial P n ( 1 3 ) for the approximation. b) (8 points) Using the correct n from part (a), approximate e 1 3 . Problem 5. (25 points) a) (20 points) Sum the series ∑ ∞ n =1 n 2 n (Hint: consider the series for f ( x ) = 1 1x ). b) (5 points) What is the 22 derivative of f ( x ) evaluated at zero? (i.e. f (22) (0))...
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 Fall '07
 McClain
 Calculus, Infinite Series, Taylor Series, Mathematical Series, general solution. xy

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