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Unformatted text preview: out the test, and state your conclusion. page 7 10. Decide if the series ∞ X n =1 (1) n n n 3 + 2 is absolutely convergent, is conditionally convergent, (8 points) or the series diverges. Say which test(s) you are using to show convergence/divergence, show your work in carrying out the test(s), and state your conclusion. 11. Find the Maclaurin series for f ( x ) = x 3x (8 points) page 8 12. The function g is given by the Taylor series g ( x ) = ∞ X k =0 ( x3) k ( k + 1)2 k (8 points) Find the interval of convergence for the Taylor series. ( Be sure to indicate which of the the end points, if any, are included in the interval! ) Bonus Find the length of the parametric curve x ( t ) = 1t 2 1 + t 2 and y ( t ) = 2 t 1 + t 2 for1 ≤ t ≤ 1. (8 points)...
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 Spring '10
 xie
 Derivative, Taylor Series, Mathematical Series, lim

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