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Unformatted text preview: 1. (4 points) Evaluate Z . 5 x 2 cos( x 2 ) dx as an inﬁnite series, and estimate the error if the series is approximated by the ﬁrst two terms. 2 2. (4 points) Find the Taylor series for f ( x ) = 1 x centered at a =3, and ﬁnd its radius of convergence. 3 3. Determine if the series below are absolutely convergent (AC), conditionally convergent (CC), or divergent (D). a) (3 points) ∞ X n =1 (1) n ( n + 1)3 n 2 2 n +1 b) (4 points) ∞ X n =1 (1) n tan1 1 n 4 4. Find the sum of the series below. a) (3 points) ∞ X n =1 ± (ln 2) n + 4 2 n ² b) (4 points) ∞ X n =1 (1) n +1 n 2 n +1 5 5. (4 points) Find the Maclaurin series for f ( x ) = ex 2 and evaluate f (99) (0) and f (100) (0). 6...
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 Fall '08
 Reshetiken
 Math, M. Daub M., Daub M. Daub, C. Raicu M. Daub M. Daub M. Daub C. Raicu H. Tran A. Boocher A. Boocher H. Chaperon H. Tran

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