hw9 - MATH 138: Calculus 2 Assignment #9 (Modified) Due:...

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Unformatted text preview: MATH 138: Calculus 2 Assignment #9 (Modified) Due: 12:30 p.m., Friday, November 26 Fall 2010 1. Find the radius of convergence and interval of convergence of the power series. ∞ (a) n=1 ∞ (−1)n xn n+1 (−1)n (x − 3) 2n + 1 n ∞ (b) n=1 ∞ √n nx (4x + 1)n n2 (c) n=1 (d) n=1 2. Find the Maclaurin series (or, power series representation about x = 0) of the function and the radius of convergence. x2 1 (Hint. differentiate ) 2 (1 − 2x) 1 − 2x (a) f (x) = (b) f (x) = (c) f (x) = sin2 x (Hint. sin2 x = (1 − cos(2x))/2) πx (e) f (x) = sin 2 3. Find the sum of the series. ∞ 3 −x−2 2 (d) f (x) = 3−x (f) f (x) = ex + 2e−x x2 (a) n=0 ∞ 3n 5n n! (−1)n π 2n 32n (2n)! (b) n=0 The following problems are only recommended, not for submission. • Course Notes: All examples in section 5.3. • Stewart: Section 11.8 Exercises 3, 5, 15, 23; Section 11.9 Exercises 3, 7, 17; Section 11.8 Exercises 29, 31, 63, 65. ...
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