A2 - MATH 222 HOMEWORK 2 DUE SEPTEMBER 26, 2011 1. P...

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Unformatted text preview: MATH 222 HOMEWORK 2 DUE SEPTEMBER 26, 2011 1. P ROBLEMS Problem 1.1. Find the interval of convergence. ∞ (3n + 2)xn (a.) n=1 ∞ (8x)n n! (b.) n=0 ∞ (n + 2)2 xn (c.) n=0 100 (d.) n=1 xn n Problem 1.2. Find the Maclaurin series for f (x). (a.) f (x) = sin (x) + x + 1 (b.) f (x) = x ln(1 + x) (c.) f (x) = cos(3x) + 4 cos(x) (d.) f (x) = ln(6 − x) 1 2 MATH 222 HOMEWORK 2 DUE SEPTEMBER 26, 2011 Problem 1.3. Find the sum of the series exactly. ∞ (a.) n=1 ∞ (b.) n=3 4 n 5n 1 n! Problem 1.4. Use a Taylor series to calculate Problem 1.5. Calculate √ 4 lim x→1 √ 3 8.01 to five decimal places. 15 + x − 2 + (x − 1)2 (x−1) 32 ...
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A2 - MATH 222 HOMEWORK 2 DUE SEPTEMBER 26, 2011 1. P...

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