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Unformatted text preview: =1 n 2 2 n = 6 by evaluating this power series at x = 1 / 2. 4. Determine the interval of convergence and the sum of the series: 1-4 x + 16 x 2-64 x 3 + = X n =0 (-1) n (4 x ) n Hint: Use n =0 x n = 1 / (1-x ) for-1 < x < 1. 5. In parts (a)(c), nd a power series representation for the function and determine the radius of convergence. (a) ln(7-x ) (b) x 3 ( x-2) 2 (c) arctan ( x/ 3) 6. Find Maclaurin series (Taylor series centered at 0) for the functions in parts (a)(c). (a) sin 2 ( x ) (b) cosh x (c) e-x 2 / 3 Hints: Part (a): sin 2 ( x ) = (1-cos 2 x ) / 2, Part (b): Recall that cosh x = ( e x + e-x ) / 2. 7. In parts (a)(b), use series to evaluate the limit. (a) lim x x-arctan x x 3 (b) lim x 1-cos x 1 + x-e x...
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- Fall '08