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: 14 x + 16 x 264 x 3 + ··· = ∞ X n =0 (1) n (4 x ) n Hint: Use ∑ ∞ n =0 x n = 1 / (1x ) for1 < x < 1. 5. In parts (a)–(c), ﬁnd a power series representation for the function and determine the radius of convergence. (a) ln(7x ) (b) x 3 ( x2) 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) ex 2 / 3 Hints: Part (a): sin 2 ( x ) = (1cos 2 x ) / 2, Part (b): Recall that cosh x = ( e x + ex ) / 2. 7. In parts (a)–(b), use series to evaluate the limit. (a) lim x → xarctan x x 3 (b) lim x → 1cos x 1 + xe x...
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 Fall '08
 Burbidge,John
 Power Series, Taylor Series, Mathematical Series, power series representation, Koray Karabina

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