hw9 - (i) f ( x ) = xe 2 x centred at a = 0 (ii) f ( x ) =...

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CALCULUS 1501 WINTER 2010 HOMEWORK ASSIGNMENT 9. Due March 26. 9.1. Find the radius and the interval of convergence of the following power series (i) X n =0 5 n x 3 n . (ii) X n =0 2 n + 1 3 n 2 + 2 ( x - 1) 3 n . (iii) X n =0 3 n 2 x n 2 . 9.2. Prove that if lim n →∞ n p | c n | = c , then the radius of convergence of the series c n ( x - a ) n equals 1 /c . 9.3. Compute X n =0 n (0 . 5) n . 9.4. Find a power series representation (centred at x = 0) of the function f ( x ) = x 2 (1 - 2 x ) 2 and find its radius of convergence. 9.5. Find the Taylor series for
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Unformatted text preview: (i) f ( x ) = xe 2 x centred at a = 0 (ii) f ( x ) = 1 x 2 centred at a = 1. (iii) f ( x ) = ln(1 + x 2 ) centred at a = 0. 9.6. Suppose that the function f ( x ) can be represented by a power series f ( x ) = ∞ X n =0 ( x + 1) n 2 n . Find the first two terms of the Taylor series of f ( x ) centred at x = 0. (Hint: use Prob-lem 9.3). 1...
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This note was uploaded on 07/15/2010 for the course MATH 1501 taught by Professor Shafikov during the Winter '10 term at UWO.

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