e4-sample

e4-sample - power series on its interval of convergence....

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Math 170, Section 01, Exam 4, Sample Monday, November 30th, 2009 Name (PRINT clearly): You will receive full credit only if you show all work and explain all steps. 1. Find the radius and interval of convergence of the following power series. (a) n =1 2 n +1 x n (b) n =1 n ! n n x n (c) n =1 x n 2 n + 1 2. Find a power series expansion (centered at the origin) for the function f ( x ) = 2 + x 2 - x . Compute the radius of convergence and determine the interval of convergence of the power series. 3. Find the radius and interval of convergence of the power series n =0 n 1 + n 2 x n . Let f denote the function deﬁned by this
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Unformatted text preview: power series on its interval of convergence. Find a power series representation f ( x ). Let F ( x ) denote an anti-derivative of f , ﬁnd the power series representation for F and f Compute their radius and interval of convergence. 4. Let f ( x ) = sin(2 x ). Find the 8th degree Taylor polynomial for f centered at the origin. Estimate the error in approximating sin(1) using this Taylor polynomial. How large a degree is required in order to approximate sin(1) to within 4 decimal places. 1...
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This document was uploaded on 10/29/2011 for the course MATH 170 at Vanderbilt.

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