4130hw8 - (3) Find the radius of convergence of the power...

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4130 HOMEWORK 8 Due Tuesday May 3 (1) Let f n : A R be functions which converge uniformly on A to a function f . Let x 0 be a cluster point of A . Suppose lim x x 0 f n ( x ) exists for all n . Let L n = lim x x 0 f n ( x ). (a) Show that the sequence { L n } converges. (b) Show that lim x x 0 f ( x ) exists and equals lim n →∞ L n . (2) Section 7.3.4 Exercise 11.
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Unformatted text preview: (3) Find the radius of convergence of the power series f ( x ) = ∞ X n =0 ( n 2 + n + 1) x n . Find a pair of polynomials p ( x ) and q ( x ) such that f ( x ) = p ( x ) q ( x ) within its radius of convergence. 1...
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This note was uploaded on 09/22/2010 for the course MATH 413 at Cornell University (Engineering School).

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