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Unformatted text preview: R be a continuous function. If lim x f ( x ) exists and is nite, then prove that f is actually uniformly continuous. (Note that Theorem 19.2 does not apply because the domain of f is not bounded.) Problem 5: Determine the radius of convergence of the series n =0 a n x n , where: a n = 5 n , if n is odd 1 2 n , if n is even Problem 6: Dene functions f n : R R by f n ( x ) = cos n x . Note that these functions are all continuous. Prove that: (a) lim n f n ( x ) = 0 if x is not a multiple of . (b) lim n f n ( x ) = 1 if x is an even multiple of . (c) lim n f n ( x ) does not exist if x is an odd multiple of ....
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This note was uploaded on 03/18/2012 for the course MATH 67 taught by Professor Schilling during the Fall '07 term at UC Davis.
- Fall '07