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Uniform convergence

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Note: all of the following _n denote n as a subscript.

Suppose {f_n} from n = 0 to infinity, is a sequence of functions converging uniformly to a function f on an interval [a,b]. Also assume that the sequence has a uniform bound i.e. there exists M1 such that for all positive integers n, | f_n(x) | < = M1 for all x belonging to [a,b], and that there exists M2 such that | f(x) | < = M2 for all x belonging to [a,b], i.e. f is also bounded. Show that the sequence f_n^2 converges uniformly to f^2.

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Solution Summary

This solution helps explore uniform convergence within the context of functions & calculus

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