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    Uniformly convergent sequence proof

    1. Homework Statement Let f_n(x) be a sequence of functions that converges uniformly to f(x) on the interval [0, 1]. Show that the sequence e^{f_n(x)} also converges uniformly to e^{f(x)} on [0,1]. 2. Homework Equations The definition of uniform convergence. 3. The Attempt at a...