-nx For n EN, consider the function f(x) = e on the interval [0, ∞). Let f(x) limn→∞ fn(x) for x = [0, ∞). (a) Describe the function f(x). Is continuous on [0, ∞). (b) Show that the sequence of functions (fn) does not converge uniformly on [0, ∞). (c) Does the sequence (fn) converge uniformly on the open interval (0, ∞)? (d) Show that for any a > 0, fn converges uniformly to f on the interval [a, ∞). =

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