Suppose {n} is a sequence of functions, differentiable on [a, b] and such that {fn (xo)} converges for some point xo on [a, b]. If {f'n} converges uniformly on [a, b], then {f} converges uniformly on [a, b], to a function f, and (a ≤ x ≤ b). f'(x) = lim f'(x) n→∞0 Can we replace [a, b] by [0, ∞o)? Why?

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