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Real Analysis : Uniform Convergence

Let (f_n) be a sequence of diffrentiable functions defined on the closed interval [a,b] and assume (f'_n) converges uniformly on [a,b]. Prove that if there exists a point xo belong to [a,b] where f_n(xo) is convergent, then (f_n) converges uniformly on [a,b].

Solution Summary

Uniform convergence is investigated.

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