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Let f: (0,1) -> R be uniformly continuous and let Xn be in (0,1) be such...

Let f: (0,1) -> R be uniformly continuous and let Xn be in (0,1) be such that Xn-> 1 as n -> infinity. Prove that the sequence f(Xn) converges
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Here bold N stand for the set of all natural numbers.

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