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Proof of Uniform Convergence of a Sequence

Let f be a function such that |f'(x)|<Mon R and let fn(x)=f(x = 1/x) for n E R. Prove that fn --> f uniformly on R .

Please show each step! Thanks
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A Proof of the Uniform Convergence of a Sequence is provided. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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