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    Power series,convergence of sequences of functions, and uniform limits

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    Suppose a sequence of continuous functions, { ?n }, has the property that ?n  ? and
    &#61474;&#61541; > 0, &#61476; &#61540; > 0 such that if | x - y | < &#61540; then &#61474;n, | ?n (x) - ?n (y)| < &#61541; Prove that ? is
    continuous.

    © BrainMass Inc. brainmass.com December 24, 2021, 4:54 pm ad1c9bdddf
    https://brainmass.com/math/real-analysis/power-series-convergence-sequences-functions-uniform-limits-15066

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    Please see the attachment.

    Suppose a sequence of continuous functions, { ƒn }, has the property that ƒn  ƒ and
     > 0,   > 0 such that if | x - y | <  then n, | ƒn (x) - ƒn (y)| <  Prove that ƒ is
    continuous.

    Proof. In order to show that ƒ is ...

    Solution Summary

    This is a proof regarding a sequence of continuous functions.

    $2.49

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