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    Sequence of Continuous Function, Uniform Convergence and Pointwise Convergence

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    Let {fn(x)} n-1 ---> infinity be a sequence of continuous functions [0,1] that converges uniformly.
    a) Show that there exists M>0 such that
    |fn(x)|<= M (nЄI 0<x<1)

    b) Does the result in part (a) hold if uniform convergence is replaced by pointwise convergence?

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    https://brainmass.com/math/graphs-and-functions/uniform-convergence-pointwise-convergence-58108

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    Sequences of Continuous Function, Uniform Convergence and Pointwise Convergence are investigated. The solution is detailed and well presented.

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