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Sequence of Continuous Function, Uniform Convergence and Pointwise Convergence

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 (n&#1028;I 0<x<1)

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