Question: Need help proving this. Let f n : X R be a sequence of continuous functions on a metric space (X,d). If the sequence {f

Need help proving this.

Let f_n : X R be a sequence of continuous functions on a metric space (X,d). If the sequence {f_n(x)} converges uniformly to a function f(x), prove directly from the definiton of uniform convergence that f(x) is continuous.

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