Question: Suppose (fn) is a sequence of continuous functions on an interval I that converges uniformly on I to a function f. If (xn) I

Suppose (fn) is a sequence of continuous functions on an interval I that converges uniformly on I to a function f. If (xn) ⊂ I converges to x0 ∈ I, show that lim(fn(xn)) = f (x0).

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