Question: Let f be a sequence of continuous, real valued functions on [0, 1] which converges uniformly to f. Prove that limnx fn(n) = f(1/2)

Let f be a sequence of continuous, real valued functions on [0,

Let f be a sequence of continuous, real valued functions on [0, 1] which converges uniformly to f. Prove that limnx fn(n) = f(1/2) for any sequence {n} which converges to 1/2. (b) Must the conclusion still hold if the convergence is only point-wise? Explain.

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