[See Solution] Suppose (f_n) is a sequence of continuous functions on an interval I that converges uniformly on I to a function f. If (x_n) ⊆ I converges


Question: Suppose \(\left(f_{n}\right)\) is a sequence of continuous functions on an interval \(I\) that converges uniformly on \(I\) to a function \(f\). If \(\left(x_{n}\right) \subseteq I\) converges to \(x_{0} \in I\), show that \(\lim \left(f_{n}\left(x_{n}\right)\right)=f\left(x_{0}\right)\).

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