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Given a metric space Y, a point L in Y, and f:[0,infinity) -> Y, f has...

Given a metric space Y, a point L in Y, and f:[0,infinity) -> Y, f has a limit L element of Y at infinity, written, if for every epsilon greater than 0 there is a C>0 such that if x>C then d(f(x),L) < epsilon. Prove, if f:[0,infinity) -> Y is continuous and has a limit at infinity, then f is uniformly continuous.

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