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**worc3247** Let $\displaystyle f: (a,b] \rightarrow \mathbb{R}$ be a real valued continuous function defined on the half open interval (a,b]. Assume that f has the property than whenever $\displaystyle (x_n)$ is a cauchy sequence contained in the open interval (a,b], then $\displaystyle (f(x_n))$ is a cauchy sequence.

Prove that the one sided limit:

$\displaystyle \lim_{x \to a+} f(x)$exists and deduce that f is uniformly continuous.

So far all I have is the definition of a cauchy sequence and the definition of a right-hand sided limit, but can't see how to start this question. Help?