Let a $\in R$, $f:(a,+\infty)$ -> R be a continuous function, and assume that the limit of f(x) as n goes to $+\infty$ exists. Show that f is uniformly continuous. Is the converse true?
I'm stuck on the second question. I was able to prove the first part, but am unsure mainly whether I should be looking for a counterexample or to prove a contradiction.