Question: Let f : (a, b) R be differentiable on (a, b) and suppose there exists an M > 0 such that |f (x)| M for

Let f : (a, b) R be differentiable on (a, b) and suppose there exists an M > 0 such that |f (x)| M for all x (a, b). Prove that f is uniformly continuous on (a, b). Moreover prove that lim xa+ f(x) and lim xb f(x) both exist.

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