(a) Let f be differentiable on (a, b) and suppose that f'(t)| < m for some m > 0 and for all t e (a, b). Prove that f is uniformly continuous on (a, b).

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Real Analysis 1
3. Choose and work either (a) or (b), NOT BOTH.
(a) Let f be differentiable on (a, b) and suppose that f'(t)| < m for some m > 0
and for all t e (a, b). Prove that f is uniformly continuous on (a, b).
(b) Let f and g be uniformly continuous on a set E C R. Prove that 2f + 3g is
uniformly continuous on E.
Transcribed Image Text:3. Choose and work either (a) or (b), NOT BOTH. (a) Let f be differentiable on (a, b) and suppose that f'(t)| < m for some m > 0 and for all t e (a, b). Prove that f is uniformly continuous on (a, b). (b) Let f and g be uniformly continuous on a set E C R. Prove that 2f + 3g is uniformly continuous on E.
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