Let f(x)=x sin() for x 0 and f(0) = 0. (a) Observe f is continuous on R; see Exercises 17.3(f) and 17.9(c). (b) Why is f uniformly continuous on any bounded subset of R? (c) Is f uniformly continuous on R?

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Let f(x)=x sin() for x 0 and f(0) = 0.
(a) Observe f is continuous on R; see Exercises 17.3(f) and 17.9(c).
(b) Why is f uniformly continuous on any bounded subset of R?
(c) Is f uniformly continuous on R?
Transcribed Image Text:Let f(x)=x sin() for x 0 and f(0) = 0. (a) Observe f is continuous on R; see Exercises 17.3(f) and 17.9(c). (b) Why is f uniformly continuous on any bounded subset of R? (c) Is f uniformly continuous on R?
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