Let f(x)=x^2*sin(1/x) for x not=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

Let f(x)=x^2*sin(1/x) for x not=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?