Let f(x) be continous on the real number line. Suppose that lim(x-> infinity) f(x) = 0 and lim(x-> negative infinity) f(x) = 0. Show that f(x) is unformly continous or else give a counterexample.
Why does it follow that it is uniformly continuous on the interval [-M,M]? I can see the intervals (-inf,-M] and [M,inf) , since the delta neighborhood of x values need not depend on x, only epsilon as the slope varys less and less towards the ends of the domain.