How do i prove that x*sin(x) is not uniformly continuous?
and so for small enough and there is a independent of such that:
So however small we make there is an which makes as large as we like.
Note: The term can be made independent of as it stands in place of a remainder term of a Taylor series which is the product of a constant , and a circular trig function at a point in all of which which is bounded by . If the reader needs the detail they can develop it them selves.