yes, this example is very good for us to understand the meaning of uniformly continuous. if we would like to Prove a fuction is not uninformly cintinuous, we should find out an esilon(e), and choose x and y in the domain. such that for all delta(d), |x-y|=e holds. I always find difficulty to find out e, x and y. are there any skill for us to find out them?

Also could you give the proof of the example, f(x)=sin(1/x) is not uniformly continuous on (0,1)