I have two homework problems that I was hoping someone could help me with:

1. Prove that f(x)= sin(1/x), where x can't equal zero and f(0)=0 is not continuous at x=0 by finding an ε for which there is no reply.

and

2. At what values of x is

f(x) = (piecewise defined) 0, if x is irrational or = sinx if x is rational

Thank you