1. The problem statement, all variables and given/known data limit as x goes to 0 of x^2 sin(1/x)=0 2. Relevant equations Use delta-epsilon proof 3. The attempt at a solution So |f(x)-L|=|x^2 sin(1/x)|=|x^2||sin(1/x)| and I know that sin(1/x) is bounded by one. I am not sure how to finish because of the x^2.