1. The problem statement, all variables and given/known data Define f(x)=sin(x)sin(1/x) if x does not =0, and 0 when x=0. Have to prove that f(x) is continuous at 0. 2. Relevant equations We can use the definition of continuity to prove this, I believe. 3. The attempt at a solution I know from previous homework assignments that sin(x) is continuous at 0, but sin(1/x) is not. Is there a way I can use this knowledge to help me solve this problem, or do I need to start from scratch? If I need to start from scratch, do I apply the definition of continuity?