This was a problem from my calculus final a year ago that I've wanted to see for a while:
Use the delta-epsilon definition of a limit to prove that the limit as x approaches 0 of f(x) = sin(x)/(x^2 +1) is 0.
I tried using the squeeze theorem in an effort to bound sin(x), because I really don't know how to deal with sin(x) in a delta epsilon proof. This problem has just been on my mind for a while. Thanks for the help!