The closer I get to 5, the closer f of x seems to be getting to 10. The closer I get to 5, the closer f of x seems to be getting to 10. You might fairly intuitively make the claim that the limit of f of x as x approaches 5 really is equal to 10. It looks that way. What we're going to do is use the epsilon delta definition to actually prove it. The way that most of these proofs typically go is we define delta in the abstract. We essentially try to come up with a way that given any epsilon, we can always come up with a delta.