Problem 1 "Prove that lim[x->2] 1/x = 1/2." You have to do it using the epsilon-delta-definition of a limit. And the truth is, I don't 'get' those epsilon-delta limits at all (except the easiest kind. Sort of). My book (Stewart's Calculus) either doesn't explain them very well, or I'm just missing something obvious. Can anyone help me here? Problem 2 "If the function f is defined by f(x) = 0 if x is rational; 1 if x is irrational, prove that lim[x->0] f(x) does not exist." Ehm, here I have simply no idea where even to start. My guess would be that there are an infinite number of rational and irrational numbers close to zero, which means f(x) infinitely oscillates, but how would one go about proving this? Is my guess even right?