1. The problem statement, all variables and given/known data Prove that the limit as x->c of f(x) = L if and only if both one sided limits also = L 2. Relevant equations Has to be an epsilon delta proof 3. The attempt at a solution Being an if and only if, I have to do two cases : If A, then B. and if NOT A, then NOT B, logically. Case 1: Let lim x->c from the left be L, and lim x->c from the right be L. then if [tex] c - \delta < x < c then |f(x) - L| < \epsilon [/tex] and if [tex] c < x < c + \delta then |f(x) - L| < \epsilon [/tex] Case 2: Let lim x->c from the left = M, and lim x->c from the right = N. This is all I have really rationalized I am kind of stumped how to do a rigorous proof of this, I.e. I know how to do specific proofs but not a rigorous general proof. \ Can anyone offer any help / a starting point =/ ?