While beginning calculus students often pick up derivatives and integrals (and the associated formulas) easily, the delta-epsilon definitions of limits and continuity are a well known stumbling block for many. I've been told that the difficulty stems from that being the first place math beginners really see nested quantifiers: (forall epsilon)(exists delta)(...). In logic though, nested quantifiers are fundamental. I don't know what happens if someone tries to study logic without first having studied calculus. Maybe it's a good idea, but few people do it that way.