Limits and Continuity Overview — AP Calculus AB
1. Unit at a Glance
Limits are the idea that lets calculus answer questions about instantaneous change, which cannot be solved with algebra alone. This unit progresses from intuitive conceptual introductions, to formal limit calculation techniques, to connecting limits to continuity and key calculus theorems.
Mastery of this unit is non-negotiable: every future concept in AP Calculus AB (including derivatives and integrals) is formally defined using limits. The sub-topics below are ordered to build your knowledge incrementally from basics to application.
Common Pitfalls
Why: $f(a)$ is the function's value at the point, while the limit describes behavior near the point, which can be very different.
Why: Most students only check that the limit exists, missing that the limit must equal $f(a)$ and $f(a)$ must be defined.
Why: IVT only holds for continuous functions on a closed interval, so misapplication leads to wrong conclusions.