Where calculus begins. Before derivatives, before integrals, there's one quiet idea that makes all of it work — what a function is heading toward. Five interactive lessons that turn limits, the algebra of computing them, and continuity into things you can watch happen — built for your very first encounter with calculus.
Work them in order for a full walkthrough of the unit, or jump straight to whatever's giving you trouble.
The idea that starts everything: what a function is heading toward, which can differ from where it actually is. Drag walkers toward a hole, shrink a speed window to an instant, and learn to read the three separate questions every graph asks.
From seeing to doing. Substitute first — and when that gives the strange symbol 0/0, dig: factor and cancel, or multiply by the conjugate, and watch the hidden hole fill in. Then diagnose any limit and pick the right tool.
Some limits resist all algebra — like sin x over x. Trap the stubborn function between two friendlier ones that meet at a point, and it has nowhere to go but the same place. The sandwich, animated.
What it means for a graph to flow through a point with no hole, jump, or break — and the full zoo of ways it can fail. Diagnose each discontinuity and name which part of the definition broke.
Limits that run to infinity, and infinity running back: vertical asymptotes, end behavior, and the degree race that decides horizontal ones. Then the Intermediate Value Theorem — why a sign change traps a root.
Put it together the way the real AP exam does — mixed multiple choice first, then full free-response — with a one-page formula sheet to review from.
Thirty multiple-choice questions across all five lessons — limits, the Squeeze Theorem, continuity, asymptotes, and the IVT — pulled in fresh batches with worked explanations that name every distractor’s mistake, plus two chained free-response problems in the classic AP Section II mold with typed answers graded against the rubric.
Begin practicing →