Where calculus begins. Learn what a limit is and how to evaluate one graphically, numerically, and algebraically; define continuity and classify discontinuities; connect limits to asymptotes; and apply the Intermediate Value Theorem.
Six ways to master Unit 1 — pick whichever fits how you like to study.
All 16 topics from the College Board CED, in order.
Unit 1 builds the single idea the rest of calculus depends on: the limit. It opens with the motivating question — can change occur at an instant? — and defines what it means for a function to approach a value. You'll learn to estimate limits from graphs and tables, evaluate them with the limit laws and algebraic manipulation (factoring and rationalizing to resolve the indeterminate form 0/0), and handle special cases with the Squeeze Theorem.
The second half turns to continuity. You'll apply the three-part definition of continuity at a point, confirm continuity over intervals, and classify removable, jump, and infinite discontinuities — even redefining a function to remove a hole. Limits then explain asymptotes: infinite limits give vertical asymptotes, and limits at infinity give horizontal asymptotes. The unit closes with the Intermediate Value Theorem, which guarantees a continuous function takes on every value between two of its outputs.
On the exam this unit is 10–12% for AB and 4–7% for BC, and takes about 22 class periods (AB). The four mathematical practices below run through every topic: