Unit 1
The vocabulary the rest of calculus is written in. A limit describes approach rather than arrival, which is why it can exist where the function does not.
20 problems · Questions and worked solutions.
Lesson 1.1 · AP topics 1.1–1.4 and 1.9
Describe what a function approaches, distinguish a limit from a function value, and connect graphical and numerical evidence.
Reading reference: Larson & Edwards §§1.1–1.2; one-sided limit ideas from §1.4
Read lesson →Lesson 1.2 · AP topics 1.5–1.7
Choose a valid algebraic method, interpret the indeterminate form 0/0, and justify each simplification.
Reading reference: Larson & Edwards §1.3
Read lesson →Lesson 1.3 · AP topics 1.8–1.9; trigonometric limit applications of 1.6
Trap a difficult function between simpler bounds, evaluate foundational trigonometric limits, and connect formulas with graphical and numerical evidence.
Reading reference: Larson & Edwards §1.3
Read lesson →Lesson 1.4 · AP topics 1.10–1.13 and 1.16
Test continuity at a point and on an interval, repair removable holes, and use the Intermediate Value Theorem to justify existence claims.
Reading reference: Larson & Edwards §1.4
Read lesson →Lesson 1.5 · AP topics 1.14–1.15
Separate unbounded output near a finite input from end behavior, use sign analysis, and identify vertical and horizontal asymptotes.
Reading reference: Larson & Edwards §§1.5, 3.5 (end behavior moved into Unit 1)
Read lesson →Work through questions with a tutor and get help with the steps you find difficult.
Get help with this topic