Everything You MUST Know Unit 1: Limits & Continuity

This lesson covers everything students need to know for Unit 1 of AP Calculus AB & BC: Limits and Continuity. It introduces limit notation, one‑sided limits, limit laws, algebraic techniques, continuity, asymptotes, infinite limits, and the Intermediate Value Theorem.

Summary

Unit 1 emphasizes evaluating limits algebraically and graphically, determining when limits exist, analyzing continuity, and justifying conclusions on AP free‑response questions. Unit 1 represents about 10–12% of the AP Calculus AB exam and 4–7% of the AP Calculus BC exam, making it a foundational unit that supports all later topics in calculus.

Key Takeaways

• A limit describes the value a function approaches as x gets close to a number, not necessarily the value of the function at that point.

• One‑sided limits use x → c⁻ (from the left) and x → c⁺ (from the right).

• Limit laws allow limits to be evaluated by splitting sums, differences, products, quotients, and constants.

• When direct substitution gives 0/0, limits can often be evaluated by factoring, using conjugates, or finding a common denominator.

• The special trigonometric limits sin(x)/x → 1 and (1 − cos x)/x → 0 as x → 0 must be memorized.

• A limit does not exist if one‑sided limits are unequal, the function goes to infinity, or the function oscillates.

• A function is continuous at x = c if the function value exists, the limit exists, and the limit equals the function value.

• The Intermediate Value Theorem (IVT) guarantees the existence of a function value but does not tell where it occurs.

Transcript

All right guys, Mr. Antonucci here. In this video I’m going to teach you everything you need to know for Unit 1 in AP Calculus. 

This unit deals with limits and continuity.