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← AP Calculus AB01

Limits and Continuity

Calculus is built on one question: what does a function approach as you get arbitrarily close to a point, even if the function never reaches it? This unit answers that question precisely, and that precision is not optional. A limit is a formal claim about behavior near a point, and you will learn to read that claim from graphs, tables, and algebraic expressions. Continuity is the property a function has when its limit and its value at a point agree, and it matters because every major theorem in this course requires it. The Intermediate Value Theorem closes the unit by showing what continuity actually guarantees.

10–12% of exam

Start with 1.1 →See all topics ↓
All UnitsNext02Differentiation: Definition and Fundamental Properties

Topics

1.1
Introducing Calculus: Can Change Occur at an Instant?
1.2
Defining Limits and Using Limit Notation
1.3
Estimating Limit Values from Graphs
1.4
Estimating Limit Values from Tables
1.5
Determining Limits Using Algebraic Properties of Limits
1.6
Determining Limits Using Algebraic Manipulation
1.7
Selecting Procedures for Determining Limits
1.8
Determining Limits Using the Squeeze Theorem
1.9
Connecting Multiple Representations of Limits
1.10
Exploring Types of Discontinuities
1.11
Defining Continuity at a Point
1.12
Confirming Continuity over an Interval
1.13
Removing Discontinuities
1.14
Connecting Infinite Limits and Vertical Asymptotes
1.15
Connecting Limits at Infinity and Horizontal Asymptotes
1.16
Working with the Intermediate Value Theorem (IVT)

Big question 1 of 3

Can change occur at an instant?

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