AP Unit 1: Limits and Continuity
Find these readings by topic
This earlier reading list remains available with its complete tasks. The current book places these resources in the following topic chapters:
- Functions, graphs, and the language of change →
Explain how instantaneous change arises from average rates; use selected prerequisite review as needed before beginning the native BC path.
- Limits and continuity →
Connect approaching values across representations and justify continuity, asymptotes, and intermediate outputs.
Read nearby behavior carefully, connect four representations, and justify limits and continuity before differentiating.
Follow the topics below, then try the 30 unit problems before opening the separate step-by-step solutions.
Course outline · Teacher guidance
This unit includes the shared AB core explicitly inside the BC book, with BC extensions where required. Each shared topic links to its AB source.
- 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) ↗