📊 Chapter 1: Limits and Continuity

AP Exam Weight: 10-12% | Multiple Choice: 4-6 questions | Free Response: Part of several questions

📚 Table of Contents

1. Understanding Limits
2. Limit Laws
3. Continuity
4. Special Limits
5. Techniques

📝 Chapter Overview

This chapter covers the foundational concepts of calculus - limits and continuity. Understanding these concepts is crucial as they form the basis for derivatives and integrals.

🎯 Learning Objectives

After completing this chapter, you should be able to:

• Evaluate limits using various methods
• Analyze one-sided limits
• Identify and classify discontinuities
• Apply the Intermediate Value Theorem
• Use the Squeeze Theorem

📚 Key Concepts

1. Understanding Limits 📊

What is a Limit?

A limit describes what a function approaches as x gets closer and closer to a specific value. Think of it as:

• Walking towards a doorway but never quite reaching it
• Zooming in on a graph closer and closer
• Getting arbitrarily close to a value
• The “tendency” of a function

Limit Definition

limx → af(x) = L means the values of f(x) get arbitrarily close to L as x gets arbitrarily close to a

Intuitive Understanding

• Values approach L from both sides