AP®︎ Calculus AB Unit 1: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 1 of AP Calculus AB – Limits and Continuity.
Unit 1: Limits and Continuity
Explore how limits help analyze change, continuity, and asymptotic behavior.
Begin with Topic 1.1: Introducing Calculus: Can...To review Unit 1, go through each of the 16 topics below.
Everything you actually need to know for your Unit 1 test, pulled directly from the AP® Calculus AB curriculum.
Introducing Calculus: Can Change Occur at an Instant?
Introducing Calculus: Can Change Occur at an Instant?
- Average Rate of Change
- From Secant Lines to the Instantaneous Rate of Change
- What the Limit Is Doing
Defining Limits and Using Limit Notation
Defining Limits and Using Limit Notation
- What a Limit Is
- Limit Notation and How to Read It
- Representing Limits Three Ways
Estimating Limit Values from Graphs
Estimating Limit Values from Graphs
- What a Limit Is From a Graph
- Estimating a Limit From a Graph
- When a Limit Does Not Exist
Estimating Limit Values from Tables
Estimating Limit Values from Tables
- What It Means to Estimate a Limit from a Table
- One-Sided Limits
- How to Estimate from a Table
Determining Limits Using Algebraic Properties of Limits
Determining Limits Using Algebraic Properties of Limits
- The Limit Laws
- Direct Substitution and When It Works
- A Step-by-Step Process for Algebraic Limits
Determining Limits Using Algebraic Manipulation
Determining Limits Using Algebraic Manipulation
- When Direct Substitution Fails
- Factoring and Canceling Common Factors
- Rationalizing with Conjugates
Selecting Procedures for Determining Limits
Selecting Procedures for Determining Limits
- How to Choose a Method to Evaluate a Limit
- Limits from a Graph
- Limits from a Table
Determining Limits Using the Squeeze Theorem
Determining Limits Using the Squeeze Theorem
- What the Squeeze Theorem Says
- The Three Conditions You Must Check
- A Classic Oscillation Example
Connecting Multiple Representations of Limits
Connecting Multiple Representations of Limits
- What a Limit Means Across Representations
- Graphical Representation
- Numerical Representation
Exploring Types of Discontinuities
Exploring Types of Discontinuities
- What Continuity at a Point Means
- The Three Types of Discontinuities
- How to Classify a Discontinuity
Defining Continuity at a Point
Defining Continuity at a Point
- What It Means for a Function to Be Continuous at \( x = c \)
- The Three Conditions Broken Down
- What This Looks Like on a Graph
Confirming Continuity over an Interval
Confirming Continuity over an Interval
- What It Means for a Function to Be Continuous on an Interval
- Function Types That Are Automatically Continuous (on Their Domains)
- How to Determine Whether a Function Is Continuous on a Given Interval
Removing Discontinuities
Removing Discontinuities
- Removable Discontinuities
- How to Remove a Hole in a Rational Function
- Making a Piecewise Function Continuous
Connecting Infinite Limits and Vertical Asymptotes
Connecting Infinite Limits and Vertical Asymptotes
- Infinite Limits and What They Mean
- Vertical Asymptotes and Their Connection to Infinite Limits
- How to Find Vertical Asymptotes Algebraically
Connecting Limits at Infinity and Horizontal Asymptotes
Connecting Limits at Infinity and Horizontal Asymptotes
- Limits at Infinity and End Behavior
- Horizontal Asymptotes and What They Mean
- Finding Horizontal Asymptotes for Rational Functions
Working with the Intermediate Value Theorem (IVT)
Working with the Intermediate Value Theorem (IVT)
- The Intermediate Value Theorem
- The Most Tested Case: Proving a Root Exists
- The Two Conditions You Must Check
Notes
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