Unit 1: Limits and Continuity

Mastering AP Calculus Unit 1: Limits and Continuity is the foundation for your multiple-choice portion of the exam. If you are looking to score a 4 or a 5 on the AP Calc exam, you need to get all the questions covering limits and continuity correct. This guide covers how to identify limit methods, solve for continuity, and apply the Intermediate Value Theorem with step-by-step video solutions.

Most students struggle because they don’t know which tool to pull out of the toolbox. My Unit 1 flashcards (found in the materials tab at the top of the page) are specifically designed to help you categorize problems instantly, so you can jump straight into the solving process.

Unit 1: Limits and Continuity Flash Cards

Click Here for PDF

Course Content

Limits Overview

Limit Notation (Left-Hand, Right-Hand, Overall)

Lesson Content

0% Complete 0/3 Steps

Left Hand Limit (LHL)

Right Hand Limit (RHL)

Finding Limits Using a Graph

Lesson Content

0% Complete 0/6 Steps

Finding Limits Using a Graph Examples from Actual AP Exams

Method: Finding Limits of a Graph

Example 1: Left Hand Limit

Example 2: Right Hand Limit

Example 3: Overall Limit Exists

Example 4: Overall Limit Does Not Exist

Finding a Limit Using Equations

Lesson Content

0% Complete 0/4 Steps

Finding Limits Using Equations Examples from Actual AP Exams

Identifier: Limit Option 1

Method: Limit Option 1

Example 1: Option 1 (Plug it in)

Lesson Content

0% Complete 0/5 Steps

Factor and Cancel Limit Examples From Actual AP Exams

Identifier: Factor and Cancel

Method: Factor and Cancel

Example 1: Factor and Cancel

Example 2: Factor and Cancel

Lesson Content

0% Complete 0/3 Steps

Identifier: Complex Fraction Limits

Method: Complex Fraction Limits

Example 1: Complex Fraction Limit

Lesson Content

0% Complete 0/3 Steps

Identifier: Square Root Limits

Method: Square Root Limits

Example 1: Square Root Limits

Lesson Content

0% Complete 0/4 Steps

Absolute Value Limit Examples from Actual AP Exams

Identifier: Absolute Value Limits

Method: Absolute Value Limits

Example 1: Absolute Value Limit

Lesson Content

0% Complete 0/4 Steps

Identifier: Trig Function Limits Category 1

Method: Trig Function Limits Category 1

Example 1: Trig Function Limit Category 1

Example 2: Trig Function Limit Category 1

Lesson Content

0% Complete 0/3 Steps

Identifier: Trig Function Category 2

Method: Trig Function Limits Category 2

Example 1: Trig Function Limit Category 2

Lesson Content

0% Complete 0/3 Steps

Identifier: Trig Function Category 3

Method: Trig Function Category 3

Example 1: Trig Function Limit Category 3

Lesson Content

0% Complete 0/7 Steps

Vertical Asymptote Examples from Actual AP Exams

Identifier: Vertical Asymptotes

Method: Vertical Asymptotes

Example 1: Vertical Asymptotes

Example 2: Vertical Asymptotes

Example 3: Vertical Asymptotes

Example 4: Vertical Asymptotes

Lesson Content

0% Complete 0/11 Steps

Horizontal Asymptote Examples From Actual AP Exams

Identifier: Horizontal Asymptotes

Method 1: Leading Behavior

Method 2: Dividing by the Highest Power of x

Example 1: Leading Behavior (Top-Heavy)

Example 2: Leading Behavior (Bottom-Heavy)

Example 3: Leading Behavior (Balanced)

Example 4: Dividing by the Highest Power of x (Top-Heavy)

Example 5: Dividing by the Highest Power of x (Bottom-Heavy)

Example 6: Dividing by the Highest Power of x (Balanced)

Example 7: 2 Different Horizontal Asymptotes (Pro Level)

Lesson Content

0% Complete 0/4 Steps

Squeeze Theorem Examples from Actual AP Exams

Identifier: Squeeze Theorem

Method: Squeeze Theorem

Example 1: Squeeze Theorem

Continuity

Lesson Content

0% Complete 0/1 Steps

Using Definition of Continuity Examples From Actual AP Exams

Lesson Content

0% Complete 0/4 Steps

Determining Continuity Given a Graph Examples from Actual AP Exams

Identifier: Continuity Using a Graph

Method: Continuity Using a Graph

Example 1: Continuity Using a Graph

Lesson Content

0% Complete 0/4 Steps

Determining Continuity of an Equation Examples From Actual AP Exams

Identifier: Continuity Using an Equation

Method: Continuity Using an Equation

Example 1: Continuity Using an Equation

Lesson Content

0% Complete 0/4 Steps

Intermediate Value Theorem Examples from Actual AP Exams

Identifier: Intermediate Value Theorem

Method: Intermediate Value Theorem

Example 1: Intermediate Value Theorem

Optimized by Optimole