About This Chapter
Limits - Chapter Summary and Learning Objectives
This chapter is designed to help you learn to define, write, graph, and understand limits of functions in calculus. The videos provide clear explanations of all the core concepts, and the short self-assessments after each lesson give you the opportunity to practice and hone your skills. The tools here will teach you everything you need, including:
- How to use notation to determine limits
- Graphing and interpreting limits
- The proper way to write one-sided limits
- Definition and examples of squeeze theorem
|Understanding Limits: Using Notation||Learn to identify limits by using notation.|
|Using a Graph to Define Limits||Discover how to graphically represent limits and see examples.|
|One-Sided Limits and Continuity||Write one-sided limits and determine how they relate to continuity.|
|How to Determine the Limits of Functions||Learn to determine the limits of functions.|
|Understanding the Properties of Limits||Explore the properties of limits.|
|Squeeze Theorem: Definition and Examples||Define the squeeze theorem and get examples.|
|Graphs and Limits: Defining Asymptotes and Infinity||Learn to define limits of asymptotes and infinity.|
1. Understanding Limits: Using Notation
Join me on a road trip as we define the mathematical notation of limits. As time goes by and I traverse hills and highways, the limit of my speed changes. Learn how to write these limits in this lesson.
2. Using a Graph to Define Limits
My mom always said I tested the limits of her patience. Use graphs to learn about limits in math. You won't get grounded as we approach limits in this lesson.
3. One-Sided Limits and Continuity
Over the river and through the woods is only fun on a continuous path. What happens when the path has a discontinuity? In this lesson, learn about the relationship between continuity and limits as we walk up and down this wildlife path.
4. Infinite Limit: Definition & Rules
In this lesson, we learn how to interpret limits whose values are unbounded, or infinite. We'll look at a few examples to show you how to compute these infinite limits.
5. How to Determine the Limits of Functions
You know the definition of a limit. You know the properties of limits. You can connect limits and continuity. Now use this knowledge to calculate the limits of complex functions in this lesson.
6. Understanding the Properties of Limits
Graphically we can see limits, but how do we actually calculate them? Three words: Divide and Conquer. In this lesson, explore some of the properties that we can use to find limits.
7. Squeeze Theorem: Definition and Examples
In the Kingdom of Rimonn there are three rivers. In this lesson, learn how these waterways demonstrate the power of the squeeze theorem for finding the limits of functions.
8. Graphs and Limits: Defining Asymptotes and Infinity
Infinity is a hard concept to understand and the word asymptote is pretty intimidating. But this fun lesson will make both seem like a walk in the park as it defines both and shows their relationship using a graph.
9. How to Determine if a Limit Does Not Exist
In this lesson, we'll discuss when a limit does not exist. We'll begin with a description of each type of limit and when that particular type does not exist. Then, we'll use a graph to show how to recognize when a limit does not exist based on the graph of a function ''f.''
10. What is L'Hopital's Rule?
A Swiss mathematician and a French mathematician walk into a bar ... and they walk out with the famous L'Hopital's rule for finding limits. In this lesson, learn what these two mathematicians came up with and how to use it to avoid the limit of zero divided by zero!
11. Applying L'Hopital's Rule in Simple Cases
L'Hôpital's rule may have disputed origins, but in this lesson you will use it for finding the limits of a range of functions, from trigonometric to polynomials and for limits of infinity/infinity and 0/0.
12. Applying L'Hopital's Rule in Complex Cases
L'Hôpital's rule is great for finding limits, but what happens when you end up with exactly what you started with? Find out how to use L'Hôpital's rule in this and other advanced situations in this lesson.
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Other chapters within the AP Calculus AB: Exam Prep course
- Graph Basics
- The Basics of Functions
- How to Graph Functions
- Continuity of Functions
- Understanding Exponentials & Logarithms
- Using Exponents and Polynomials
- Properties of Derivatives
- The Derivative at a Point
- The Derivative as a Function
- Second Derivatives
- Using Derivatives
- Computing Derivatives
- Properties of Definite Integrals
- Applications of Integrals
- Using the Fundamental Theorem of Calculus
- Understanding & Applying Integration Techniques
- Approximating Definite Integrals
- Using a Scientific Calculator for Calculus
- About the AP Calculus Exam
- AP Calculus AB Flashcards