About This Chapter
Overview of Limits of Functions - Chapter Summary
Within this chapter, our experts explain the overview of limits and functions. Become familiar with how to use a graph to define limits, properties of limits, and determining if a limit does not exist. Once you finish this chapter, you should be able to:
- Understand limits using notation
- Analyze graphs to define limits
- Become familiar with one-sided limits and continuity
- Define infinite limit and squeeze theorem
- Analyze the properties of limits
- Understand the limits of functions and how to determine if a limit does not exist
- Define asymptotes and infinity using graphs
- Detect asymptotes using limits
- Understand how to compare relative magnitudes of functions
Use the timeline tags within the videos to review a concept you are unfamiliar with. The Dashboard allows you to track your progress and see the overview of the course. Once you have completed a lesson, make sure to complete the self-assessment quiz to make sure you fully understand each concept.
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. Symbolic Logic: Definition & Examples
In this lesson, we'll cover the definition of symbolic logic, introduce some of the common symbols used, and work out some truth tables for a few logical expressions.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.''
11. Finding Asymptotes Using Limits
A function can have a vertical asymptote, a horizontal asymptote and more generally, an asymptote along any given line (e.g., y = x). In this lesson, we learn how to find all asymptotes by evaluating the limits of a function.
12. Comparing Relative Magnitudes of Functions
The magnitude of a function can be thought of as how it behaves when it is graphed. In this lesson, we will investigate five function types and how to compare their magnitudes.
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Other chapters within the AP Calculus AB & BC: Exam Prep course
- Graph Basics
- The Basics of Functions
- How to Graph Functions
- Overview of Function Continuity
- Understanding Exponentials & Logarithms
- Using Exponents and Polynomials
- Parametric, Polar and Vector Functions
- Overview of Properties of Derivatives
- The Derivative at a Point
- The Derivative as a Function
- Second Derivatives
- Derivative Applications
- Finding Derivatives
- Properties of Definite Integrals
- Applications of Integrals
- Using the Fundamental Theorem of Calculus
- Applying Integration Techniques
- Approximation of Definite Integrals
- Understanding Sequences & Series
- Series of Constants
- Taylor Series
- Using a Scientific Calculator for Calculus
- AP Calculus AB & BC Flashcards