About This Chapter
Who's it for?
Anyone who needs help learning or mastering high school precalculus material will benefit from taking this course. There is no faster or easier way to learn high school precalculus. Among those who would benefit are:
- Students who have fallen behind in understanding functions, graphing and limits
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about limits
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How it works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Limits chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Limits chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any limits question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
In this chapter, you'll learn the answers to questions including:
- How do I use a graph to define limits?
- How can notation help me understand limits?
- What are the definitions for continuity and one-sided limits?
- How can I determine the limits of functions?
- What are the properties of limits?
- What is the squeeze theorem?
- What are the definitions for an asymptote and infinity?
1. 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.
2. 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.
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. 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.
5. 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.
6. 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.
7. 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.
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Other chapters within the High School Precalculus: Help and Review course
- Working with Linear Equations: Help and Review
- Working With Inequalities: Help and Review
- Absolute Value Equations: Help and Review
- Working with Complex Numbers: Help and Review
- Systems of Linear Equations: Help and Review
- Mathematical Modeling: Help and Review
- Introduction to Quadratics: Help and Review
- Working with Quadratic Functions: Help and Review
- Geometry Basics for Precalculus: Help and Review
- Functions - Basics for Precalculus: Help and Review
- Understanding Function Operations: Help and Review
- Graph Symmetry: Help and Review
- Graphing with Functions: Help and Review
- Rate of Change: Help and Review
- Polynomial Functions Basics: Help and Review
- Higher-Degree Polynomial Functions: Help and Review
- Rational Functions & Difference Quotients: Help and Review
- Rational Expressions and Function Graphs: Help and Review
- Exponential Functions & Logarithmic Functions: Help and Review
- Using Trigonometric Functions: Help and Review
- Trigonometric Graphs: Help and Review
- Solving Trigonometric Equations: Help and Review
- Trigonometric Identities: Help and Review
- Trigonometric Applications in Precalculus: Help and Review
- Graphing Piecewise Functions: Help and Review
- Vectors, Matrices and Determinants: Help and Review
- Mathematical Sequences and Series: Help and Review
- Sets in Algebra: Help and Review
- Analytic Geometry and Conic Sections: Help and Review
- Polar Coordinates and Parameterizations: Help and Review
- Continuity: Help and Review