About This Chapter
Who's it for?
This unit of our AP Calculus Homeschool course will benefit any student who is trying to learn about forms of continuity. There is no faster or easier way to learn about continuity. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn about discontinuity, intermediate value theorem and functions.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a calculus curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a continuity unit exam confirm understanding or identify any topics that require review.
Continuity Unit Objectives:
- Define continuity as it relates to calculus.
- Review examples of discontinuities through graphs and equations.
- Explore continuous functions, also known as regions of continuity.
- Receive an explanation of the intermediate value theorem.
- Read applications and examples of intermediate value theorems.
1. Continuity in a Function
Travel to space and explore the difference between continuous and discontinuous functions in this lesson. Learn how determining continuity is as easy as tracing a line.
2. Discontinuities in Functions and Graphs
In this lesson, we talk about the types of discontinuities that you commonly see in functions. In particular, learn how to identify point, jump and asymptotic discontinuities.
3. Regions of Continuity in a Function
Can Earth ever compete with extraterrestrial UFOs? In this lesson, you'll learn that not all functions are continuous, but most have regions where they are continuous. Discover how to define regions of continuity for functions that have discontinuities.
4. Intermediate Value Theorem: Definition
A UFO and a jet take off and ascend to 30,000 feet along discontinuous and continuous paths, respectively. In this lesson, learn about the intermediate value theorem and why the jet has to cross 15,000 feet.
5. Intermediate Value Theorem: Examples and Applications
Many problems in math don't require an exact solution. Some problems exist simply to find out if any solution exists. In this lesson, we'll learn how to use the intermediate value theorem to answer an age-old question.
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Other chapters within the AP Calculus AB & BC: Homeschool Curriculum course
- Functions - AP Calculus: Homeschool Curriculum
- Graphing & Functions - AP Calculus: Homeschool Curriculum
- Sequences & Series - AP Calculus: Homeschool Curriculum
- Limits - AP Calculus: Homeschool Curriculum
- Exponentials & Logarithms: Homeschool Curriculum
- Exponents & Polynomials - AP Calculus: Homeschool Curriculum
- Applications of Derivatives - AP Calculus: Homeschool Curriculum
- Calculating Derivatives & Derivative Rules - AP Calculus: Homeschool Curriculum
- Differential Equations - AP Calculus: Homeschool Curriculum
- Area Under the Curve & Integrals - AP Calculus: Homeschool Curriculum
- Graphing Derivatives & L'Hopital's Rule - AP Calculus: Homeschool Curriculum
- Integration & Integration Techniques - AP Calculus: Homeschool Curriculum
- Integration Applications - AP Calculus: Homeschool Curriculum
- Rate of Change - AP Calculus: Homeschool Curriculum
- Geometry and Trigonometry - AP Calculus: Homeschool Curriculum
- Using Scientific Calculators - AP Calculus: Homeschool Curriculum