About This Chapter
Who's It For?
Anyone who needs help learning or mastering AP calculus material will benefit from taking this course. There is no faster or easier way to learn AP calculus. Among those who would benefit are:
- Students who have fallen behind in understanding continuity functions and theorems
- 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 continuity in AP calculus
- 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 continuity in AP calculus 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 continuity in AP calculus chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any question on continuity in AP calculus. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
This chapter helps students review the concepts in a continuity unit of a standard AP Calculus AB and BC course. Topics covered include:
- Continuity in a function
- Discontinuities in functions and graphs
- Regions of continuity in a function
- Intermediate Value Theorem
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.
6. Removable Discontinuities: Definition & Concept
There are actually two ways you can get a removable discontinuity. Learn about them in this lesson along with how to identify them and what you can do with them.
7. Difference Between an Open Interval & a Closed Interval
We'll discuss the difference between an open and closed interval in terms of definition and notation in this lesson. We'll determine if different types of intervals are open and closed and look at how to write them using interval notation.
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Other chapters within the AP Calculus AB & BC: Help and Review course
- Functions in AP Calculus: Help and Review
- Graphing and Functions in AP Calculus: Help and Review
- Sequences and Series in AP Calculus: Help and Review
- Limits in AP Calculus: Help and Review
- Exponentials and Logarithms in AP Calculus: Help and Review
- Exponents and Polynomials in AP Calculus: Help and Review
- Applications of Derivatives in AP Calculus: Help and Review
- Calculating Derivatives & Derivative Rules in AP Calculus: Help & Review
- Calculus - Derivatives Calculations & Rules: Help & Review
- Differential Equations in AP Calculus: Help and Review
- Area Under the Curve and Integrals in AP Calculus: Help and Review
- L'Hopital's Rule & Graphing Derivatives: Help & Review
- Integration Applications in AP Calculus: Help and Review
- Rate of Change in AP Calculus: Help and Review
- Geometry and Trigonometry in AP Calculus: Help and Review
- How to Use Scientific Calculators for AP Calculus: Help and Review