Continuity is a fundamental concept in calculus that helps us...
AP Calculus AB/BC183 views·Updated Jul 7, 2026·1 pageMastering Limits and Continuity: AP Calc AB Guide
Denise Suarez@denisesuarez_ttpc
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Continuity and Limits Review
When we say a function is continuous at a point, we mean the function's graph doesn't have any breaks, jumps, or holes at that point. Think of it as drawing without lifting your pencil!
For a function to be continuous at a point x = c, three key conditions must be met:
- The function value f must exist (the function is defined at that point)
- The limit of f as x approaches c must exist
- The limit must equal the function value: lim f = f
💡 Quick Tip: When checking continuity, think "Does, Exists, Equals" - Does the function exist at the point? Does the limit exist? Do they equal each other?
Horizontal asymptotes are connected to limits - they occur when a function approaches a specific y-value as x gets very large (positive or negative). This happens when lim f = L as x approaches infinity.
Remember that trigonometric functions like sin and cos are continuous everywhere, while rational functions might have points of discontinuity where denominators equal zero.
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AP Calculus AB/BC183 views·Updated Jul 7, 2026·1 pageMastering Limits and Continuity: AP Calc AB Guide
Denise Suarez@denisesuarez_ttpc
Continuity is a fundamental concept in calculus that helps us understand when functions behave predictably without sudden jumps or breaks. This concept builds on our understanding of limits and is critical for many calculus applications.
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Continuity and Limits Review
When we say a function is continuous at a point, we mean the function's graph doesn't have any breaks, jumps, or holes at that point. Think of it as drawing without lifting your pencil!
For a function to be continuous at a point x = c, three key conditions must be met:
- The function value f must exist (the function is defined at that point)
- The limit of f as x approaches c must exist
- The limit must equal the function value: lim f = f
💡 Quick Tip: When checking continuity, think "Does, Exists, Equals" - Does the function exist at the point? Does the limit exist? Do they equal each other?
Horizontal asymptotes are connected to limits - they occur when a function approaches a specific y-value as x gets very large (positive or negative). This happens when lim f = L as x approaches infinity.
Remember that trigonometric functions like sin and cos are continuous everywhere, while rational functions might have points of discontinuity where denominators equal zero.
We thought you’d never ask...
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
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Students love us — and so will you.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user