Ch 2: Continuity

About This Chapter

Watch online math video lessons to learn about discontinuities, regions of continuity, the intermediate value theorem and more. Take the lesson quizzes and chapter exam to test your understanding of the materials.

Calculus: Continuity

When functions are continuous, you're able to trace them with your finger on a graph, and at no point will the line break. If you trace a function with your finger and have to lift it off the paper at any point, then you know the function is discontinuous.

In this chapter's series of video lessons on continuity, you'll watch as fighter jets chase alien UFOs on a graph to help you understand continuous and discontinuous functions. Throughout these lessons, you'll learn about the various types of discontinuities and figure out if the fighter jets will eventually catch up to the UFOs.

You'll look at the three different types of discontinuities: removable discontinuity, jump discontinuity and asymptotic discontinuity. Watch as a UFO stops at one point and immediately reappears at another point along the graph. It may jump, separate or launch to positive and negative infinity at a particular point, which illustrates the discontinuity types.

Then, when graphing discontinuous functions, you'll learn how they may go through regions of continuity by sticking to one unbroken path. You'll also learn the intermediate value theorem, which will show why the fighter jet, at a certain point, will cross paths with the UFO.

After watching each lesson, you'll be able to test your knowledge through a short, multiple-choice quiz. There's also a chapter-ending test to measure your mastery of continuity.

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