Types of discontinuity

There are four types of discontinuities you have to know: jump, point, essential, and removable.

1. What are the 3 types of discontinuity?
2. What kinds of discontinuity are there?
3. How do you know what type of discontinuity?
4. What are discontinuities examples?

What are the 3 types of discontinuity?

There are three types of discontinuities: Removable, Jump and Infinite.

What kinds of discontinuity are there?

There are two types of discontinuities: removable and non-removable. Then there are two types of non-removable discontinuities: jump or infinite discontinuities. Removable discontinuities are also known as holes. They occur when factors can be algebraically removed or canceled from rational functions.

How do you know what type of discontinuity?

Point/removable discontinuity is when the two-sided limit exists, but isn't equal to the function's value. Jump discontinuity is when the two-sided limit doesn't exist because the one-sided limits aren't equal. Asymptotic/infinite discontinuity is when the two-sided limit doesn't exist because it's unbounded.

What are discontinuities examples?

In an infinite discontinuity (Examples 3 and 4), the one-sided limits exist (perhaps as ∞ or −∞), and at least one of them is ±∞. An essential discontinuity is one which isn't of the three previous types — at least one of the one-sided limits doesn't exist (not even as ±∞).