## What are the conditions to satisfy continuity at a point?

For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point. Discontinuities may be classified as removable, jump, or infinite.

### Are jump discontinuities removable?

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.

#### What are the 3 rules of continuity?

Answer: The three conditions of continuity are as follows:

• The function is expressed at x = a.
• The limit of the function as the approaching of x takes place, a exists.
• The limit of the function as the approaching of x takes place, a is equal to the function value f(a).

What is non-removable discontinuity?

Non-removable discontinuity is the type of discontinuity in which the limit of the function does not exist at a given particular point i.e. lim xa f(x) does not exist.

What are jump discontinuities?

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 the three properties to satisfy in order for a function f to be continuous at a?

Determine whether the following are continuous….Note that in order for a function to be continuous at a point, three things must be true:

• The limit must exist at that point.
• The function must be defined at that point, and.
• The limit and the function must have equal values at that point.

### Which are removable discontinuities?

A removable discontinuity is a point on the graph that is undefined or does not fit the rest of the graph. There are two ways a removable discontinuity is created. One way is by defining a blip in the function and the other way is by the function having a common factor in both the numerator and denominator.

#### What is a non removable discontinuity on a graph?

A point in the domain that cannot be filled in so that the resulting function is continuous is called a Non-Removable Discontinuity.