A removable discontinuity, also known as a point of discontinuity, is a point on a graph where the function is undefined or has a hole, but can be made continuous by filling in the hole.
A removable discontinuity can be identified by looking for a point on the graph where the function has a hole or is undefined, but the function approaches the same value from both sides of the hole.
Yes, a function can have multiple removable discontinuities. This occurs when there are multiple points on the graph where the function has a hole or is undefined, but the function approaches the same value from both sides.
To remove a discontinuity in a function, you can use a process called "limiting." This involves finding the limit of the function as it approaches the point of discontinuity, and then replacing the undefined point with the limit value.
Removable discontinuities are important in calculus because they allow us to make a function continuous at a specific point, which can help us analyze and understand the behavior of the function. They also play a role in determining the domain and range of a function.