Question

What is removable discontinuity?

Answer 1

Hint: Here we are going to know about what is removable discontinuity and how do you solve a removable discontinuity.

Complete step by step solution:
Removable discontinuity:
A removable discontinuity is a point on the graph that is undefined or does not fit the rest of the graph. There is a gap at that location when you are looking at the graph. When graphed, a removable discontinuity is marked by an open circle on the graph at the point where the graph is undefined or is a different value like this.
Removable discontinuity is a point at which a graph is not connected but can be made connected by filling in a single point.
Formal definition:
A discontinuity removable at a point $x=a$ if the $\underset{x\to a}{lim}f\left(x\right)$ exists and this limit is finite. There are two types of removable discontinuities,
The function is undefined at $x=a$.
The value of the function at $x=a$ does not match the limit.
When a function has a removable discontinuity, it can be redefined to make it a continuous function.
How do you solve a removable discontinuity?
First factor the numerator and the denominator and then identify the factors that occur in both the numerator and the denominator then set the common factors equal to zero and finally solve the given variable.

Note: Formally, a removable discontinuity is one at which the limit of the function exists but does not equal the value of the function at that point. This may be because the function does not exist at that point.