DanielJackins said:Are the limits not -inf and inf?
A removable discontinuity, also known as a point discontinuity, occurs when a function has a hole at a specific point. This means that the function is undefined at that point, but can be made continuous by simply filling in the hole with a single point.
To identify a removable discontinuity, you can look for a point on the graph where the function is undefined, but there is no jump or break in the graph. This indicates that there is a hole at that point, making it a removable discontinuity.
Removable discontinuities can be caused by factors such as division by zero or the presence of a radical expression in the denominator of a rational function. These factors result in an undefined value at a particular point, creating a hole in the graph.
The limit at a removable discontinuity can be found by evaluating the function at the point where the hole is located. This will give you the value of the limit, which is the same from both the left and right sides of the hole.
Yes, a removable discontinuity can be removed by filling in the hole at the specific point with a single point. This will make the function continuous at that point and remove the discontinuity.