What are removable discontinuities?
Holes
Removable discontinuities are a type of discontinuity that occur in a function when there is a hole in the graph at a certain point or points. These points are typically marked by a point where the function appears to be undefined but can be made continuous by assigning a value to the function at that point.
A removable discontinuity can occur in a function when the denominator of a fraction has a zero value but the numerator does not. This means that the function is undefined at that point, but there may be a value that can be substituted to fill the hole and make the function continuous. This situation can also arise if the numerator also has a zero value at that point and is factorable, meaning that the common factor can be canceled out from the fraction to form a new, continuous function.
Removable discontinuities are different from other types of discontinuities such as jump discontinuities or essential discontinuities because they can be removed or filled in to make the function continuous. They can be identified by looking for a hole in the graph of the function, typically marked by a point where the function appears to be undefined.
More Answers:
Mastering The Formula And Definition Of Derivatives In CalculusHow To Apply The Intermediate Value Theorem In Calculus: Techniques And Applications
Non-Removable Discontinuities In Functions: Causes And Differences From Removable Discontinuities