Removable Discontinuity
Definition
A removable discontinuity occurs when a function has a hole at a certain point, but the limit of the function exists at that point.
Analogy
Imagine you have a cake with a missing piece in the middle. Even though there is a gap, you can still determine what the missing piece would be by looking at the surrounding parts of the cake.
Related terms
Limit: The value that a function approaches as it gets arbitrarily close to a particular point.
Hole: A missing point on the graph of a function where there is an open circle indicating that it is not included in the graph.
Asymptote: A line that a curve approaches but never touches or crosses.
"Removable Discontinuity" appears in:
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Practice Questions (5)
If a function has a removable discontinuity, what can be done to the rational expression?
If a function has a removable discontinuity at x = 2, what can be done to make the function continuous at that point?
How can you remove a removable discontinuity?
What is a removable discontinuity?
Which property allows us to evaluate an improper integral when the integrand contains a removable discontinuity?
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