Home > Calculus > Classifying Topics of Discontinuity (removable vs. non-removable)

What is a removable Discontinuity?

Answer 1

#f(x)# has a removable discontinuity at #x=a# when #lim_{x to a}f(x)# EXISTS; however, #lim_{x to a}f(a) ne f(a)#. A removable discontinuity looks like a single point hole in the graph, so it is "removable" by redefining #f(a)# equal to the limit value to fill in the hole.

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Answer 2

Elijah Abram

A removable discontinuity, also known as a removable singularity or removable point, is a type of discontinuity in a function where a hole appears in the graph. It occurs when a function is undefined at a particular point, but the limit of the function exists at that point. This means that the function can be modified or redefined at that specific point to make it continuous. The hole in the graph can be filled by assigning a value to the function at that point, resulting in a continuous function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.