What is the difference between a removable and non-removable discontinuity?

1 Answer
Jim H
Nov 9, 2015

See the explanation below.

Explanation:

Geometrically, a removable discontinuity is a hole in the graph of #f#.

A non-removable discontinuity is any other kind of discontinuity. (Often jump or infinite discontinuities.)

Definition

If #f# has a discontinuity at #a#, but #lim_(xrarra)f(x)# exists, then #f# has a removable discontinuity at #a#
("Infinite limits" are "limits" that do not exists.)

We remove the discontinuity by defining:

#g(x) = {(f(x),"if",x != a" and "x in "domain"(f)),(lim_(xrarra)f(x),"if",x=a) :}#

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