How do I know if a discontinuity in a function is removable or not?

1 Answer
Apr 16, 2018

If the limit exists, it is removable. Otherwise, not.

Explanation:

If #f# is discontinuous at #a#,

then #lim_(xrarra)f(x) != f(a)#

This could be for any of 3 reasons:

#lim_(xrarra)f(x)# fails to exist

#f(a)# fails to exist

Both exist, but they are unequal.

If the limit exists, the discontinuity is removable.