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.