Question

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

Answer 1

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.