# How do you find a removable discontinuity for a function?

A discontinuity $a$ of a function $f$ is removable if ${\lim}_{x \to a} f \left(x\right)$ exists (that is, is a finite number). If the limit fails to exist (for instance, if it is infinite, or there are different one-sided limits, etc), the discontinuity is non-removable.
Thus, to decide if a discontinuity $a$ of a function $f$ is removable, you need to examine ${\lim}_{x \to a} f \left(x\right)$.