In calculus, a one-sided limit refers to either one of the two limits of a function ${\displaystyle f(x)}$ of a real variable ${\displaystyle x}$ as ${\displaystyle x}$ approaches a specified point either from the left or from the right.

The limit as ${\displaystyle x}$ decreases in value approaching ${\displaystyle a}$ (${\displaystyle x}$ approaches ${\displaystyle a}$ "from the right" or "from above") can be denoted:

The limit as ${\displaystyle x}$ increases in value approaching ${\displaystyle a}$ (${\displaystyle x}$ approaches ${\displaystyle a}$ "from the left" or "from below") can be denoted:

If the limit of ${\displaystyle f(x)}$ as ${\displaystyle x}$ approaches ${\displaystyle a}$ exists then the limits from the left and from the right both exist and are equal. In some cases in which the limit

It is possible for exactly one of the two one-sided limits to exist (while the other does not exist). It is also possible for neither of the two one-sided limits to exist.