Onesided limit
From Exampleproblems
In mathematics, a one-sided limit is where the limit of a function of one real variable is defined in moving in the positive or negative direction, but not both.
For example, consider the function
![f(x) =
\left\{
\begin{matrix}
2x^3\ \mbox{if}\ x\isin (-\infty, 1] \\
5-x\ \mbox{if}\ x\isin (1, \infty) \\
\end{matrix}\right.](/wiki/images/math/5/4/a/54ae87771b116d60b18c85ed77151bb3.png)
If one takes the limit moving from smaller values of x to 1, one finds
If one takes the limit moving from larger values of x to 1, one gets
These two limits are not identical and so f has a one-sided limit at the point x=1.
If these two limits are identical, f is said to have a two-sided limit at that point.
See also: Two-sided limit
