Science Fair Project Encyclopedia
One-sided limit
In mathematics, a one-sided limit is where the limit of a function is defined in moving in the positive or negative direction, but not both.
For example, consider the function
![f(x) =
\left\{
\begin{matrix}
1\ \mbox{if}\ x\isin (-\infty, 1] \\
0\ \mbox{if}\ x\isin (1, \infty) \\
\end{matrix}\right.](a/../upload/math/cba0aa1e90e278d3612f1ed1d0872bf9.png)
Now, if we take the limit moving from smaller values of x to 1, noted,
but if we take the limit moving from larger values of x to 1, noted,
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
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details