# Question #5b210

Feb 13, 2017

It depends on the details of your treatment of limits.

#### Explanation:

There is no emperor and no controlling council for mathematical terminology and notation.

In some treatments of limits, $f$ must be defined in some open interval containing $a$ (except possibly at $a$ itself) in order for the limit to exist.

In this way of defining limit, you function does not have a limit at $0$

In other treatments , limits at endpoints of closed interval domains are defined to be the one-sided limit (from the appropriate side.)

In this treatment, is is possible that the function has a limit.

Example

$f \left(x\right) = \sqrt{x} + 5$

In the first treatment, we have ${\lim}_{x \rightarrow 0} f \left(x\right)$ does not exist.

But, ${\lim}_{x \rightarrow {0}^{+}} f \left(x\right) = 5$

So the second treatment allows ${\lim}_{x \rightarrow 0} f \left(x\right) = 5$