# When is a one sided limit undefined?

Dec 12, 2014

A one sided limit does not exist when:

1."" there is a vertical asymptote.

ex.) ${\lim}_{x \to {0}^{+}} \frac{1}{x} = \frac{1}{{0}^{+}} = + \infty$

So, the limit does not exist.

2."" there are violent oscillations.

ex.) ${\lim}_{x \to {0}^{-}} \sin \left(\frac{1}{x}\right)$ does not exist

due to violent oscillations, which looks like:

I hope that this was helpful.