When is a one sided limit undefined?

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Answer 1 · 2014-12-12T10:05:46

A one sided limit does not exist when:

1.#""# there is a vertical asymptote.

ex.) #lim_{x to 0^+} 1/x =1/{0^+}=+infty#

So, the limit does not exist.

2.#""# there are violent oscillations.

ex.) #lim_{x to 0^-}sin(1/x)# does not exist

due to violent oscillations, which looks like:

enter image source here

I hope that this was helpful.