# Question #fbfbb

May 12, 2017

Find the left- and right-sided limit, if they are the same, then the two-sided limit has the same value, otherwise the two-sided limit does not exist. Answer: ${\lim}_{x \to 0} \frac{1}{x}$ does not exist

#### Explanation:

Formatted question: Find ${\lim}_{x \to 0} \frac{1}{x}$

Since clearly we cannot find the limit by simply substituting, because $x = 0$ is a vertical asymptote, we need to find the limit as $x$ approaches $0$ from the left- and right-sided limits:
${\lim}_{x \to {0}^{-}} \frac{1}{x} = - \infty$
${\lim}_{x \to {0}^{+}} \frac{1}{x} = \infty$

Since left-sided limit does not equal the right-sided limit, therefore, the two-sided limit does not exist:
${\lim}_{x \to 0} \frac{1}{x}$ does not exist