# How do you find the limit of 1/(x-1) as x approaches 1?

Oct 18, 2015

See the explanation.

#### Explanation:

It is relevant for the limit from which side we approach to specific point; in the other words we have to solve two limits:

Let $\epsilon \in {R}^{+} , \epsilon \to 0$, then:

Form the left:
${\lim}_{x \to 1 - \epsilon} \frac{1}{x - 1} = {\lim}_{\epsilon \to 0} \frac{1}{1 - \epsilon - 1} = {\lim}_{\epsilon \to 0} \frac{1}{-} \epsilon = - {\lim}_{\epsilon \to 0} \frac{1}{\epsilon} = - \infty$

Form the right:
${\lim}_{x \to 1 + \epsilon} \frac{1}{x - 1} = {\lim}_{\epsilon \to 0} \frac{1}{1 + \epsilon - 1} = {\lim}_{\epsilon \to 0} \frac{1}{\epsilon} = + \infty$