# How do you find the limit of  (1)/(x-2) as x approaches 2+?

Jun 30, 2016

$= \infty$

#### Explanation:

let's say that this amounts to setting $x = 2 + \epsilon q \quad \textcolor{red}{\epsilon > 0}$

so we have

${\lim}_{x \to {2}^{+}} \frac{1}{x - 2} = {\lim}_{\epsilon \to 0} \frac{1}{2 + \epsilon - 2} = {\lim}_{\epsilon \to 0} \frac{1}{\epsilon}$

because of the statement in red above, this term is positive and so $\frac{1}{\epsilon} \to + \infty$ as $\epsilon \to 0$

so

${\lim}_{x \to {2}^{+}} \frac{1}{x - 2} = \infty$