# Is this limit true or false lim 1/x^2=-oo as x->0?

Nov 25, 2017

False.

#### Explanation:

${\lim}_{x \to 0} \frac{1}{x} ^ 2 = \infty$

Because the denominator is squared it will always be positive, regardless as to whether we approach $0$ from the left or right. So:

as $x \to {0}^{-}$ $\textcolor{w h i t e}{88} \frac{1}{x} ^ 2 \to \infty$

as $x \to {0}^{+}$ $\textcolor{w h i t e}{88} \frac{1}{x} ^ 2 \to \infty$

$\therefore$

${\lim}_{x \to 0} \frac{1}{x} ^ 2 = \infty$