# What is the limit as x approaches infinity of (x^2-4)/(2x-4x^2)?

Mar 22, 2018

Mar 22, 2018

$- \frac{1}{4}$

#### Explanation:

$\text{divide terms on numerator/denominator by the highest}$
$\text{power of x, that is } {x}^{2}$

$\Rightarrow \frac{{x}^{2} / {x}^{2} - \frac{4}{x} ^ 2}{\frac{2 x}{x} ^ 2 - \frac{4 {x}^{2}}{x} ^ 2} = \frac{1 - \frac{4}{x} ^ 2}{\frac{2}{x} - 4}$

$\Rightarrow {\lim}_{x \to \infty} \frac{{x}^{2} - 4}{2 x - 4 {x}^{2}}$

$= {\lim}_{x \to \infty} \frac{1 - \frac{4}{x} ^ 2}{\frac{2}{x} - 4}$

$= \frac{1 - 0}{0 - 4} = - \frac{1}{4}$