# What is the limit of  (x^3 - 2x +3) / (5-2x^2) as x goes to infinity?

Oct 23, 2015

${\lim}_{x \rightarrow \infty} \frac{{x}^{3} - 2 x + 3}{5 - 2 {x}^{2}} = - \infty$

#### Explanation:

${\lim}_{x \rightarrow \infty} \frac{{x}^{3} - 2 x + 3}{5 - 2 {x}^{2}}$ has indeterminate form $\frac{\infty}{\infty}$.

For all $x \ne 0$ we get $\frac{{x}^{3} - 2 x + 3}{5 - 2 {x}^{2}} = \frac{{x}^{2} \left(x - \frac{2}{x} + \frac{3}{x} ^ 2\right)}{{x}^{2} \left(\frac{5}{x} ^ 2 - 2\right)}$

So
${\lim}_{x \rightarrow \infty} \frac{{x}^{3} - 2 x + 3}{5 - 2 {x}^{2}} = {\lim}_{x \rightarrow \infty} \frac{x - \frac{2}{x} + \frac{3}{x} ^ 2}{\frac{5}{x} ^ 2 - 2} = \frac{\infty}{-} 2 = - \infty$