# How do you find the limit of (x+x^3-x^5)/(1-x^2-x^4) as x approaches infinity?

Aug 9, 2016

$\infty$

#### Explanation:

$L = {\lim}_{x \to \infty} \frac{x + {x}^{3} - {x}^{5}}{1 - {x}^{2} - {x}^{4}}$

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

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

..... and as $= {\lim}_{x \to \infty} \frac{1}{x} ^ n = 0 , n > 0$

this has a slant asymptote $y = x$

$\therefore L = {\lim}_{x \to \infty} x = \infty$