# limits and horz asymptote

• Feb 1st 2010, 07:04 PM
bigwave
limits and horz asymptote
$\lim_{x \to -\infty} \frac{x^2}{x^2+x-2}$

and

$\lim_{x \to \infty} \frac{x^2}{x^2+x-2}$

apparently they both approach the horz asymptote of y=1 which must mean they the limit of both is 1

however what steps are taken from the expression to arrive at this
• Feb 1st 2010, 07:09 PM
jass10816
Divide the top and bottom by x^2. Since limits like 1/x go to zero as x goes to infinity, you should get 1/1 in both cases.
• Feb 1st 2010, 07:30 PM
bigwave
so with

$\frac{1}{1 + \frac{1}{x} - \frac{2}{x^2}}$

by observation as ${x \to \pm\infty}$ it will go to $\frac{1}{1} = 1$ being the horz asymtope