f(x)= 2x/(x^2 + 2)^(1/2).
How do I find the negative infinity limit part of the problem? I found one Horizontal asymptote at x =2, how do I find the other?
follow these rules
This procedure leads to the following general result:
* 1 * If the degree of the denominator exceeds that of the numerator, y = 0 is a horizontal asymptote;
* 2 * If the leading coefficient of the numerator is a and the leading coefficient of the denominator is b and their degrees are equal then is a horizontal asymptote;
* 3 * If the degree of the numerator exceeds that of the denominator, there is no horizontal asymptote.
http://www.math.csusb.edu/math110/src/rationals/hasym.html
as x goes to infinity, the 2 in the denominator essentially does not matter. thus we have that:
$\displaystyle \lim_{x \to \pm \infty} \frac {2x}{\sqrt{x^2 + 2}} = \lim_{x \to \pm \infty} \frac {2x}{\sqrt{x^2}} = $ $\displaystyle \lim_{x \to \pm \infty} \frac {2x}{|x|} = \left \{ \begin{array}{lr} 2 & \mbox{ as } x \to \infty \\ -2 & \mbox { as } x \to - \infty \end{array} \right.$