# Horizontal Asymptote

1. Sep 16, 2009

### Loppyfoot

1. The problem statement, all variables and given/known data
Find the horizontal asymptote to the graph: f(x) = 2x2/(x4-81)1/2

2. Relevant equations

How do I factor the bottom? Because for, the HA, I compare the coefficients.

2. Sep 16, 2009

### rock.freak667

x4-81=x4(1-81/x4)

and remember that √(ab)=√a * √b

3. Sep 17, 2009

### Loppyfoot

How do I prove that the HA: is y=2?

4. Sep 17, 2009

### Staff: Mentor

Look at
$$f(x)~=~\frac{2x^2}{\sqrt{x^4(1 - 81/x^4)}}$$
and simplify the denominator.

What is the limit of f(x) as x gets large in either direction?