Horizontal Asymptote of f(x) = 2x2/(x4-81)1/2 - How to Factor Bottom

[Loppyfoot]

Homework Statement

Find the horizontal asymptote to the graph: f(x) = 2x²/(x⁴-81)^1/2

Homework Equations

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

 

[rock.freak667]

x⁴-81=x⁴(1-81/x⁴)

and remember that √(ab)=√a * √b

 

[Loppyfoot]

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

 

[Mark44]

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?