Solving an Indeterminant Limit Problem with L'Hopital's Rule

[Feldoh]

Homework Statement

Find $$\lim_{x-> \inf} \frac{(8-x)^{200}}{8^{x+2}}*\frac{8^x}{(3-x^2)^{100}}$$

Homework Equations

The Attempt at a Solution

Simplified to:

$$\lim_{x-> \inf} \frac{(8-x)^{200}}{64(3-x^2)^{100}}$$

Indeterminant form, so I suppose L'hopital's, but it doesn't seem very efficient?

 

[jhicks]

Write the first two or 3 highest order terms of the expansions of the numerator and denominator. You'd agree that all lower order terms become increasingly insigificant as x becomes large, right?