High School Calculus/Infinite Limits

The limit as $$x$$ approaches gives you the horizontal asymptote.

You can use L'Hopital rule to help you with these limits

This is an indeterminate form so you can use L'Hopital's rule.

To do this you need to take $$\frac{f'(x)}{g'(x)}$$. From this you get
 * $$\lim_{x\to\infty}\frac{2}{4x}$$

This gives you
 * $$\frac{2}{\infty}$$

This is no longer in indeterminate form so, we get
 * $$L=0$$