High School Calculus/Infinite Limits

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

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

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

To do this you need to take $\frac{f^{\prime }(x)}{g^{\prime }(x)}$ . From this you get

$\underset{x\to \mathrm{\infty }}{\lim }\frac{2}{4x}$

This gives you

$\frac{2}{\mathrm{\infty }}$

This is no longer in indeterminate form so, we get

$L=0$