High School Calculus/Infinite Limits

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

${\begin{aligned}&\lim _{x\to -\infty }x\\&\lim _{x\to \infty }x=L\end{aligned}}$

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

${\begin{aligned}&f(x)=\lim _{x\to \infty }{\frac {2x}{2x^{2}}}\\&f(x)={\frac {\infty }{\infty }}\end{aligned}}$

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

$L=0$