# High School Calculus/Infinite Limits

The limit as x approaches gives you the horizontal asymptote.

${\displaystyle \lim _{x\to -\infty }x}$

${\displaystyle \lim _{x\to \infty }x=L}$

${\displaystyle f(x)=\lim _{x\to \infty }{\frac {2x}{2x^{2}}}}$

${\displaystyle f(x)={\frac {\infty }{\infty }}}$

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

To do this you need to take ${\displaystyle {\frac {f\prime (x)}{g\prime (x)}}}$

From this you get

${\displaystyle \lim _{x\to \infty }{\frac {2}{4x}}}$

This gives you

${\displaystyle {\frac {2}{\infty }}}$

This is no longer in indeterminate form so, we get

${\displaystyle L=0}$