Tutorial Exercise

Find the limit$.$ Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it$.$

lim$$x$0+$

$8$x

$$

$8$tan$($x$)$

Step $1$

We first rewrite the given limit such that we have a single rational expression as follows.

lim$$x$0+$

$8$x

$$

$8$tan$($x$)$

$=$lim$$x$0+$

$$$8$tan$($x$)8$x

x tan$($x$)$

Step $2$

As

x$0+,$

$8($tan$($x$)$ x$)$

$,$

and

x tan$($x$)$