EXAMPLE $1$ Find the following limit$.$

lim$$x $1$

$3$ ln$($x$)$x $1$

SOLUTION Since

lim$$x $13$ ln$($x$)=3$ ln$(1)=$and$$lim$$x $1($x $1)=$

we can apply l'Hospital's Rule:

lim$$x $1$

$3$ ln$($x$)$x $1$

$=$

lim$$x $1$

ddx

$(3$ ln$($x$))$

ddx

$($x $1)$

$=$

lim$$x $1$

$1$

$=$

lim$$x $1$

$=$