Find the limit L$.$ Then use the $-$ definition to prove that the limit is L$.$

$$lim$$x$0$

$3$x

$$

L $=$

Use the $-$ definition to prove that the limit is L$.$

Given $>0,$ assume

$|$f$($x$)$ L$|<,$

then

$3$x

$$

$<|$

$3$x

$|<|$x$|<.$

Let

$=.$

If $0<|$x$|<$when $=,$ you have

$|$x$|<|$

$3$x

$|<$

$3$x

$$

$<|$f$($x$)$ L$|<.$