Let

g$($x$)=$

x$2+$ x $20|$x $4|$

$.$

$($a$)$

Find the following limits$.($If an answer does not exist, enter DNE.$)$

$($i$)$

lim$$x $4+$g$($x$)$

$($ii$)$

lim$$x $4$g$($x$)$