Given that

$$lim$$x$1$f$($x$)=4$lim$$x$1$g$($x$)=4$lim$$x$1$h$($x$)=0,$

find each limit$,$ if it exists. $($If an answer does not exist, enter DNE.$)$

$($a$)$

lim$$x$1[$f$($x$)+3$g$($x$)]$