f$($x$)=$

x$2+2$if x $<1($x $2)2$if x $1$

$.$

$($a$)$

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

lim$$x $1$f$($x$)=$

lim$$x $1+$f$($x$)=$

$($b$)$

Does

lim$$x $1$f$($x$)$

exist?

YesNo$$