limx$$e$3($lnx$+5)2=$

lim$3($ln$+5)2=$

Justification: Notice that$($lnx$+5)2=$f$($g$($x$))($ln$+5)2=(()),$ where

f$($x$)=$

andg$($x$)=$

$()=()=$

The functionf$$is

continuous

on$($$,$$)($$,$$).$

The functiong$$is a

sum

of two continuous functions,lnxln$$and$.$ Therefore,g$$is

continuous

on its domain$(,)(,).$

So$,$ we can apply

Composition

limit law