$\mathrm{.}5$Determine the following limits$.$No proofs are required, but show any relevant algebra. $($a$)$lim sn where sn $=$n$2+1$n$,($b$)$lim$($n$2+$n $$n$),($c$)$lim$(4$n$2+$n $2$n$).$Hint for $($a$)$: First show sn $=1$n$2+1+$n $.$