$7\mathrm{.}5$ 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 $.$