Asymptotic Notation.

$[10$ pts$.]$ Prove that n$2+5$n log$2$ n $=$ O$($n$2).$ Your answer must clearly specify the constants c and n$0.$

$[10$ pts$.]$ Let f$($n$)=5$n $+20$ and let g$($n$)=3$n $100.$ Find positive constants n$0,$ c$1$ and c$2$ such that c$1$g$($n$)<=$ f$($n$)<=$ c$2$g$($n$)$ for all n $>=$ n$0.$ Be sure to explain how you arrived at the constants. What does this imply about the relationship between f and g$?$