Problem $3$: Give asymptotic estimates, using the $\backslash$Theta $-$notation, for the following functions: $($a$)5$n$4+5$n$3+$n$2($b$)$ n$2\mathrm{.}5$log$5$ n$+$n$3$ logn$+5$n$3($c$)5$n$3$ log n $+4$n$3$n $+3$n$4($d$)3$n$5+$n$4$ logn$+$n$3$n $($e$)$ n$5+$n$26$n $+$n$4$n Justify your answer, using asymptotic relations between the basic reference functions: nb$,$ log n$,$ and cn$.$ Problem $3$: Give asymptotic estimates, using the $\backslash$Theta $-$notation, for the following functions: $($a$)5$ n$^4+5$ n$^3+$n$^2($b$)$ n$^2\mathrm{.}5$log $^5$ n$+$n$^3$log n$+5$ n$^3($c$)5$ n$^3$log n$+4$ n$^3($n$)+3$ n$^4($d$)3$ n$^5+$n$^4$log n$+$n $3^$n $($e$)$ n$^5+$n$^26^$n$+$n $4^$n Justify your answer, using asymptotic relations between the basic reference functions: n$^$b$,$ log n$,$ and c$^$n$.$