$1.$ Give asymptotic upper and lower bounds for T$($n$).$ Assume that T$($n$)$ is constant for sufficiently small n$.$ Justify your answers.

$1.$ T$($n$)=4$T$($n$/3)+$nlogn $2.$ T$($n$)=4$T$($n$/2)+$ n$2$n $3.$ T$($n$)=$T$($n$1)+1/$n $4.$ T$($n$)=$T$($n$1)+$logn