$(30$ points$)1.$ Compute and explain the time complexity of the following recursive functions.

$(6$ points$)1\mathrm{.}1T(n)=2T(\frac{n}{3})+\sqrt[\phantom{2}]{n}$

$(7$ points$)1\mathrm{.}2T(n)=T(\frac{n}{2})+\sqrt[\phantom{2}]{n}logn$

$(7$ points$)1\mathrm{.}3T(n)=3T(\frac{n}{3})+\frac{\sqrt[\phantom{2}]{n}}{lo{g}^{2}n}$

$(10$ points$)1\mathrm{.}4T(n)=3T(\frac{n}{2})+n^2($It is required to use the iterative method.$)$