Please solve the following examples without coding and use only $($Master method, Recursion tree, Chaining variables, Substition method, and Iteraiton method$)$

Note: I need the answer to clear and with steps.

$4-3$ More recurrence examples

Give asymptotic upper and lower bounds for $T(n)$ in each of the following recur$-$

rences. Assume that $T(n)$ is constant for sufficiently small $n.$ Make your bounds

as tight as possible, and justify your answers.

a$.T(n)=4T(\frac{n}{3})+nlgn.$

b$.T(n)=3T(\frac{n}{3})+\frac{n}{l}gn.$

c$.T(n)=4T(\frac{n}{2})+n^2\sqrt[\phantom{2}]{n}.$

d$.T(n)=3T(\frac{n}{3}-2)+\frac{n}{2}.$

e$.T(n)=2T(\frac{n}{2})+\frac{n}{l}gn.$

f$.,T(n)=T(\frac{n}{2})+T(\frac{n}{4})+T(\frac{n}{8})+n.$

g$.T(n)=T(n-1)+\frac{1}{n}.$

h$.T(n)=T(n-1)+lgn.$

i$.,T(n)=T(n-2)+\frac{1}{l}gn.$

j$.,T(n)=\sqrt[\phantom{2}]{n}T(\sqrt[\phantom{2}]{n})+n.$