Exercise $3$

Give asymptotically upper bounds for $T(n)$ in each of the following algorithmic

recurrences. Justify your answers.

a$)T(n)=2T(\frac{n}{2})+n^3$

b$)T(n)=T(8\frac{n}{11})+n$

c$)T(n)=16T(\frac{n}{4})+n^2$

d$)T(n)=4T(\frac{n}{2})+n^{2}lgn$

e$)T(n)=8T(\frac{n}{3})+n^2$

f$)T(n)=7T(\frac{n}{2})+n^{2}lgn$

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