Recurrence examples

Give asymptotic upper and lower bounds for T $.$n$/$ in each of the following recurrences. Assume that T $.$n$/$ is constant for n $2.$ Make your bounds as tight as

possible, and justify your answers.

a$.$ T $.$n$/$ D $2$T $.$n$=2/$ C n$4.$

b$.$ T $.$n$/$ D T $\mathrm{.}7$n$=10/$ C n$.$

c$.$ T $.$n$/$ D $16$T $.$n$=4/$ C n$2.$

d$.$ T $.$n$/$ D $7$T $.$n$=3/$ C n$2.$

e$.$ T $.$n$/$ D $7$T $.$n$=2/$ C n$2.$

f$.$ T $.$n$/$ D $2$T $.$n$=4/$ C pn$.$

g$.$ T $.$n$/$ D T $.$n $2/$ C n$2$