give the asymptotic lower and upper bounds of:

a) T(n) = T(9n/10) + n

b) T(n) = 32T(n/3) + n2

c) T(n) = 32T(n/2) + n2

d) T(n) = 2T(n/4) + sqrt(n) where sqrt(n) is the square root of n

make the bounds as tight as possible, and justify the answer