(10 pts) Give tight asymptotic bounds for T (n) in each of the following recurrences. Assume that T (1) = 1. (Hint: Use the master method, as presented in the class notes on the Master Method.)

(a) T (n) = 8T (n/2) + (n³ log n)

(b) T (n) = 3T (n/2) + (n)

(c) T (n) = 3T (n/2) + (n²)

(d) T (n) = 16T (n/2) + (n³ log n)

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