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.

DO NOT USE MASTERS THEOREM.

a) T (n) = 2T (n/2) + n⁴.

b) T (n) = 16T (n/4) + n².

c) T (n) = 7T (n/3) + n².

d) T (n) = 7T (n/2) + n².

e) T (n) = T (n-2) + n².

Please show your detailed work! And remember... DO NOT USE MASTERS THEOREM. Thank you!