Solve the following recurrence relations and give a Θ bound for each of them.(a) T (n) = 2...

Solve the following recurrence relations and give a Θ bound for each of them.

(a) T (n) = 2T (n/3) + 1

(b) T(n) = 5T(n/4) + n

(c) T(n) = 7T(n/7) + n

(d) T(n) = 9T(n/3) + n2

(e) T(n) = 8T(n/2) + n3

(f) T(n) = 49 T(n/25) + n3/2 log n

(g) T (n) = T (n − 1) + 2

(h) T (n) = T (n − 1) + nc, where c ≥ 1 is a constant

(i) T (n) = T (n − 1) + cn, where c > 1 is some constant

(j) T(n) = 2T(n − 1) + 1