Please solve at least 6, indicate which case of masters theorem was used and please show all work.

Problem 1 Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for n s 10. Make your bounds as tight as possible, and justify your answers. (a) T(n) = 2T(n/3) + n lg n (b) T(n) 3T(n/5) +1g2n (c) T(n) = T(n/2) + 2n (d) T(n) = T(V+ (lg lg n) (e) T(n) 10T(n/3)+ 17n12 (f) T(n) = 7T(n/2)-m3 (g) T(n) = T(n/2+ + v6046 (h) T(n) T(n -2) +Ign (i) T(n) = T(n/5) + T(4n/5) + (n) (j) T(n) = Vii T(G) +100n