4-3 More recurrence examples Give asymptotic upper and lower bounds for T(n) in each of the following recur- rences. Assume that T(n) is constant for sufficiently small n. Make your bounds as tight as possible, and justify your answers. a. T(n) = 4T(n/3) + n lgn. b. T(n) = 3T (n/3) + n/lgn. c. T(n) = 4T(n/2) + n2 . d. T(n) = 3T(n/3 2) + n/2. e. T(n) = 2T (n/2) + n/lgn. f. T(n) = T(n/2) + T(n/4) + T(n/8) + n. g. T(n) = T(n 1) + 1. h. T(n) = T(n 1) + Ign. i. T(n) = T(n 2) + 1/ Ign. j. T(n) = VT (vn) +n