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. Make your bounds as tight as possible, and justify your answers. a. T(n)= 4T(n/3)+ n lg n . b. T(n) = 3T(n/3) + n/ lg n. c. T(n) = 4T(n/2) + n2 . d. T(n) = 3T(n/3-2) + n/2. e. T(n)=2T(n/2)+ n/ lg n . f, T(n) = T(n/2) + T(n/4) + T(n/8) + n. g. T(n) T(n-1) + 1. 1. T(n) = T(n-1) + lg n . i. T(n)=T(n-2)+1/l gn