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Problem 2. (24 points) Let T(n) be defined by the recurrence T(n)=3T(n/2)+f(n) and T(1)=d for a constant d>0, where lgn=log2n in each of the four parts below, (a) f(n)=nlgn, (b) f(n)=nlg3/lgn, (c) f(n)=nlg3lg2n, or (d) f(n)=n2/lgn. For each of the four forms of f(n), explain whether the Master Theorem can be applied to the recurrence. If it is applicable, indicate which case of the theorem is applicable and show the steps of obtaining the solution to T(n). Otherwise, explain why none of the three cases of the theorem is applicable