Question: Consider the recurrence T (n) = T (n/4) + T (n/3) + n with T (1) = 1. (a) (4 Points) Using a recursion tree,

Consider the recurrence T (n) = T (n/4) + T (n/3) + n with T (1) = 1.

(a) (4 Points) Using a recursion tree, determine a tight asymptotic upper bound on T(n).

(b) (4 Points) Prove your upper bound using induction.

(c) (4 Points) Using a suitable variable change, solve the recurrence U (n) = 3U (n^(1/3) ) + 7 with U(2) = 1.

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