Problem 1. Solve the following recurrences using the Master Theorem if pos- sible; otherwise, explain why the Theorem does not apply. In each recurrence, discuss the height of the recursion tree and the number of leaves in the tree. Also, discuss helpful assumptions made on n, and make sure they do not af- fect the generality of your solution (Take-home exercise: Try and solve each recurrence without using Master's Theorem). 1. T(n) = 9T(n/3) + 2n 2. T(n) = 3T(n/7) + nlog73 3. T(n) =T(m - 1)+1 4. T(n) =T(3/8) + 32 5. T(n) =T(3/4) + 25 6. T(n) = 6T(n/3) + 2n log n 7. T(n) = 9T(n/3) + 2n log n 8. T(n) = 2T(n/8) + 4n Problem 2. Without using the Master Theorem, what is the solution for the following recurrences? 1. T(n) = T(n/4) + 6n 2. T(n) = 2T(1/2) +3 3. T(n) = T(3n/4) +T(n/4) + 2n