Purpose: Demonstrate the ability to design, analyze, and prove correctness of algorithms based on Divide-and-Conquer techniques. Question 1 (15 POINTS): Using asymptotic upper bound definition for "O, show that 2n+1-O(2). Please show your work. Question 2. (20 POINTS): Given the recurrence: T(n) = T(n-1) + 1 use substitution method to check whether T(n) (n). Please show your work. Question 3. (20 POINTS - 10 POINTS each) Given following recurrences, use recursion tree method to determine the asymptotic bound for each recurrence. Please show your work. 3.A.) T(n) T(n - 1)+n 3.B.) T(n) = 2T() + n