1. Suppose that you have two different algorithms for solving a problem. To solve a problem of size n, the first algorithm uses exactly n(log(n)) operations and the second algorithm uses exactly n^3/2 operations. As n grows, which algorithm uses fewer operations? Justify your answer using Definitional proof.

2. Using Definitional Proof, determine whether each of the functions log(n+1) and log(n² + 1) is O(log(n)).

3. Using Definitional Proof, determine whether each of the functions 2ⁿ⁺¹ and 2²ⁿ is O(2ⁿ).