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 n3/2 operations. As n grows, which algorithm uses fewer operations? Justify your answer using Definitional proof.
Using Definitional Proof, determine whether each of the functions log(n+1) and log(n2 + 1) is O(log(n)).
Using Definitional Proof, determine whether each of the functions 2n+1 and 22n is O(2n).