Question

Why is the Big O of 5N(log2 N) + N x sqrt(N) equals to O(N^1.5)?

Answer 1

I'm just learning Big O notation myself now so this is my interpretation

5N(log2 N) + N x sqrt(N) =
5N(log2 N) + (N x N^0.5)
5N(log2 N) + N^1.5

BigO of the above should take the term which will grow the largest as n approaches infinity and that will be N^1.5 therefore your answer O(N^1.5).

Answer 2

\[O(an ^{x} + bn ^{y} + cn ^{z}) = O(an ^{x}) = O(n ^{x}) \] for x>y>z