List these functions so that each function is big- O of the next function in the list: (logn)3, n3/1000000, . 100n+ 101.3n.n!, 2nn2.

Step 1:

In this problem, we need to arrange the list of these functions so that each function is big-O of the next function.

Step 2:

The definition for Big- O:

Let f and g be functions from the real numbers to the real numbers. Then f is O(g) if there are constants c and k

Such that

That means O(g(x)) is the set of all functions with a smaller or the same order of growth as f(x).

Example: O(x2) = {x2 , 50x +40 , logx,.....}