(Requires calculus) Show that if d is positive and b > I, then nd is O(bn) but bn is not O(nd).

Step 1</p>

In this problem we have to show that if d is a positive and b > 1, then but .

Step 2</p>

Function is called if there exist constant c and k such that

where

We have , and d is positive

So, ,

We get indeterminate form.

So, using L’ hospital’s rule

Using again and again we get,

Or,

Or,

For

We can express

Therefore .