# Big O Notation

I'm having some trouble with this discrete question:

Find the least natural number n such that
√(x² + x³ + 3) is O(xⁿ).

With the value of n that you have found, is it true that
xⁿ is O( √(x² + x³ + 3) )?

Can anyone help?

HallsofIvy
Homework Helper
Well, starting with the definition of "O" would be a good idea. What is it?

Hurkyl
Staff Emeritus
$$\frac{\sqrt{x^2+x^3+ 3}}{x^n}$$