# Help with Big-O homework [duplicate]

"er" is the Danish equivalent of "is" in English. I need some help with the square root one. Additionally, it would be nice to know if the other ones are correct.

You can use this fact that $$\log(n) = O(n^k)$$ for any constant $$k > 0$$ and $$k \in \mathbb{R}$$. $$k$$ in your case is $$\frac{1}{2}$$. Hence, $$\sqrt{n}$$ is not $$O(2\log(n))$$.
• But I think I remember that sqrt(x) isn't a polynomial. In other words $x^{0.5}$ isn't a polynomial. – Alexander Nielsen Sep 1 '19 at 14:47
• @AlexanderNielsen it doesn't matter. It is true for any $k > 0$ (not just for integers). – OmG Sep 1 '19 at 14:48