\documentclass{article}

\begin{document}

Big-O definition:

$f$ is $O(g) \equiv \exists c > 0, k > 0$ such that $\forall n > k$, $f(n) \le c g(n)$

Big-O questions:

1. Show that $2n^2$ is $O(n^2)$.

2. Show that $10n^2 + 100n + 1000$ is $O(n^2)$

\end{document}