Techniques for Order Notation:
Suppose that $f(n) > 0$ and $g(n) > 0$ for all $n\ge n_0$. Suppose that
$$ L = \lim_{n\to\infty} \frac{f(n)} {g(n)}$$Then
\[ f(n) \in \begin{cases} o(g(n)) &\text{if }\,\,L=0 \\ \Theta(g(n)) &\text{if }\,\,0 < L < \infty \\ \omega(g(n)) &\text{if }\,\,L=\infty \end{cases} \]