Can someone provide concrete reasoning for how to solve the following equations with respect to Big-Oh, Big-Omega, and Big-Theta?
\begin{equation} 6n^2 + 20n = O(n^3) \end{equation} \begin{equation} 6n^2 + 20n = Ω(n^3) \end{equation} \begin{equation} 6n^2 + 20n = Θ(n^3) \end{equation}
My teacher began discussing these concepts but I was confused when he explained it. Any help would be appreciated.
Intuitively, it's all about how fast the function grows. Big-O says upper limit-- $f(n)$ doesn't grow any faster(/slower) than $g(n)$ when $f(n)=O(n)$ (/$\Omega(n)$).
Your 2nd & 3rd equations are wrong. 1st is more accurate with small o.