Big O Notation and finding witnesses I am trying to figure out some stuff here with Big O Notation. I mean I understand the concept of it and can generally be able to tell what the efficiency of something is, but I do not really understand how to find witnesses. Here is an example of one that I need to do. Can anyone help me understand this? Thanks in advance! 
Example 1:
$n^2$ is $O(0.001n^3)$.
Example 2:
$25n^4 − 19n^3 + 13n^2 − 106n + 77$ is $O(n^4)$.

HINTS: For (1), try $c=1000$. For (2), try $c=25+19+13+106+77$. In each case think about why I suggested those particular numbers. (Note that they’re not the only ones that work; anything bigger works just as well, for instance. But they are the most obvious ones to try.)
