Is it possible to prove from the definition of big O that $5n^3+7n+1$ is $O(n^3)$? Can this be generalised to any case where you have to (and what is the procedure for working it out?) I guess the main question is there a specific term for this kind of procedure?
from the workings I've been given in class given $T\le O(f(n))$ if $n=1$ then $5n^3+7n+1 = 5^3+7+1 (23)$. Although I'm not sure how that relates to proving the above.