Is it sufficient to use $O(n)$ repeatedly on $1^{\infty},\frac{0}{0},0\times\infty,{\infty}^0,0^0$ to get determinate forms? For example if we look at $\frac{0}{0}$ then $\frac{O(f(n))}{O(g(n))}$ should simplify the matters, and if needed repeat again to get $\frac{O(O(f(n)))}{O(O(g(n)))}$
My question is: at most would it be sufficient to repeatedly apply $O(n)$ to find the limit? Using this approach what type of limits would still after an infinite application of above process remain indeterminate?
By using of $O(f(x))$ we mean what is given in this example , e.g. Just substitution of dominant terms in place of the function.
Update : separated the L'Hopitals aspect of the question into Examples of applying L'Hôpitals rule ( correctly ) leading back to the same state?, tried to clarify what I tried to mean by using of $O(f(x))$