I got a lot of limits questions that I am able to find there limits, but I do not know if they meet the qualification to be l'Hopital's or not. SO how to know that ?
For example:
Q1) $ \lim_{t \rightarrow \infty} \dfrac{(\ln t )^ 2}{t}$
I would say yes, infinity/infinity
Q2) $ \lim_{y \rightarrow 0} \dfrac{2y}{y^2}$
I would say yes 0/0
Q3) $ \lim_{x \rightarrow \infty} \dfrac{e^{−x}}{ 1 + \ln x }$
I would say no, 0/number
Q4) $\lim_{\theta \rightarrow 0} \dfrac{\arctan \theta}{7\theta}$
I would say yes, 0/0
Q5) $\lim_{x \rightarrow 0+ } \dfrac{\cot x}{\ln x}$
I don't know if the 0+ would make a difference of the 0. But The answer would be no because 0/undefined
So bottom line is there any rules to know if it is l'Hospital's or not? I just feel that 0/0 and infinity/infinity are the ones that can determine. BUt is there any other forms ? such as 0/1 or 1/0 or infinity/0 ?