How to determine if it is l'Hopital's or not? 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 ?  
 A: The only allowable forms by L'Hopital are $$\frac{0}{0} \,\,\text{and} \,\, \frac{\pm \infty}{\pm \infty} \,\,.$$
Hopefully this suffices to answer your question. If not, let me know. Note the $\pm$ in both the numerator and denominator of the latter form. Usually, the aim is to play with the limit until it is in one of these forms and then apply L'Hopital's rule. Summarizing, there are no other forms (even indeterminate forms) that are allowable under this rule.
A: You can use L'Hopital when
$$\lim_{x\to a} \dfrac{f'(x)}{g'(x)} = L \in [-\infty,\infty]$$
and if either
$$\lim_{x\to a} f(x) = \lim_{x\to a} g(x) = 0 \quad \text{or}\quad \lim_{x\to a} g(x) = \pm\infty$$
Each of these conditions are important. For example, you cannot use L'Hopitals rule to determine $\lim_{x\to \infty}\frac{x+\sin(x)}{x}$ even though the denominator tends to $\infty$. This is because the limit $\lim_{x\to \infty}\frac{1+\cos(x)}{1}$
does not exist.
To answer your question, there are no other forms which L'Hopital's rule may be applied. You may be able to convert your limit into a form where the rule can be applied but you cannot directly apply it to other limits. 
