Respuesta :

bbyluv
Since you are approaching it from the positive side you should not use L'Hopitals rule. 
You should instead use very small values of x to see the trend 

if you look at x=.0001, then ln(.0001)/(.0001)= -92103.4 
where as x=1, ln(1)/1=0 
as you can see as x approaches 0, the answer goes to - infiniti
HomertheGenius
I think that a question is not complete: But if it is :[tex] \lim_{x \to \infty} \frac{ln x}{x} [/tex]then it is a form:infinity/infinity and we will use l´Hospitals rule:[tex] \lim_{x \to \infty} \frac{1/x}{1} [/tex]=1/∞ = 0.