Question

What is the limit of LN x / x

Answer 1

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

Answer 2

I think that a question is not complete: But if it is :
`\lim_(x \to \infty) (ln x)/(x)`then it is a form:infinity/infinity and we will use l´Hospitals rule:
`\lim_(x \to \infty) (1/x)/(1)`=1/∞ = 0.