Answer
$$0$$
Work Step by Step
Our aim is to evaluate the expression $\lim\limits_{x \to + \infty} \dfrac{\ln x }{x}$.
But $\lim\limits_{x \to + \infty} \dfrac{\ln x }{x}=\dfrac{\infty}{\infty}$
We can see that the numerator and denominator have a limit of $\infty$, so the limit shows the indeterminate form of the type $\dfrac{\infty}{\infty}$. So, we will apply L'Hopital's rule which can be defined as: $\lim\limits_{x \to a} \dfrac{A(x) }{B(x)}=\lim\limits_{x \to a}\dfrac{A'(x)}{B'(x)}$
where, $a$ can be any real number, infinity or negative infinity.
$\lim\limits_{x \to + \infty} \dfrac{\ln x }{x}=\lim\limits_{x \to + \infty} \dfrac{1/x}{1}\\=\lim\limits_{x \to + \infty} \dfrac{1}{x}\\=0$
