What is the range of the function $\frac{\log{x}}{x}$.
I want an approach to this problem and not just an answer.
How do I approach such problems?
2026-03-27 04:04:49.1774584289
Need an approach for this
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$$\left(\frac{\ln{x}}{x}\right)'=\frac{1-\ln{x}}{x^2},$$ which says that $x_{max}=e$ and $\frac{\ln{x}}{x}\leq\frac{1}{e}$.
By the way, the domain is $(0,+\infty)$ and $\lim\limits_{x\rightarrow0^+}\frac{\ln{x}}{x}=-\infty$.
Since our function is a continuous function, we get the answer: $\left(-\infty,\frac{1}{e}\right]$.