4. Among the following four numbers, the largest is ( )
A: $\ln \sqrt{2}$
B: $\frac{1}{e}$
C: $\frac{\ln \pi}{\pi}$
D: $\frac{\sqrt{10} \ln 10}{20}$
Answer B.
Analysis Consider the function $f(x)=\frac{\ln x}{x}$, then the four options are $f(2), f(e), f(\pi), f(\sqrt{10})$. Since $f^{\prime}(x)=\frac{1-\ln x}{x^{2}}$, it is clear that $f(x)$ is monotonically increasing on $(0, e)$ and monotonically decreasing on $(e,+\infty)$, so the maximum value of $f(x)$ on $(0,+\infty)$ is $f(e)$.