16. Given the function $f(x)=\frac{\ln x}{x}$.
(1) Suppose a real number $k$ makes $f(x)<k x$ always true, find the range of $k$;
(2) Let $g(x)=f(x)-k x(k \in \mathbf{R})$, if the function $g(x)$ has two zeros in the interval $\left[\frac{1}{\mathrm{e}}, \mathrm{e}^{2}\right]$, find the range of $k$.
Let $h(x)=\frac{\ln x}{x^{2}}, x>0$, then $h^{\prime}(x)=\frac{1-2 \ln x}{x^{3}}$. The properties of $f(x)$ in the interval $\left[\frac{1}{\mathrm{e}}, \mathrm{e}^{2}\right]$ are listed as follows:
\begin{tabular}{|c|c|c|c|c|c|}
\hline$x$ & $\frac{1}{\mathrm{e}}$ & $\left(\frac{1}{\mathrm{e}}, \sqrt{\mathrm{e}}\right)$ & $\sqrt{\mathrm{e}}$ & $\left(\sqrt{\mathrm{e}}, \mathrm{e}^{2}\right)$ & $\mathrm{e}^{2}$ \\
\hline$h^{\prime}(x)$ & & + & 0 & - & \\
\hline$h(x)$ & $-\mathrm{e}^{2}$ & increasing & $\frac{1}{2 \mathrm{e}}$ & decreasing & $\frac{2}{\mathrm{e}^{4}}$ \\
\hline
\end{tabular}
(1) From the table above, we know that $k>h(x)_{\max }=\frac{1}{2 \mathrm{e}}$, so the range of $k$ is $\left(\frac{1}{2 \mathrm{e}},+\infty\right)$.
(2) From the table above, we know that the range of $k$ is $\left[\frac{2}{\mathrm{e}^{4}}, \frac{1}{2 \mathrm{e}}\right)$.