28.61. Calculate the limit $\lim _{x \rightarrow a} \frac{a^{x}-x^{a}}{x-a}$.
28.61. By L'Hôpital's rule

$$
\begin{aligned}
& \lim _{x \rightarrow a} \frac{a^{x}-x^{a}}{x-a}=\lim _{x \rightarrow a}\left(a^{x}-x^{a}\right)^{\prime}=\lim _{x \rightarrow a}\left(\ln a \cdot a^{x}-a x^{a-1}\right)= \\
&=\ln a \cdot a^{a}-a^{a}=a^{a}(\ln a-1)
\end{aligned}
$$