问题：求极限limx^(1/1-x)
求极限
结论/结果
A
解答
令\frac{1}{1-x}=t, 则x=1-\frac{1}{t}, 从而
\begin{aligned}
&\lim_{x\to 1}x^{\frac{1}{1-x}}\\
=& \lim_{t\to\infin}(1-\frac{1}{t})^t\\
=& \lim_{t\to\infin}((1-\frac{1}{t})^{-t})^{-1}\\
=& e^{-1}
\end{aligned}