Chapter 4 - Section 4.5 - Indeterminate Forms and L'Hôpital's Rule - Exercises - Page 248: 51

$e^{-1}$

Here, $\lim\limits_{x \to 0} f(0)=\dfrac{0}{0}$ This shows an indeterminate form of the limit, so we need to use L'Hospital's rule. $\lim\limits_{x \to 1} e^{(\lim\limits_{x \to 1} \frac{\ln x}{1-x})}=\dfrac{0}{0}$ This shows an indeterminate form of the limit, so we need to use L'Hospital's rule. $\lim\limits_{x \to 1} \dfrac{1/x}{-1}=e^{-1}$