Chapter 6 - Inverse Functions - 6.8 Indeterminate Forms and I'Hospital's Rule - 6.8 Exercises - Page 500: 18

$0$

Given: $\lim\limits_{\theta\to\pi}\dfrac{1+\cos\theta}{1-\cos\theta}$ This does not show an indeterminate form of type $\dfrac{0}{0}$, and so no need to apply L'Hospital Rule. In fact no, elementary method. Thus, $=\dfrac{1+\cos(\pi)}{1-\cos(\pi)}$ or, $=\dfrac{1+(-1)}{1-(-1)}$ or, $=0$