## Calculus (3rd Edition)

We have $$\lim _{\theta \rightarrow 0} \frac{\cos \theta -2}{\theta}=\frac{1-2}{0}=\frac{-1}{0}.$$ The one-sided limits are $$\lim _{\theta \rightarrow 0^-} \frac{\cos \theta -2}{\theta}=\frac{1-2}{0^-}=\frac{-1}{0^-}=\infty.$$ $$\lim _{\theta \rightarrow 0^+} \frac{\cos \theta -2}{\theta}=\frac{1-2}{0^+}=\frac{-1}{0^+}=-\infty.$$ So the limit does not exist.