Use \( \lim \limits _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1 \) to find \( \lim \limits _{\theta \rightarrow 0} \frac{2\theta}{\tan \theta} \)

\( \lim \limits _{\theta \rightarrow 0} \frac{2\theta}{\tan \theta} = 2 ( \lim \limits _{\theta \rightarrow 0} \cos \theta ) (\lim \limits _{\theta \rightarrow 0} \frac{\theta}{\sin \theta})=(2)(1) \frac{1}{ \lim \limits _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}} = \frac{2}{1}=2 \)