Chapter 2: Limits and Continuity - Section 2.4 - One-Sided Limits - Exercises 2.4 - Page 75: 37

$$\lim _{\theta \rightarrow 0} \theta \cos \theta=0 $$

Given $$\lim _{\theta \rightarrow 0} \theta \cos \theta $$ So, we get \begin{aligned} L&=\lim _{\theta \rightarrow 0} \theta \cos \theta\\ &= 0 \cdot \cos 0\\ &=0 \end{aligned}