Chapter 1 - Limits and Continuity - 1.6 Continuity of Trigonometric Functions - Exercises Set 1.6 - Page 105: 13

$$3$$

Given $$\lim_{\theta \to 0} \frac{\sin 3\theta }{\theta}$$ Then \begin{align*} \lim_{\theta \to 0} \frac{\sin 3\theta }{\theta}&=\lim_{\theta \to 0} \frac{3\sin 3\theta }{3\theta}\\ &=3\lim_{3\theta \to 0} \frac{ \sin 3\theta }{3\theta}\\ &=3(1)\\ &=3 \end{align*}