Chapter 1 - Limits and Continuity - 1.6 Continuity of Trigonometric Functions - Exercises Set 1.6 - Page 105: 18

$$0$$

Given $$\lim_{\theta\to 0 }\frac{\sin^2 \theta }{\theta }$$ Then \begin{align*} \lim_{\theta\to 0 }\frac{\sin^2 \theta }{\theta }&= \lim_{\theta\to 0 }\sin \theta \frac{\sin \theta }{\theta } \\ &= \lim_{\theta\to 0 }[\sin \theta] \lim_{\theta\to 0 }\frac{\sin \theta }{\theta }\\ &=(0)(1)\\ &=0 \end{align*}