Chapter 2: Limits and Continuity - Section 2.4 - One-Sided Limits - Exercises 2.4 - Page 75: 34

$$\lim _{h \rightarrow 0} \frac{\sin (\sin h)}{\sin h} =1$$

Given $$\lim _{h \rightarrow 0} \frac{\sin (\sin h)}{\sin h} $$ Let $ x=\sin h \ \Rightarrow $ at $ h=0 $, we get $ x\rightarrow \sin 0=0$ So, we get \begin{aligned} L&=\lim _{h \rightarrow 0} \frac{\sin (\sin h)}{\sin h} \\ &= \lim _{x \rightarrow 0} \frac{\sin x}{x} \\ &=1 \end{aligned}