Chapter 1 - Limits and Continuity - 1.6 Continuity of Trigonometric Functions - Exercises Set 1.6 - Page 106: 21

$$0$$

Given $$\lim_{x\to 0^+}\frac{\sin x}{5\sqrt{x}}$$ Then \begin{align*} \lim_{x\to 0^+}\frac{\sin x}{5\sqrt{x}}&=\lim_{x\to 0^+}\frac{\sin x}{5\sqrt{x}}\frac{\sqrt{x}}{\sqrt{x}}\\ &=\lim_{x\to 0^+} \sqrt{x}\frac{\sin x}{5x} \\ &=\lim_{x\to 0^+} \frac{\sqrt{x}}{5}\lim_{x\to 0^+}\frac{\sin x}{ x} \\ &=(0)(1)\\ &=0 \end{align*}