Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

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

Answer

$$0$$

Work Step by Step

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*}
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