Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.4 Derivatives of Trigonometric Functions - 2.4 Exercises - Page 151: 43


$$\lim _{x \rightarrow 0} \frac{\sin 3 x}{5 x^{3}-4 x}=-\frac{3}{4}$$

Work Step by Step

Given $$\lim _{x \rightarrow 0} \frac{\sin 3 x}{5 x^{3}-4 x}$$ So, \begin{align} \lim _{x \rightarrow 0} \frac{\sin 3 x}{5 x^{3}-4 x}&=\lim _{x \rightarrow 0}\left(\frac{\sin 3 x}{3 x} \cdot \frac{3}{5 x^{2}-4}\right)\\ &=\lim _{x \rightarrow 0} \frac{\sin 3 x}{3 x} \cdot \lim _{x \rightarrow 0} \frac{3}{5 x^{2}-4}\\ &=1 \cdot\left(\frac{3}{-4}\right)=-\frac{3}{4} \end{align}
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