Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.5 Derivatives of Trigonometric Functions - 3.5 Exercises - Page 169: 8


$\lim\limits_{x \to 0}{\frac{sin (5x)}{3x}} =\frac{5}{3}$

Work Step by Step

$\lim\limits_{x \to 0}{\frac{sin (5x)}{3x}} = \frac{5}{3}\times\lim\limits_{x \to 0}{(\frac{sin (5x)}{3x} \times \frac{3}{5})} =\frac{5}{3}\times\lim\limits_{x \to 0}{\frac{sin (5x)}{5x}}$ Let $t=5x$ $\frac{5}{3}\times\lim\limits_{t \to 0}{\frac{sin (t)}{t}} = \frac{5}{3}\times1=\frac{5}{3}$
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