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: 7

Answer

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

Work Step by Step

$\lim\limits_{x \to 0}{\frac{sin (3x)}{x}} = 3\times\lim\limits_{x \to 0}{(\frac{sin (3x)}{x} \times \frac{1}{3})} =3\times\lim\limits_{x \to 0}{\frac{sin (3x)}{3x}}$ Let $t=3x$ $3\times\lim\limits_{t \to 0}{\frac{sin (t)}{t}} = 3\times1=3$
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