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: 9

Answer

$\lim\limits_{x \to 0}{\frac{sin (7x)}{sin(3x)}}=\frac{7}{3}$

Work Step by Step

$\lim\limits_{x \to 0}{\frac{sin (7x)}{sin(3x)}} $ Multiply and divide by 7 and 3 $=\lim\limits_{x \to 0}{\frac{\frac{7sin (7x)}{7x}}{\frac{3sin(3x)}{3x}}}$ Let $t=7x$ in numerator and $u = 3x$ in denominator $=\frac{7}{3}\frac{\lim\limits_{t \to 0}{\frac{sin(7x)}{7x}}}{\lim\limits_{u \to 0}{\frac{sin(3x)}{3x}}}$ $=\frac{7}{3}\times\frac{1}{1}=\frac{7}{3}$
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