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: 46

Answer

1

Work Step by Step

The argument of the limit can be rewritten as $$sin(sin(x))/sin(x)$$ Taking the derivative of the top and bottom (L'hopital) $$cos(sin(x))*cos(x)/cos(x)= cos(sin(x))$$ Plugging in $0$, $cos(0) = 1$
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