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 $0$,
$cos(0) = 1$
Calculus 8th Edition
by Stewart, James
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
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