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 152: 57

Answer

$1$

Work Step by Step

$s$ = $rθ$ $sin{\frac{θ}{2}}$ = $\frac{\frac{d}{2}}{r}$ $d$ = $2r{sin{\frac{θ}{2}}}$ $\lim\limits_{θ \to 0^{+}}{\frac{s}{d}}$ = $\lim\limits_{θ \to 0^{+}}{\frac{rθ}{2r{sin{\frac{θ}{2}}}}}$ = $\lim\limits_{θ \to 0}{\frac{\frac{θ}{2}}{{sin{\frac{θ}{2}}}}}$ = $1$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.