Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 4 - Differentiation - 4.1 Linear Approximation and Applications - Exercises - Page 173: 28



Work Step by Step

Consider $ f(x)=\sin{x}$, $a=\pi/3 $ and $\Delta x= \pi/180 $, since \begin{align*} f'(x) &= \cos{x}\\ f'( \pi/3)&=\frac{1}{2} \end{align*} Then \begin{align*} f(a+\Delta x)&=f(a)+f^{\prime}(a) \Delta x\\ f( 61 )&= \sin (60)+\frac{1}{2} \frac{\pi}{180} \\ \sin (61)-\sin (60)& \approx \frac{\pi}{360} \\ & \approx0.00872 \end{align*}
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