Calculus (3rd Edition)

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

Chapter 4 - Applications of the Derivative - 4.1 Linear Approximation and Applications - Exercises - Page 172: 13


$\Delta y\approx-0.007$

Work Step by Step

For small $\Delta x$, $\Delta y\approx dy$. That is, $\Delta y\approx f'(a) dx$. $f'(a)=-\sin a=-\sin \frac{\pi}{6}= -\frac{1}{2}$ $dx=0.014$ $\implies \Delta y\approx -\frac{1}{2}\times0.014=-0.007$
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