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: 6



Work Step by Step

To estimate $\Delta f = f (3.02) − f (3)$, we fhave $$ f'(x)=\frac{\pi }{3}\sec^2 \frac{\pi x}{3}$$ Now, we have $$\Delta f= f'(3)\Delta x= \frac{\pi }{3}\sec^2 \frac{\pi 3}{3} (0.02)=\frac{\pi }{3}(0.02)=\approx 0.021 $$
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