University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.11 - Linearization and Differentials - Exercises - Page 199: 55


% error in circumference is 2% % error in area is 4%

Work Step by Step

The given % error change in radius is: $\frac{dr}{r}$ = 0.02 since % error change = $\frac{change\ in\ dimension}{original\ dimension}$ $C=2\pi r$ $dC=2\pi dr$ $A=\pi r^2$ $dA=2\pi r dr$ % error in circumference = $\frac{dC}{c}=\frac{2\pi dr}{2\pi r}=0.02$ % error in area = $\frac{dA}{A}=\frac{\pi 2r\times dr}{\pi r^2}=0.04$
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