Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.10 - Linear Approximations and Differentials. - 3.9 Exercises - Page 257: 39

Answer

The relative error in calculating $I$ is the same in magnitude as the relative error in $R$.

Work Step by Step

$V = R~I$ $I = \frac{V}{R}$ $dI = -\frac{V}{R^2}~dR$ We can find an expression for the relative error in calculating $I$: $\frac{dI}{I} = \frac{-\frac{V}{R^2}~dR}{V/R}$ $\frac{dI}{I} = -\frac{dR}{R}$ Therefore, the relative error in calculating $I$ is the same in magnitude as the relative error in $R$.
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