## Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning

# 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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