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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

If a current I passes through a resistor with resistance R, Ohm’s Law states that the voltage drop is V = RI. If V is constant and R is measured with a certain error, use differentials to show that the relative error in calculating I is approximately the same (in magnitude) as the relative error in R.

To determine

To show: The relative error in calculating I is approximately the same as the relative error in R. That is, ΔIIdRR.

Explanation

Given:

The current I passes through the resistor with resistance R and V is constant and R is measured certain error.

Proof:

The ohms law state that the voltage drop is, V=RI.

That is, the current I=VR.

The differential is dI=f(R)dR.

The derivative of the function f(R)=VR is computed as follows,

f(R)=ddR(VR)=VddR(1R)=V(1R11)=VR2

Substitute

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