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The measurement of the radius of the end of a log is found to be 8 inches, with a possible error of 1/8 inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.

Sagot :

By using the differentials to approximate the possible propagated error in computing the area of the end of the log is ±2π

The measurement of the radius of the end of a log = 8 inches

The possible error of radius = 1/8 inches

The area of cross section of the end of the log = πr^2

A =  πr^2

dA / dr = 2πr

dA = 2πr(dr)

Here the possible error of radius = 1/8 inches

dr = 1/8 inches

Substitute the values in the equation

dA = 2π × 8 × (± 1/8)

= ±2π

Therefore, the possible propagated error in computing the area is ±2π

Learn more about area here

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