Question

The side of a square is measured to be $10 \mathrm{ft},$ with a possible error of $\pm 0.1 \mathrm{ft}$. (a) Use differentials to estimate the error in the calculated area. (b) Estimate the percentage errors in the side and the area.

          The side of a square is measured to be $10 \mathrm{ft},$ with a possible error of $\pm 0.1 \mathrm{ft}$.
(a) Use differentials to estimate the error in the calculated area.
(b) Estimate the percentage errors in the side and the area.

Added by Elisa H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

01/05/2023

Step 1

We want to find the change in area, $\Delta A$, when there is a small change in side length, $\Delta s$. We can use differentials to approximate this change. The differential of $A$ is $dA = 2s \cdot ds$. Given that $s = 10$ ft and $ds = 0.1$ ft, we can substitute Show more…

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The side of a square is measured to be $10 \mathrm{ft},$ with a possible error of $\pm 0.1 \mathrm{ft}$. (a) Use differentials to estimate the error in the calculated area. (b) Estimate the percentage errors in the side and the area.