Question

Area The measurement of the side of a square floor tile is 10 inches, with a possible error of $\frac{1}{32}$ inch. (a) Use differentials to approximate the possible propagated error in computing the area of the square. (b) Approximate the percent error in computing the area of the square.

          Area The measurement of the side of a square floor tile is
10 inches, with a possible error of $\frac{1}{32}$ inch.
(a) Use differentials to approximate the possible propagated error in computing the area of the square.
(b) Approximate the percent error in computing the area of the square.

Added by Robin H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert William Semus

07/18/2022

Step 1

The differential of $A$ is $dA = 2x \, dx$. Here, $x = 10$ inches and $dx = \frac{1}{32}$ inch. Substituting these values into the differential, we get $dA = 2(10) \left(\frac{1}{32}\right) = \frac{5}{8}$ square inches. This is the approximate propagated error in Show more…

Show all steps

Thanks for your feedback!

Area The measurement of the side of a square floor tile is 10 inches, with a possible error of $\frac{1}{32}$ inch. (a) Use differentials to approximate the possible propagated error in computing the area of the square. (b) Approximate the percent error in computing the area of the square.