## The length and width of a rectangle are measured as 42 cm and 38 cm, respectively, with an error in measurement of at most 0.1 cm in each. U

Question

The length and width of a rectangle are measured as 42 cm and 38 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.

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2021-09-13T17:05:04+00:00
2021-09-13T17:05:04+00:00 1 Answer
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## Answers ( )

Answer:d(A) = 8 cm²Step-by-step explanation:Area of a rectangle is:A(r) = L * wL is the length, and w is the width, thend(A) = L* dw + w*dlFrom problem statement we know:L = 42 cm w = 38 cmWith an error in measurement of 0,1 cm in each case, thendw = dl = 0,1 cmAndd(A) = 42*0,1 + 38*0,1 ⇒ d(A) = 4.2 + 3.8 ⇒ d(A) = 8 cm²