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Working with maximum resulting error in calculation of area

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The dimensions of a closed rectangular box are found by measurement to be 10 cm by 15 cm by 20 cm, but there is a possible error of 0.1 cm in each. Use differentials to estimate the maximum resulting error in computing the total surface area of the box.

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Clear explanations and all mathematical steps are provided. It provides a discussion of working with maximum resulting error in calculation area.

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Denote the three dimensions of the box by x, y, and z. Then the surface area is given by
S = ...

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