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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.

Solution Preview

Denote the three dimensions of the box by x, y, and z. Then the surface area is given by
S = 2(xy + ...

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Clear explanations and all mathematical steps are provided.

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