F x y be the quantity to be measured and dx be the

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f x y be the quantity to be measured, and dx be the error for x and dy be the error for y , the error for z is given by: | | z z dz dx dy x y and the relative error for z is given by: dz z dx z dy z x z y z and the percentage error for z is given by: 100% dz z Example 6 A box with square base and height t is measured with the possible error of 0.02cm. Calculate the maximum possible error for its volume if the length is 12cm and the height is 5cm. Analysis of Error
7 Chapter 1: Functions of Several Variables 2 2 dV xtdx x dt 2 |2(12)(5)(0.02) | (12) (0.02) = 5.28 Thus, the maximum possible error for volume is 3 5.28 cm .

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