The length, width, and height of a box are measured as 6 ft, 8 ft, and 4 ft, respectively, with an error in measurement of at most 0.2 ft in each. Use differentials to estimate the maximum error (in feet) in the calculated volume of the box.
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The differential of V is given by dV = wdh + hdw + lwh. Given that the error in measurement is at most 0.2 ft for each dimension, we have dl = dw = dh = 0.2 ft. Substituting these values into the differential, we get dV = 8*0.2 + 4*0.2 + 6*0.2 = 3.6 ft^3. Show more…
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