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The side of a square floor tile is measured to be 16 inches, with a...

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Basic Math

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The side of a square floor tile is measured to be 16 inches, with a possible error of 1/32 inch. Use differentials to approximate the possible error and the relative error in computing the area of the square.Step 1Recall that the formula for the area of a square is A = x2 where x is the side of the square.We are given that the side of the square floor tile is x = 16 inches and the possible error ?x = dx = 1/32Step 2To approximate the possible propagated error in computing the area of the square, differentiate A =x with respect to x.dA /dx=dA=Step 3Substitute the given values of x and dx into the equation.dA = 2x dxStep 4Assuming that ?A=dA, we can conclude that the approximate possible propagated error in computing the area of the square isin.

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