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 1 2 2 Recall that the formula for the area of a square is A = x 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 is Ax = dx = 1 32 Step 2 To approximate the possible propagated error in computing the area of the square, differentiate A = x with respect to x. dA = 2 2 x dx dA = 2 2 x dx Step 3 Substitute the given values of x and dx into the equation. dA = 2x dx = 2(16 16 () 32 32 32 == in 32 Step 4 Assuming that AA = dA, we can conclude that the approximate possible propagated error in computing the area of the square is in