The side of a square floor tile is measured to be 16 inches, with a possible error of 1/32 inch. Use differentials to

Question

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

Recall 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 
Δx = dx = ±1/32

Step 2

To approximate the possible propagated error in computing the area of the square, differentiate A =x² with respect to x.
dA /dx=
dA=

Step 3
Substitute the given values of x and dx into the equation.
dA = 2x dx

Step 4
Assuming that ΔA=dA, we can conclude that the approximate possible propagated error in computing the area of the square is
in².

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