Calculus problem

Question

The side of a square is measured to be 16 ft with a possible error of ±0.1 ft. Use differentials to estimate the error in the calculated area. Include units please, thank you!

Answer 1

Let x = length of a side of the square

Then, A(x) = area of the square = x²

Estimated error in measuring the area = dA = A'(x)dx = 2xdx = 2(16 ft)(±0.1 ft) = ± 3.2 ft²