Final answer:
To estimate the error in the area of a square with a side error of ±0.1 ft, one can use the formula dA = 2s ds, leading to an approximate area error of ±3.2 square feet.
Step-by-step explanation:
The student is asking how to estimate the error in the calculated area of a square when the side of the square is measured to be 16 ft with a possible error of ±0.1 ft using linear approximation or differentials. To calculate the error in area, we can use the concept of differentials in calculus. The area A of a square is given by A = s^2, where s is the length of a side. Using differentials, the change in area ΔA can be approximated by dA, which is given by dA = 2s ds. With s = 16 ft and ds = ±0.1 ft, the estimated error in the area is dA = 2 × 16 ft × 0.1 ft = ±3.2 ft^2. Therefore, the error in the calculated area is approximately ±3.2 square feet.