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 in your answer.
What a horribly vague answer Steve. To someone who had a similar problem, you were of no help. can you at least say what the letters/variables represent?
steve is bad
To estimate the error in the calculated area of a square with a given side length and a possible error, we can use differentials.
Given:
Side length of the square, s = 16 ft
Possible error in the side length, Δs = ±0.1 ft
The formula for the area of a square is A = s^2.
To find the differential of the area, we differentiate both sides of the equation with respect to s:
dA = 2s ds
Now, we substitute the given values:
s = 16 ft
ds = ±0.1 ft
dA = 2(16 ft)(±0.1 ft)
dA = 3.2 ft^2
Therefore, the estimated error in the calculated area is 3.2 ft^2.
a = s^2
da = 2s ds