## Calculus: Early Transcendentals 8th Edition

The maximum possible error when computing the area of the window is $~~16.7~cm^2$
Let $x$ be the length of one side of the square. Then the radius of the semicircle is $\frac{x}{2}$ We can find an expression for the area: $A = x^2+\frac{1}{2}~\pi~(\frac{x}{2})^2$ $A = x^2+\frac{\pi~x^2}{8}$ We can find $dA$: $dA = (2x+\frac{2\pi ~x}{8})~dx$ $dA = (2x+\frac{\pi ~x}{4})~dx$ $dA = [2(60)+\frac{60\pi}{4}]~(0.1)$ $dA = 16.7~cm^2$ The maximum possible error when computing the area of the window is $~~16.7~cm^2$