Chapter 3 - Section 3.10 - Linear Approximations and Differentials. - 3.10 Exercises - Page 259: 20

(a) $dy = -\pi~(sin~\pi x)~dx$ (b) $dy = 0.0544$

(a) $y = cos~\pi x$ $\frac{dy}{dx} = (\pi)(-sin~\pi x)$ $\frac{dy}{dx} = -\pi~(sin~\pi x)$ $dy = -\pi~(sin~\pi x)~dx$ (b) $dy = -\pi~(sin~\pi x)~dx$ $dy = -\pi~[sin~\pi (\frac{1}{3})]~(-0.02)$ $dy = (0.02~\pi)~sin~\frac{\pi}{3}$ $dy = (0.02~\pi)~(\frac{\sqrt{3}}{2})$ $dy = 0.0544$