Chapter 4 - Differentiation - 4.1 Linear Approximation and Applications - Exercises - Page 173: 28

$$0.00872$$

Consider $ f(x)=\sin{x}$, $a=\pi/3 $ and $\Delta x= \pi/180 $, since \begin{align*} f'(x) &= \cos{x}\\ f'( \pi/3)&=\frac{1}{2} \end{align*} Then \begin{align*} f(a+\Delta x)&=f(a)+f^{\prime}(a) \Delta x\\ f( 61 )&= \sin (60)+\frac{1}{2} \frac{\pi}{180} \\ \sin (61)-\sin (60)& \approx \frac{\pi}{360} \\ & \approx0.00872 \end{align*}