Answer
$\frac{1}{4.002} \approx 0.249875$
Work Step by Step
Let $y = \frac{1}{x}$
$\frac{dy}{dx} = -\frac{1}{x^2}$
$dy = -\frac{1}{x^2}~dx$
Let $x = 4$ and let $dx = 0.002$
$dy = -\frac{1}{4^2}~(0.002)$
$dy = -\frac{1}{8000}$
We can find an approximation for $\frac{1}{4.002}$:
$\frac{1}{4.002} \approx \frac{1}{4} -\frac{1}{8000}$
$\frac{1}{4.002} \approx \frac{2000}{8000} -\frac{1}{8000}$
$\frac{1}{4.002} \approx \frac{1999}{8000}$
$\frac{1}{4.002} \approx 0.249875$
