Chapter 2 - Derivatives - 2.9 Linear Approximations and Differentials - 2.9 Exercises - Page 193: 24

$0.249875$

We can rewrite the expression as $\frac{1}{2*2.001}$ Let us consider the function $f(x)=1/(2x)$ and find the linearization near $x=2$ $f'(x) = -1/(2x^2)$ which at 2 is $-1/8$ Since $x$ goes up $2.001-2 = 0.001 = 1/1000$, because of the slope, $y$ goes down $1/8000$ $1/4 - 1/8000= 0.249875$