Consider a function f(x), the linear approximation L(x) of f(x) is given by
[tex]L(x)=f(a)+(x-a)f'(a)[/tex]
Given the quantity: [tex] \frac{1}{203} [/tex]
We approximate the quantity using the function [tex]f(x)= \frac{1}{x} [/tex], where x = 203.
We choose a = 200, thus the linear approximation is given as follows:
[tex]L(203)=f(200)+(203-200)f'(200) \\ \\ = \frac{1}{200} - \frac{3}{200^2} = \frac{200-3}{200^2} = \frac{197}{40,000} =0.004925[/tex]
