Question

Need help with linear approximation

Answer 1

Consider a function f(x), the linear approximation L(x) of f(x) is given by

$L(x)=f(a)+(x-a)f'(a)$

Given the quantity: $\frac{1}{203}$

We approximate the quantity using the function $f(x)= \frac{1}{x}$, where x = 203.

We choose a = 200, thus the linear approximation is given as follows:

$L(203)=f(200)+(203-200)f'(200) \\ \\ = \frac{1}{200} - \frac{3}{200^2} = \frac{200-3}{200^2} = \frac{197}{40,000} =0.004925$