Question

Need help with linear approximation

Use linear approximation to estimate the following quantities. Choose a value of a to produce a small error.
1/203

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:
`(1)/(203)`

We approximate the quantity using the function
`f(x)= (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) \\ \\ = (1)/(200) - (3)/(200^2) = (200-3)/(200^2) = (197)/(40,000) =0.004925`