Find the percentage error

Question

Approximate1/98 to four decimal places using the linearization L(x) of f(x) = 1/x at a = 100 and use a calculator to compute the percentage error.

(Use decimal notation. Give your answer to two decimal places.)

The percentage error ≈

Answer 1

f(100) = .01 ; f^'(x) = - 1/x² ; f^'(100) = - .0001

L(98) = .01 - .0001(-2) = .0102

f(98) = .0102041863

[f(98) - L(98)] / f(98) = .0004 = .04 %