Find the linear approximation of the function f(x) = sqrt(1 − x) at a = 0.

Question

L(x)=

Use L(x) to approximate the numbers

0.9

and

0.99

.

 (Round your answers to four decimal places.)

Answer 1

L(x) = f(a) + f'(a)(x-a) where a is the point you are linearizing from

In this case: f(a) = sqrt(1-a) = 1 and f'(a) = -(1/2)(1-a)^-(1/2) = -1/2

L(x) = 1 - (1/2) x

Enjoy!