Find the linear approximation of the function f(x) = √1-x at a = 0 and use it to approximate the numbers √0

Math Jan 16, 2021

Find the linear approximation of the function f(x) = √1-x at a = 0 and use it to approximate the numbers √0.9 and √0.99. (Round your answers to four decimal places.)

L(x) =

√0.9 ≈

√0.99 ≈

Expert Solution

f(x) = sqrt (1 - x)

f(0) = 1

pt (0,1)

f'(x) = 1/2*(1-x)^(-1/2)*-1
f'(x) = (-1/2)*(x-1)^(-1/2)

T(x) = 1 - 1/2*(x)

To estimate 0.9 we need to put in 0.1 and 0.01

T(0.1) = 1 - 1/2*0.1 = 1 - 0.05 = 0.95 <ANSWER
T(0.01) = 1 - 1/2*0.01 = 0.995 <ANSWER

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