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. L(x) =         √0.9    √0.99

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section: Chapter Questions
Problem 23CLR
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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.

L(x) =  

 
 

 

√0.9   

√0.99  

 

Expert Solution
Step 1

The linear approximation of the function y=1-x=fx at a=0 is given by

y=f0+xf'0.

First to find f'(x), 

f'x=-121-x32

And f'0=-12.

Hence the approximation is 

y=1-12x.

That is Lx=1-12x.

 

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