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
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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Question
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 at a=0 is given by
.
First to find f'(x),
And .
Hence the approximation is
.
That is .
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