Find the linear approximation of the function f(x)=\sqrt{1-x} at a=0 and use it to approximate the numbers \sqrt{0.9} and \sqrt{0.99}.

ossidianaZ 2021-06-11 Answered

Find the linear approximation of the function f(x)=1x at a=0 and use it to approximate the numbers 0.9 and 0.99.

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Expert Answer

wheezym
Answered 2021-06-12 Author has 103 answers

The formula for linearization L(x) is
L(x)=f(a)+f(x)(xa)
we have
f(x)=1x with a=0
f(a)=10=1
f(x)=(1x)=(1x)(1x)=1211x
f(a)=12110=12
L(x)=112(xa)=112x
1x=0.99 so x=0.01
L(0.01)=1120.01=0.95
1x=0.999 so x=0.001
L(0.01)=1120.001=0.995

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