Find the linear approximation of the function f(x)=\sqrt{4-x} at a=0Use L(x) to approximate the numbers sqrt (3.9) and sqrt (3.99) Round to four decimal places

abondantQ 2021-06-01 Answered

Find the linear approximation of the function \(f(x)=\sqrt{4-x}\) at \(a=0\)
Use L(x) to approximate the numbers \(\sqrt{3.9}\) and \(\sqrt{3.99}\) Round to four decimal places

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estenutC
Answered 2021-06-02 Author has 20167 answers
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content_user
Answered 2021-09-09 Author has 10511 answers

\(L(x)=2-\frac{1}{4}(x)\)

Since you are looking for v 3.9, substiute \(x=0,1\) so that \(4-0,1=3,9\)

\(L(0,1)=f(3.9)=2-(\frac{0.1}{4})=1.975\)

Now substitute \(x=0,01\)

\(L(0,01)=f(3,99)=2-(\frac{0.01}{4})=1.9975\)

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