Find the Taylor polynomial of degree n=4 for each function expanded about the given value of x_0 f(x)=sqrt(x), x_0 =1

Alex Baird 2022-07-26 Answered
Find the Taylor polynomial of degree n=4 for each function expanded about the given value of ${x}_{0}$.
$f\left(x\right)=\sqrt{x},{x}_{0}=1$
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Answers (1)

Ragazzonibw
Answered 2022-07-27 Author has 15 answers
Find the Taylor polynomial of degreen=4 for each function expanded about the given value of ${x}_{0}$.
$f\left(x\right)=\sqrt{x}⇒f\left(1\right)=1$
${f}^{\prime }\left(x\right)=1/\left(2\sqrt{x}\right)⇒{f}^{\prime }\left(1\right)=1/2$
...
$f\left(x\right)=1+\frac{x-1}{2}-\frac{\left(x-1{\right)}^{2}}{8}+\frac{\left(x-1{\right)}^{3}}{16}-\frac{5\left(x-1{\right)}^{4}}{128}+..$
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