(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find an approximated value for [tex]\sqrt[ ]{9.03}[/tex] using a Taylors polynomial of third degree and estimate the error.

2. Relevant equations

3. The attempt at a solution

I thought of solving it by using

[tex]f(x)=\sqrt[]{x}[/tex] centered at [tex]x_0=9[/tex]

So

[tex]P_n(x)=3+\dysplaystyle\frac{(x-9)}{6}-\dysplaystyle\frac{(x-9)^2}{216}+\dysplaystyle\frac{3(x-9)^3}{3888}[/tex]

Then I evaluated it at x=9.03, so I get:

[tex]P_n(x)=3+\dysplaystyle\frac{(0.3)}{6}-\dysplaystyle\frac{(0.3)^2}{216}+\dysplaystyle\frac{3(0.3)^3}{3888}\approx{3.049604167}[/tex]

I don't know if this is right, I've tried with the calculator and it gives 3.00500.... Now, how do I estimate the error? just by resting to the value the calculator gives the one I get?

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# Homework Help: Taylors polynomials

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