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Thread: approximations using Taylor sries

  1. #1
    Member akhayoon's Avatar
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    approximations using Taylor sries

    I hear you could use taylor polynomials or series to approximate things like $\displaystyle \sqrt9.04$ for example or something like that...is that true and how can that be done?

    post number 100 yay!!!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by akhayoon View Post
    I hear you could use taylor polynomials or series to approximate things like $\displaystyle \sqrt9.04$ for example or something like that...is that true and how can that be done?

    post number 100 yay!!!!
    The Taylor series for a function $\displaystyle f $ about $\displaystyle x$ can be writen:

    $\displaystyle f(x+\varepsilon)=f(x)+\varepsilon f'(x) + \left(\frac{\varepsilon}{2}\right)^2f''(x)+ ... + \left(\frac{\varepsilon}{n!}\right)^nf^{(n)}(x)+ ...$

    In your case $\displaystyle f(x)=x^{1/2}$ , and so we have:

    $\displaystyle
    (9.04)^{1/2} \approx (9)^{1/2}+0.04 \times (1/2) \times 9^{-1/2} - 0.04^2 \times (1/8) \times 9^{-3/2} ...

    $

    Which is pretty good even after just the first two terms

    RonL
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