Use Newton's method to approximate the given number correct to eight decimal places

130Radical130

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- May 15th 2010, 06:17 PMsheva2291Newton's method
Use Newton's method to approximate the given number correct to eight decimal places

130Radical130 - May 15th 2010, 08:48 PMmathaddict
Use the Newton method to approximate $\displaystyle \sqrt{130}$ , then multiply this approximation with 130 .

then let $\displaystyle x=\sqrt{130} $

square them , and let $\displaystyle f(x)=x^2-130$

then find f'(x) , and let the initial approximation be 10 ,

make use of

$\displaystyle

X_{n+1}=X_n-\frac{f(x)}{f'(x)}

$ - May 16th 2010, 02:46 AMHallsofIvy
Unless, of course, you mean $\displaystyle \sqrt[130]{130}$. In that case, use Newton's method with $\displaystyle f(x)= x^{130}- 130$.