Newton's method

May 2010
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Use Newton's method to approximate the given number correct to eight decimal places

130Radical130
 
Sep 2008
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539
West Malaysia
Use Newton's method to approximate the given number correct to eight decimal places

130Radical130
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

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

MHF Helper
Apr 2005
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Unless, of course, you mean \(\displaystyle \sqrt[130]{130}\). In that case, use Newton's method with \(\displaystyle f(x)= x^{130}- 130\).
 
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