# Newton's method

• May 15th 2010, 06:17 PM
sheva2291
Newton's method
Use Newton's method to approximate the given number correct to eight decimal places

• May 15th 2010, 08:48 PM
Quote:

Originally Posted by sheva2291
Use Newton's method to approximate the given number correct to eight decimal places

Use the Newton method to approximate $\sqrt{130}$ , then multiply this approximation with 130 .

then let $x=\sqrt{130}$

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

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

make use of

$
X_{n+1}=X_n-\frac{f(x)}{f'(x)}
$
• May 16th 2010, 02:46 AM
HallsofIvy
Unless, of course, you mean $\sqrt[130]{130}$. In that case, use Newton's method with $f(x)= x^{130}- 130$.