# Newtons method help

• Mar 17th 2012, 08:19 AM
house2012
Newtons method help
Hey guys, need some help with this question. I am stuck and don't know what to do.

Q: Show that using newton's method to $1-\frac{R}{x^n}$ and to $x^n-R$ for determining $(R)^{\frac{1}{n}}$ results in 2 similar, but different iterative formulas, with $n \ge 2$ and $R >0$

• Mar 27th 2012, 02:04 PM
thelostchild
Re: Newtons method help
Ok so Newton's method is a way of determining a root of the equation
$f(x)=0$

in both of the cases above for $f(x)$ we obtain $f(x) =0 \Rightarrow x = (R)^{1/n}$ so we just need to apply Newton's method.

This works by calculating the tangent line at a point $x_n$ finding where it intersects the x-axis and assuming that this gives a better approximation to the root than $x_n$

Graphically you can see it at work here
$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$
So work out the derivatives of the two functions you have above then plug it into the formula and you should have two iterative formulas which will converge on $(R)^{1/n}$