# Math Help - Newton Raphson, help please!

1. ## Newton Raphson, help please!

Using the Newton Raphson method, which I'm not too clear on, I need to solve: x^3 + x -1 = 0, to 3 d.p
and also
cos x = x^2

2. Newton-Raphson :

$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$

Solve then by taking $f(x)=x^3+x-1$ and $f'(x)=3x^2+1$ and find the initial value $x_2=\frac{x_1+x_0}{2}$, where approx root lies between $x_0$ and $x_1$

and then

$x_{2}=x_1-\frac{f(x_1)}{f'(x_1)}$

$x_{3}=x_2-\frac{f(x_2)}{f'(x_2)}$

etc..