# Math Help - newton's method

1. ## newton's method

use newtons method to find the roots of the equation

sinx=x^(2)+3^(x)-1

correct to sic decimal places

2. Originally Posted by thecount
use newtons method to find the roots of the equation

sinx=x^(2)+3^(x)-1

correct to sic decimal places
Newton's methof gives us an itterative methof for finding a root of the equation $f(x)=0$. This is:

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

So for this we have:

$f(x)=x^2+3^x-1-\sin(x)$

with:

$f'(x)=2x+\ln(3)3^x-\cos(x)$

Now you need an initial guess, well there is an obvious root at $x=0$, and a bit of investigation suggests that there is another root to the left of this, so we could take an initial guess $x=-1$.

CB

3. You should understand the theory behind this method, but here is a cool online tool to help check if you're doing it correctly.

Newton's Method

Don't cheat though!