# Thread: newton raphson iterative method

1. ## newton raphson iterative method

okay so i got a question conserning newton-raphson method to find a root to 4 d.p.

the equation is $\displaystyle e^x-3x = 0$ now i've got the equation

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

i have been given the information to start with $\displaystyle x_{0} = 2.$

my question is how do i use the equation. I have no idea. I know what im looking for but i have no idea how to use the equation.

Cheers guys!

okay so i got a question conserning newton-raphson method to find a root to 4 d.p.

the equation is $\displaystyle e^x-3x = 0$ now i've got the equation

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

i have been given the information to start with $\displaystyle x_{0} = 2.$

my question is how do i use the equation. I have no idea. I know what im looking for but i have no idea how to use the equation.

Cheers guys!
Ummm... Plug it into the formula?

$\displaystyle f(x) = e^x - 3x$

$\displaystyle f^{\prime} = e^x - 3$

So
$\displaystyle x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} = x_n - \frac{e^{x_n} - 3x_n}{e^{x_n} - 3}$

With [tex]x_0 = 2 we have
$\displaystyle x_1 = 2 - \frac{e^2 - 3 \cdot 2}{e^2 - 3} \approx 1.6835182627834$

Then do it again with $\displaystyle x_1 = 1.6835182627834$ to get $\displaystyle x_2$, etc.