# NRM approximation

• Apr 13th 2010, 06:11 AM
sigma1
NRM approximation
can someone show me how this is done.. the lnx function has me a bit confuse

lnx = 4-x

starting with 2.9 as s first approximation to this roots use newton-rapson method to evaluate successive approximations to this root to 2 decimal places.
• Apr 13th 2010, 06:32 AM
We want to find the solution to...

$f(x) = 0$ where $f(x) = \ln(x) + x - 4$.

We also have,

$f'(x) = \frac{1}{x} + 1$

Newtons Method (aka Newton-Rapson Method) is

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

Which for our problem is...

$x_{n+1} = x_n - \frac{\ln(x_n) + x_n - 4}{1/x_n + 1}$

So we get...

$x_0 = 2.9$

$x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 2.9 - \frac{f(2.9)}{f'(2.9)}$

$x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}$

Etc...

I'll leave it to you to compute each $x_n$