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.
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.
We want to find the solution to...
$\displaystyle f(x) = 0$ where $\displaystyle f(x) = \ln(x) + x - 4$.
We also have,
$\displaystyle f'(x) = \frac{1}{x} + 1$
Newtons Method (aka Newton-Rapson Method) is
$\displaystyle x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$
Which for our problem is...
$\displaystyle x_{n+1} = x_n - \frac{\ln(x_n) + x_n - 4}{1/x_n + 1}$
So we get...
$\displaystyle x_0 = 2.9$
$\displaystyle x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 2.9 - \frac{f(2.9)}{f'(2.9)}$
$\displaystyle x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}$
Etc...
I'll leave it to you to compute each $\displaystyle x_n$