Newton's Method
Q. Taking x = 1.5 as a first approximation, use one step of Newton's method to find a better approximation to this root, ln x = 2 - x

Question

Newton's Method 
Q. Taking x = 1.5 as a first approximation, use one step of Newton's method to find a better approximation to this root, ln x = 2 - x

phi · Answer

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

butterflydreamer · Answer

so would that mean x1 = 1.5 and we're trying to find x2 ?
But how do we get f(x) ? 
Would it just be f(x) = ln x - 2 + x ?

phi · Answer

yes

phi · Answer

you need a calculator to evaluate f(1.5)
f'(x) = 1/x + 1
and f'(1.5) = 5/3

the new estimate for x will be
=  1.5 -  3/5 *  ( ln(1.5) + 1.5 -2)

butterflydreamer · Answer

thankk you :D @phi . I ended up with x2 = 1. 56

dan815 · Answer

do u know how newtons method works

dan815 · Answer

okay suppose you are given some function of x, we first rewrite in the form
f(x) =0
okay lets just suppose this f(x) is a parabola for simplifcity sake, u will be able to see why it extend all almost all other polynomial functions

dan815 · Answer

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