Newton's Method

[jinNjoe]

Hey, im stuck on a couple of problems using Newton's Method
hope you can help!

1) Use Newton's Method to solve e^x = 3-2x

2)
a) apply Newton's Method to the equation x^2 - a = 0 to drive the following square root algorithm

Xn+1 = (Xn + a/Xn) / 2

b) use (a) to compute sqt. (1000) correct to 6 decimal places.

Thank you

 

[galactus]

Newton's method os just a matter of iterating.

\(\displaystyle f(x)=e^{x}+2x-3\)

\(\displaystyle f'(x)=e^{x}+2\)

Now use \(\displaystyle x_{n+1}=x_{n}-\frac{f(x)}{f'(x)}\)

Start with an initial guess of, say, \(\displaystyle x=0.5\)

Then, keep iterating by plugging the last answer into the formula. It will converge very quickly, to the value you need.