# 3 ques regarding diffrentiation: Taylor Polynomial, Newton-Raphson

• Oct 31st 2007, 11:07 PM
samtrix
3 ques regarding diffrentiation: Taylor Polynomial, Newton-Raphson
http://img139.imageshack.us/img139/4...iondiffhl3.gif

any help will be appreciated. thanks!! :)
• Oct 31st 2007, 11:47 PM
earboth
Quote:

Originally Posted by samtrix
http://img139.imageshack.us/img139/4...iondiffhl3.gif

any help will be appreciated. thanks!! :)

Hello,

to #3:

You are supposed to know the Raphson-Newton formula:

If you are looking for the solutions of T(x) = 0 where T(x) is a term in x and you have found an initial approximate value for a solution then the next approximate value is:

$\displaystyle x_{n+1}=x_n-\frac{T(x_n)}{T'(x_n)}$ With your problem:

$\displaystyle x_{n+1}=x_n-\frac{\cos(x_n) - 1.4 \cdot \sqrt{x_n^3}}{-\sin(x_n) - 2.1 \cdot \sqrt{x_n}}$

Start with $\displaystyle x_0 = 1$
Code:

x_0        1 x_1        0.70773205 x_2        0.677232264 x_3        0.676832564 x_4        0.676832494
All following values equal $\displaystyle x_4$ (but that depends on the calculator you use)
• Oct 31st 2007, 11:54 PM
earboth
Hello,

to #3:

you'll find additional information on Raphson-Newton method here: http://www.mathhelpforum.com/math-he...ns-method.html