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

1. ## 3 ques regarding diffrentiation: Taylor Polynomial, Newton-Raphson

any help will be appreciated. thanks!!

2. Originally Posted by samtrix

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:

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

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

Start with $x_0 = 1$
Code:
x_0        1
x_1        0.70773205
x_2        0.677232264
x_3        0.676832564
x_4        0.676832494
All following values equal $x_4$ (but that depends on the calculator you use)

3. Hello,

to #3:

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