Newton Raphson Method for Finding Roots: Bessel's Function J0(x) near x=5

[ruby_duby]

Homework Statement

Bessel's funtion J₀(x) is assumed to have a root near x=5. Use the Newton raphson method to find this root to 3 decimal places by taking the first 4 terms of the series.

I have found this link which helps me solve the question:

http://www.vibrationdata.com/Newrap.pdf

PLEASE LOOK AT PAGES 15-16

Homework Equations

Newton raphson equation: x= a- f(a)$$/$$ f'(a)

The Attempt at a Solution

well I assume that as the root is near x=5, my first value that I substitute into the Newton raphson equation should be 5.

However, I get the value 3.895752124 which i do not think is right.

The table of values on page 16 of the link I have attached are the correct values I should have obtained, but I do not know where I am going wrong.

Can anyone confirm the values I should expect to obtain?

 

[D H]

You are correct; 3.895752124 as the value for the first iteration is not correct; you should replicate the table in that attachment.

It's kinda hard to tell you where you went wrong because you didn't tell us what you did to get that erroneous value. What did you do, in detail?