Newton-Raphson Method for Solving Tan(x) = x with 3 Iterations

[Student2010]

Hi Please can somebody help


The equation governing the buckling load P of a strut with one end fixed and the other end simply supported is given by tan (Mu)L = (Mu)L where (Mu) = Sqrt (P/EI), L the length of the strut and EI the flexural rigidity of the strut.
By writing x = (Mu)L, solve the equation tan x = x using three iterations of the Newton-Raphson method, taking
an initial approximation x0 = 4.5



I got the equation for the first derivative to be
f(1)(x)= sec^2(x)-1

x1= x0 - (tan(x0)-x0)/(sec^2(x0)-1)

but i can't get a value out of the equation which seems right, when i carry on to the 3rd iteration it says i should get an answer of around 4.49340946


Would really appreciate help

Thank You

 

[hotvette]

but i can't get a value out of the equation which seems right, when i carry on to the 3rd iteration it says i should get an answer of around 4.49340946

What makes you think it isn't right? There is an easy way to verify. Calculate tan(x) - x and see how close to zero it is.