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Newton's method


Hi all,
I am trying to use the Newton-Raphson method to find the root to an
equation.
The formula looks like this:

newton[f_, x_, x0_, n_, opts___] :=
  With[{df = D[f, x]}, FixedPointList[(x - f/df) /. x -> # &, N[x0], n,
opts]]

with f=Sqrt[x^2 - 2584] * Coth[0.00128 * Sqrt[x^2 - 2584]]+ Sqrt[x^2 -
1013].

When I set

newton[f, x, 31, 20]

I end up getting values which do not converge. However, if I were to plot
the function using the Plot function in Mathematica (between x values of 32
and 51), it seems like the root is somewhere near 33.

I would thus like to know if perhaps there is something wrong with this
formulation for the Newton's method, or that there is some quirk in the Plot
function and the function, f, in fact do not have a root at all.

Thanks.

Derek





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