Show that the iteration is convergent to the root near = 3.9 of the equation tan

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Show that the iteration

On+ tan-'(tanh0,), with 0o = t ~ 3.9

is convergent to the root near θ = 3.9 of the equation tan θ =  tanh θ (see Figure 9.4).

Figure 9.4 Roots of the equation tan 0 = tanh . YA O  y = tan 0 = tanh   5 4 77 2TT

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