Question: The equation x tan x = 4 was considered earlier in Example 9.16. Apply the NewtonRaphson method to find the root near x = 1.

The equation x tan x = 4 was considered earlier in Example 9.16. Apply the Newton–Raphson method to find the root near x = 1.


Data from Example 9.16

The equation x tan x = 4 has an infinite number of roots. To find the root near x = 1, we may use the iteration

Xn+1 tan = +| Xn

Show that this is a first-order process. Starting with x0 = 1, find x3 and assess its accuracy.

Xn+1 tan = +| Xn

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