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Find n for which the nth iteration by the fixed point method is guaranteed to approximate...

Find n for which the nth iteration by the fixed point method is guaranteed to approximate the root of f(x) = x − cos x on [0, π/3] with an accuracy within 10−8 using x0 = π/4

Answer: n = 127 iterations or n = 125 iterations.

Please show work to get to answer

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