Question

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

Answer #1

Newton's method: For a function ?(?)=ln?+?2−3f(x)=lnx+x2−3
a. Find the root of function ?(?)f(x) starting with
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Your task will be to derive the equations describing the
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