Question

Newton’s Method can be used to compute reciprocals without performing division. Letc > 0 and set f (x) = x
−1 −c.
(a) Show that x − (f (x)/f' (x)) = 2x − cx2.
(b) Calculate the first three iterates of Newton’s Method with c = 10.3 and the two initial guesses x0 = 0.1 and x0 = 0.5.
(c) Explain graphically why x0 = 0.5 does not yield a sequence converging to 1/10.3.

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