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6) (a) Denote the successive intervals that arise in the bisection method by [a0,b0, [a1,b1] , [a2,b2],...

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Advance Math

6) (a) Denote the successive intervals that arise in thebisection method by [a0,b0,[a1,b1] , [a2,b2], andso on

   Show that   bn – an= 2-n(b0-a0)

(b) The bisection method is said to have a linear convergence.Explain as clearly as possible what that means

c) For the bisection method, prove that |cn –cn+1| = 2-n-2 (b0 –a0)

   where cn is the midpoint of each interval (ie)cn = (an + bn) /2

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