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1- Let the bisection method be applied to a continuous function, resulting in the intervals[a0,b0],[a1,b1], and...

1- Let the bisection method be applied to a continuous function, resulting in the intervals[a0,b0],[a1,b1], and so on. Letcn=an+bn2, and let r=lim n→∞cn be the corresponding root. Let en=r−c

a. 1-1) Show that|en|≤2−n−1(b0−a0).

b. Show that|cn−cn+1|=2−n−2(b0−a0).

c Show that it is NOT necessarily true that|e0|≥|e1|≥···by considering the function f(x) =x−0.2on the interval[−1,1].

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