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Let f1 be a continuous function with different signs at a,b, with a < b and...

Let f1 be a continuous function with different signs at a,b, with a < b and let {pn}∞ n=1 be bisection method’s sequence of approximations on f1 using starting interval [a,b]. Let f2 be a continuous function with different signs at a,b, with a < b and let {qn}∞ n=1 be bisection method’s sequence of approximations on f2 using starting interval [a,b].
(a) Prove (perhaps by induction) if pk = qk, for some k, then pi = qi for all i < k.

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