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**Unformatted text preview: **, we know that the root lies in or . In any case, our change-of-sign interval is now half as large as before. Repeat this process with the new change of sign interval until the interval is sufficiently small and declare victory. We are guaranteed to converge. We can even compute the maximum number of steps this will take, because if the original change-of-sign interval has length then after one bisection the current change-of-sign interval is of length , etc . We know in advance how well we will approximate the root . These are very powerful facts, which make bisection a robust algorithm--that is, it is very hard to defeat it....

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