Bolzano's Theorem

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Bolzano's theorem states that if is a continuous function in the closed interval with and of opposite sign, then there is a in the open interval such that .

Contributed by: Julio Cesar de la Yncera (May 2008)
Open content licensed under CC BY-NC-SA


Snapshot 1: The function is positive in the interval and therefore for all in .

Snapshot 2: The function is negative in the interval so for all in .

Snapshot 3: The function is positive for and negative for , therefore there is a in such that .


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