If you are a student who studies mathematics to a more or less serious extent, no matter on what academic level: high school, college, university, you are sure to deal with a Bolzano’s theorem assignment sooner or later.
Bolzano’s theorem or, as it is sometimes called, the intermediate value theorem, is a part of mathematical analysis. In this or that way it is used in solutions of many mathematical problems within the sphere of mathematical analysis, for it states such a crucial idea as this: if a continuous function possesses two values, then it also possesses all the values between these two. In other words, for every value of a continuous function between the least upper bound and the most lower bound of its graph there is a point in its domain that corresponds to this value. The Bolzano’s theorem homework very often involves the usage of the theorem’s implication in solving some tasks: if the continuous function possesses negative and positive values at the ends of a segment then at some point it equals zero. Another thing to remember when dealing with a Bolzano’s theorem math homework is that every polynomial of an uneven degree possesses at least one zero.
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