intermediate value theoremの例文

• That fact can also be proven by using the intermediate value theorem.
• Hence, the intermediate value theorem ensures that the equation has a solution.
• The intermediate value theorem says that every continuous function is a Darboux function.
• Thus f satisfies a property stronger than the conclusion of the intermediate value theorem.
• Thus f is a spectacular counterexample to the converse of the intermediate value theorem.
• From the intermediate value theorem, has at least roots.
• In this case, the Brouwer fixed-point theorem follows almost immediately from the intermediate value theorem.
• Using this definition, he proved the Intermediate Value Theorem.
• The main mathematical tool used by Austin's procedure is the intermediate value theorem ( IVT ).
• Another proof can be given by combining the mean value theorem and the intermediate value theorem.
• If the degree is odd, then by the intermediate value theorem at least one of the roots is real.
• By the intermediate value theorem, the image of " X " under this continuous function is the entire unit interval.
• He also gave the first purely analytic proof of the intermediate value theorem ( also known as Bolzano's theorem ).
• However, not every Darboux function is continuous; i . e ., the converse of the intermediate value theorem is false.
• The Brouwer fixed-point theorem is a related theorem that, in one dimension gives a special case of the intermediate value theorem.
• Therefore, by the intermediate value theorem and the connectedness of the circle, g ( x ) = 0 for some x.
• We can imagine the intermediate value theorem's failure as resulting from the ability of an infinitesimal segment to straddle a line.
• It is also continuous by construction so by the intermediate value theorem, it crosses " r " = 1 exactly once.
• *PM : proof of generalized intermediate value theorem, id = 9639 new !-- WP guess : proof of generalized intermediate value theorem-- Status:
• Some theorems of standard and non-standard analysis are false in smooth infinitesimal analysis, including the intermediate value theorem and the Banach Tarski paradox.