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In calculus, the squeeze theorem known also as the pinching theorem, the sandwich theorem, the sandwich rule and sometimes the squeeze lemma is a theorem regarding the limit of a function. The squeeze theorem is used in calculus and mathematical analysis. It is typically used to confirm the limit of a function via comparison with two other functions whose limits are known or easily computed. It was first used geometrically by the mathematicians Archimedes and Eudoxus in an effort to compute , and was formulated in modern terms by Gauss. In many languages (e.g. French, German, Italian and Russian), the squeeze theorem is also known as the two policemen (and a drunk) theorem, or some variation thereof. The story is that if two policemen are escorting a drunk prisoner between them, and both officers go to a cell, then (regardless of the path taken, and the fact that the prisoner may be wobbling about between the policemen) the prisoner must also end up in the cell. == Statement == The squeeze theorem is formally stated as follows.
* The functions ''g'' and ''h'' are said to be lower and upper bounds (respectively) of ''f''. * Here ''a'' is ''not'' required to lie in the interior of ''I''. Indeed, if ''a'' is an endpoint of ''I'', then the above limits are left- or right-hand limits. * A similar statement holds for infinite intervals: for example, if ''I'' = (0, ∞), then the conclusion holds, taking the limits as ''x'' → ∞. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Squeeze theorem」の詳細全文を読む スポンサード リンク
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