In this calculus video I will show you what is the squeeze or sandwich or pinching theorem and how and where we can apply it for finding limits.
Sandwich theorem is mostly for limits that involve trigonometric functions in the form of sin(1/x) or cos(1/x).
In calculus, the squeeze theorem, also known as the pinching theorem, the sandwich theorem, the sandwich rule, the police theorem, the between theorem and sometimes the squeeze lemma, is a theorem regarding the limit of a function. In Italy, the theorem is also known as theorem of carabinieri.
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 π, and was formulated in modern terms by Carl Friedrich Gauss.
In many languages (e.g. French, German, Italian, Hungarian and Russian), the squeeze theorem is also known as the two officers (and a drunk) theorem, or some variation thereof. The story is that if two police officers 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 officers) the prisoner must also end up in the cell.
20 мар 2022
