page_title: Squeeze theorem
section_title: First example
hierarchical_section_title: Squeeze theorem / Examples / First example
caption_attribution_description: Svenska: Instängningssatsen
context_page_description: In calculus, the squeeze theorem, also known as the pinching theorem, the sandwich theorem, the sandwich rule, 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, the squeeze theorem is also known as the two policemen 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 the prisoner must also end up in the cell.
context_section_description: The limit
  cannot be determined through the limit law
  because
  does not exist.
  However, by the definition of the sine function,
  It follows that
  Since , by the squeeze theorem,  must also be 0.
caption: x2 sin(1/x) being squeezed in the limit as x goes to 0
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