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.

Why do you use the squeeze theorem?

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.

How do you prove a squeeze lemma?

Theorem 0.1 (The Squeeze Theorem). Suppose that g(x) ≤ f(x) ≤ h(x) for all x in some open interval containing c except possibly at c itself. If limx→c g(x) = L = limx→c h(x) then limx→c f(x) = L. Proof.