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Squeeze theorem - Wikipedia

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In calculus, the squeeze theorem (also known as the sandwich theorem, among other names[a]) is a theorem regarding the limit of a function that is trapped between two other functions. The squeeze theorem is used in calculus and mathematical analysis, typically to confirm the limit of a function via comparison with two other functions whose limits are known. 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. The squeeze theorem is formally stated as follows.[1] Theorem — Let I be an interval containing the point a. Let g, f, and h be functions defined on I, except possibly at a itself. Suppose that for every x in I not equal to a, we have This theorem is also valid for sequences. Let (an), (cn) be two sequences converging to ℓ, and (bn) a sequence. If ∀ 𝑛 ≥ 𝑁 , 𝑁 ∈ 𝑁 we have an ≤ bn ≤ cn, then (bn) also converges to ℓ. According to the above hypotheses we have, taking

Squeeze theorem - Wikipedia Jump to content From Wikipedia, the free encyclopedia Method for finding limits in calculus This article needs more citations . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . Find sources: "Squeeze theorem" – news · newspapers · books · scholar · JSTOR ( April 2010 ) ( Learn how and when to remove this message ) "Sandwich theorem" redirects here. For the result in measure theory, see Ham sandwich theorem . For Sandwich theory (physics), see Sandwich theory . Illustration of the squeeze th

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