Squeeze Theorem

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Let , , and be functions satisfying for all near , except possibly at . By the squeeze theorem, if then . Hence, equals zero if , or , since is squeezed between and . The theorem does not apply if , since is trapped but not squeezed. For the limit does not exist, because no matter how close gets to zero, there are values of near zero for which and some for which .

Contributed by: Bruce Atwood (Beloit College) (March 2011)
After work by: Selwyn Hollis (Armstrong Atlantic State University)
Open content licensed under CC BY-NC-SA


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