Wolfram Demonstrations Project

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)

After work by: Selwyn Hollis (Armstrong Atlantic State University)

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Squeeze Theorem