Squeeze Theorem
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The Squeeze Theorem (also called the Sandwich Theorem or the Squeeze Play Theorem) is a relatively simple theorem that deals with calculus, specifically limits.
Theorem
Suppose is between and for all in the neighborhood of . If and approach some common limit L as approaches , then .
Proof
If is between and for all in the neighborhood of , then either or for all in the neighborhood of . Since the second case is basically the first case, we just need to prove the first case.
For all , we must prove that there is some for which .
Now since, , there must exist such that,
and,
Now let . If , then
So . Now by the definition of a limit, we get .