Difference between revisions of "Squeeze Theorem"
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The '''Squeeze Play Theorem''' (also called the '''Squeeze Theorem''' or the '''Sandwich Theorem''') is a relatively simple [[theorem]] that deals with [[calculus]], specifically [[limit]]s. | The '''Squeeze Play Theorem''' (also called the '''Squeeze Theorem''' or the '''Sandwich Theorem''') is a relatively simple [[theorem]] that deals with [[calculus]], specifically [[limit]]s. | ||
Revision as of 21:08, 3 May 2008
This is an AoPSWiki Word of the Week for May 4-11 |
The Squeeze Play Theorem (also called the Squeeze Theorem or the Sandwich 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.
If increases to , then goes to either or , where . If decreases to , then goes to either or , where . Since can't go to or , then must go to . Therefore, .