Difference between revisions of "Squeeze Theorem"
| Line 1: | Line 1: | ||
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. | ||
| − | [[Image:Squeeze theorem example.jpg | + | [[Image:Squeeze theorem example.jpg]] |
==Theorem== | ==Theorem== | ||
Revision as of 15:16, 1 May 2008
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, .
