Squeeze Theorem
From AoPSWiki
The Squeeze Theorem (also called the Sandwich Theorem or the Squeeze Play Theorem) is a relatively simple theorem that deals with calculus, specifically limits.
| Error creating thumbnail: sh: /usr/bin/convert: No such file or directory |
Contents |
Theorem
Suppose 
is between 
and 
for all 
in a neighborhood of the point 
. If 
and 
approach some common limit 
as approaches , then 
.
Proof
If is between and for all in the neighborhood of , then either 
or 
for all in this neighborhood. The two cases are the same up to renaming our functions, so assume without loss of generality that .
We must show that for all 
there is some 
for which 
implies 
.
Now since 
, there must exist 
such that
Now let 
. If then
So . Now by the definition of a limit we get as desired.
Applications and examples
This section is incomplete. You can help us out by completing it.
