# Difference between revisions of "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 [[limit]]s. | The '''Squeeze Theorem''' (also called the '''Sandwich Theorem''' or the '''Squeeze Play Theorem''') is a relatively simple [[theorem]] that deals with [[calculus]], specifically [[limit]]s. | ||

## Revision as of 20:50, 19 May 2008

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 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