Our immediate motivation for the squeeze theorem is to so that we can evaluate the following limits, which are necessary in determining the derivatives of sin and cosine:

If there exists a positive number `p` with the property that

This statement is sometimes called the ``squeeze theorem'' because it
says that a function ``squeezed'' between two functions approaching
the same limit `L` must also approach `L`.

Intuitively, this means that the function
`f`(`x`) gets squeezed between the other
functions. Since `g`(`x`) and `h(x)`
are equal at `x` = `a`, it must also be
the case that
`f`(`x`)=`f`(`x`)=L
since there is no room for `x` to be anything else.

For the formal proof, let epsilon be given, and chose positive numbers

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watko@mit.edu Last modified October 9, 2001