The Squeeze Theorem
Formal look at limits
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
The squeeze theorem is applied to these very useful limits on the page
Useful Trig Limits.
The Squeeze Theorem:
If there exists a positive number p with the property that
for all x that satisfy the inequalities
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
since there is no room for x to be anything else.
For the formal proof, let epsilon be given, and chose
both less than p, so that
to be the smallest of the numbers
and the proof is complete.
The Squeeze Theorem applied to Trig Limits |
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Last modified October 9, 2001