Difference between revisions of "Jenny's Favorite theorem MA453Fall2008walther" - Rhea

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-My favorite theorem is the Squeeze Theorem:
-Let ''I'' be an interval containing the point ''a''. Let ''f'', ''g'', and ''h'' be functions defined on ''I'', except possibly at ''a'' itself. Suppose that for every ''x'' in ''I'' not equal to ''a'', we have:
-<p>
-: <math>g(x) \leq f(x) \leq h(x)</math>
-and also suppose that:
-: <math>\lim_{x \to a} g(x) = \lim_{x \to a} h(x) = L.</math>
-Then <math>\lim_{x \to a} f(x) = L</math>.</p>
-<p>I have seen it used quite a bit in proving other theorems. For instance, in MA301 we used it when proving an example like:</p>
-<p>2.1412.....<br>
-+1.3376.....</p>
-<p>is 3.47 rounded to two decimal places, regardless of what the complete decimal expansion is.</p>

Revision as of 05:06, 31 August 2008