Difference between revisions of "Jenny's Favorite theorem MA453Fall2008walther" - Rhea
User
Log in
Actions
View source
History
Recent Changes
Slectures
Squad
Practice
Formulas
Donations
Disclaimer
Home
Print
Revision as of 06:03, 31 August 2008
(
view source
)
Jstraete
(
Talk
)
(Jesse's Favorite Theorem)
Revision as of 06:06, 31 August 2008
(
view source
)
Jstraete
(
Talk
)
(Removing all content from page)
Newer edit →
Line 1:
Line 1:
−
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 06:06, 31 August 2008
Shortcuts
Help
Main Wiki Page
Random Page
Special Pages
Log in
Search
Alumni Liaison
Prof. Math. Ohio State and Associate Dean
Outstanding Alumnus Purdue Math 2008
Read more »
Jeff McNeal
Currently Active Pages
x
+
x
Chat
x