I was wondering is there a very short trick to find weather a given function is uniformly continuous or not without using epsilon and delta definition.Can someone give me a graphical insight of uniform continuity?
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http://math.stackexchange.com/questions/1249552/what-is-the-geometrical-difference-between-continuity-and-uniform-continuity/1249643#1249643 – ThePortakal Mar 08 '16 at 10:08
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Thanks Sir. By I wanted to know is there a quick method to guess uniform continuity? – Rayees Ahmad Mar 08 '16 at 10:16
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If the domain is not compact, check for a bounded derivative – user251257 Mar 08 '16 at 11:43
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The most important principle is the following:
An elementary function ("analytical expression" in $x^k$, $\sqrt{\mathstrut}$, $\exp$, $\cos$, etc.) is continuous on its full domain of definition, i.e., the set $\Omega$ of points where it can be evaluated without asking questions.
Such a function is then uniformly continuous on any compact subset of $\Omega$.
Christian Blatter
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