152
edits
Changes
Jump to navigation
Jump to search
Line 1:
Line 1: − A '''limit''' is a process in [[mathematics]] which aims to find the value of a [[constant]] of a [[function]] as it approaches a certain number or [[infinity]]. <ref>http://www.freemathhelp.com/find-limit.html</ref>+ − + − + + + + + +
no edit summary
Let <math>f(x)</math> be a real valued function in one variable. We say that
==References==
<math>
<references/>
\lim_{x\to p} f(x) = L
</math>
if for any error <math>\varepsilon</math>, we can find a sufficiently small neighbhorhood of <math>p</math> so that <math>f(x)</math> is within <math>\varepsilon</math> of the value <math>L</math> for any <math>x\neq p</math> in that neighborhood. One says that the limit of ''f(x)'' at ''p'' exists and is equal to ''L''.
The standard, though more verbose, way of saying this is that for any <math>\varepsilon > 0</math> there exists a sufficiently small <math>\delta > 0</math> such that <math>|f(x)-L| <\varepsilon</math> whenever <math>0<|x-p|<L</math>.
[[category:mathematics]]
[[category:mathematics]]