Changes

Let <math>f(x)</math> be a real valued function in one variable. We say that

Let <math>f(x)</math> be a real valued [[function]] in one [[variable]]. We say that

<math>

<math>

</math>

</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''.

if for any error <math>\varepsilon</math>, we can find a sufficiently small neighborhood 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|<\delta</math>.

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|<\delta</math>.

[[category:mathematics]]

[[category:mathematics]]