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OpenMath Content Dictionary: limit1

Canonical URL:
http://www.openmath.org/cd/limit1.ocd
CD Base:
http://www.openmath.org/cd
CD File:
limit1.ocd
CD as XML Encoded OpenMath:
limit1.omcd
Defines:
above, below, both_sides, limit, null
Date:
2004-03-30
Version:
3
Review Date:
2006-03-30
Status:
official

This document is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

The copyright holder grants you permission to redistribute this
document freely as a verbatim copy. Furthermore, the copyright
holder permits you to develop any derived work from this document
provided that the following conditions are met.
a) The derived work acknowledges the fact that it is derived from
this document, and maintains a prominent reference in the
work to the original source.
b) The fact that the derived work is not the original OpenMath
document is stated prominently in the derived work.  Moreover if
both this document and the derived work are Content Dictionaries
then the derived work must include a different CDName element,
chosen so that it cannot be confused with any works adopted by
the OpenMath Society.  In particular, if there is a Content
Dictionary Group whose name is, for example, `math' containing
Content Dictionaries named `math1', `math2' etc., then you should
not name a derived Content Dictionary `mathN' where N is an integer.
However you are free to name it `private_mathN' or some such.  This
is because the names `mathN' may be used by the OpenMath Society
for future extensions.
c) The derived work is distributed under terms that allow the
compilation of derived works, but keep paragraphs a) and b)
intact.  The simplest way to do this is to distribute the derived
work under the OpenMath license, but this is not a requirement.
society at http://www.openmath.org.

This CD holds the basic notion of the limits of unary functions whilst its variable tend (either from above, below or both sides) to a particular value.

limit

Role:
application
Description:

This symbol is used to denote the limit of a unary function. It takes 3 arguments: the limiting value of the argument, the method of approach (either null, above, below or both_sides) and the function.

Example:
The limit of sin(x) as x tends to 0
$\underset{x\to 0}{\mathrm{limit}}\phantom{\rule{0.1em}{0ex}}\mathrm{sin}\left(x\right)$
Signatures:
sts

 [Next: both_sides] [Last: null] [Top]

both_sides

Role:
constant
Description:

This symbol is used within a limit construct to show the limit is being approached from both sides. It takes no arguments.

Example:
The limit of sin(x) as x tends to 0 from either direction
$\underset{x\to 0}{\mathrm{limit}}\phantom{\rule{0.1em}{0ex}}\mathrm{sin}\left(x\right)$
Signatures:
sts

 [Next: above] [Previous: limit] [Top]

above

Role:
constant
Description:

This symbol is used within a limit construct to show the limit is being approached from above. It takes no arguments.

Example:
The limit of sin(x) as x tends to 0 from above
$\underset{x\to {0}^{+}}{\mathrm{limit}}\phantom{\rule{0.1em}{0ex}}\mathrm{sin}\left(x\right)$
Signatures:
sts

 [Next: below] [Previous: both_sides] [Top]

below

Role:
constant
Description:

This symbol is used within a limit construct to show the limit is being approached from below. It takes no arguments.

Example:
The limit of sin(x) as x tends to 0 from below
$\underset{x\to {0}_{-}}{\mathrm{limit}}\phantom{\rule{0.1em}{0ex}}\mathrm{sin}\left(x\right)$
Signatures:
sts

 [Next: null] [Previous: above] [Top]

null

Role:
constant
Description:

This symbol is used within a limit construct to avoid specifying the method of approach to the limit. It takes no arguments.

Example:
The limit of sin(x) as x tends to 0
$\underset{x\to 0}{\mathrm{limit}}\phantom{\rule{0.1em}{0ex}}\mathrm{sin}\left(x\right)$
Signatures:
sts

 [First: limit] [Previous: below] [Top]

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