OpenMath Content Dictionary: limit1

Canonical URL:
http://www.openmath.org/cd/limit1.ocd
CD File:
limit1.ocd
CD as XML Encoded OpenMath:
limit1.omcd
Defines:
above, below, both_sides, limit, null
Date:
2001-03-12
Version:
2
Review Date:
2003-04-01
Status:
official
Uses CD:
fns1, transc1

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

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
<OMOBJ>
  <OMA>
    <OMS cd="limit1" name="limit"/>
    <OMI> 0 </OMI>
    <OMS cd="limit1" name="both_sides"/>
    <OMBIND>
      <OMS cd="fns1" name="lambda"/>
        <OMBVAR>
        <OMV name="x"/>
        </OMBVAR>
        <OMA>
          <OMS cd="transc1" name="sin"/>
          <OMV name="x"/>
        </OMA>
    </OMBIND>
  </OMA>
</OMOBJ>

limit ( 0 , both_sides, lambda [ x ] . (sin ( x) ) )

Signatures:
sts


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

both_sides

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
<OMOBJ>
  <OMA>
    <OMS cd="limit1" name="limit"/>
    <OMI> 0 </OMI>
    <OMS cd="limit1" name="both_sides"/>
    <OMBIND>
      <OMS cd="fns1" name="lambda"/>
        <OMBVAR>
        <OMV name="x"/>
        </OMBVAR>
        <OMA>
          <OMS cd="transc1" name="sin"/>
          <OMV name="x"/>
        </OMA>
    </OMBIND>
  </OMA>
</OMOBJ>

limit ( 0 , both_sides, lambda [ x ] . (sin ( x) ) )

Signatures:
sts


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

above

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
<OMOBJ>
  <OMA>
    <OMS cd="limit1" name="limit"/>
    <OMI> 0 </OMI>
    <OMS cd="limit1" name="above"/>
    <OMBIND>
      <OMS cd="fns1" name="lambda"/>
        <OMBVAR>
        <OMV name="x"/>
        </OMBVAR>
        <OMA>
          <OMS cd="transc1" name="sin"/>
          <OMV name="x"/>
        </OMA>
    </OMBIND>
  </OMA>
</OMOBJ>

limit ( 0 , above, lambda [ x ] . (sin ( x) ) )

Signatures:
sts


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

below

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
<OMOBJ>
  <OMA>
    <OMS cd="limit1" name="limit"/>
    <OMI> 0 </OMI>
    <OMS cd="limit1" name="below"/>
    <OMBIND>
      <OMS cd="fns1" name="lambda"/>
        <OMBVAR>
        <OMV name="x"/>
        </OMBVAR>
        <OMA>
          <OMS cd="transc1" name="sin"/>
          <OMV name="x"/>
        </OMA>
    </OMBIND>
  </OMA>
</OMOBJ>

limit ( 0 , below, lambda [ x ] . (sin ( x) ) )

Signatures:
sts


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

null

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
<OMOBJ>
  <OMA>
    <OMS cd="limit1" name="limit"/>
    <OMI> 0 </OMI>
    <OMS cd="limit1" name="null"/>
    <OMBIND>
      <OMS cd="fns1" name="lambda"/>
      <OMBVAR>
        <OMV name="x"/>
      </OMBVAR>
      <OMA>
        <OMS cd="transc1" name="sin"/>
        <OMV name="x"/>
      </OMA>
    </OMBIND>
  </OMA>
</OMOBJ>

limit ( 0 , null, lambda [ x ] . (sin ( x) ) )

Signatures:
sts


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