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Author: OpenMath Consortium
SourceURL: https://github.com/OpenMath/CDs
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.
limitThis 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.
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<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>
<math xmlns="http://www.w3.org/1998/Math/MathML"> <apply><csymbol cd="limit1">limit</csymbol> <cn type="integer">0</cn> <csymbol cd="limit1">both_sides</csymbol> <bind><csymbol cd="fns1">lambda</csymbol> <bvar><ci>x</ci></bvar> <apply><csymbol cd="transc1">sin</csymbol><ci>x</ci></apply> </bind> </apply> </math>
limit1.limit(0, limit1.both_sides, fns1.lambda[$x -> sin($x)])
This symbol is used within a limit construct to show the limit is being approached from both sides. It takes no arguments.
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<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>
<math xmlns="http://www.w3.org/1998/Math/MathML"> <apply><csymbol cd="limit1">limit</csymbol> <cn type="integer">0</cn> <csymbol cd="limit1">both_sides</csymbol> <bind><csymbol cd="fns1">lambda</csymbol> <bvar><ci>x</ci></bvar> <apply><csymbol cd="transc1">sin</csymbol><ci>x</ci></apply> </bind> </apply> </math>
limit1.limit(0, limit1.both_sides, fns1.lambda[$x -> sin($x)])
This symbol is used within a limit construct to show the limit is being approached from above. It takes no arguments.
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<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>
<math xmlns="http://www.w3.org/1998/Math/MathML"> <apply><csymbol cd="limit1">limit</csymbol> <cn type="integer">0</cn> <csymbol cd="limit1">above</csymbol> <bind><csymbol cd="fns1">lambda</csymbol> <bvar><ci>x</ci></bvar> <apply><csymbol cd="transc1">sin</csymbol><ci>x</ci></apply> </bind> </apply> </math>
limit1.limit(0, limit1.above, fns1.lambda[$x -> sin($x)])
limit x → 0 + sin ( x )
This symbol is used within a limit construct to show the limit is being approached from below. It takes no arguments.
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<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>
<math xmlns="http://www.w3.org/1998/Math/MathML"> <apply><csymbol cd="limit1">limit</csymbol> <cn type="integer">0</cn> <csymbol cd="limit1">below</csymbol> <bind><csymbol cd="fns1">lambda</csymbol> <bvar><ci>x</ci></bvar> <apply><csymbol cd="transc1">sin</csymbol><ci>x</ci></apply> </bind> </apply> </math>
limit1.limit(0, limit1.below, fns1.lambda[$x -> sin($x)])
limit x → 0 - sin ( x )
This symbol is used within a limit construct to avoid specifying the method of approach to the limit. It takes no arguments.
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<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>
<math xmlns="http://www.w3.org/1998/Math/MathML"> <apply><csymbol cd="limit1">limit</csymbol> <cn type="integer">0</cn> <csymbol cd="limit1">null</csymbol> <bind><csymbol cd="fns1">lambda</csymbol> <bvar><ci>x</ci></bvar> <apply><csymbol cd="transc1">sin</csymbol><ci>x</ci></apply> </bind> </apply> </math>
limit1.limit(0, limit1.null, fns1.lambda[$x -> sin($x)])
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