Difference between revisions of "LimitBelow Command"

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<noinclude>{{Manual Page|version=4.0}}</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}}
{{command|function}}
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;LimitBelow( <Function>, <Value> )
;LimitBelow[ <Function>, <Value> ]
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:Computes the left [[w:Limit of a function#One-sided limits|one-sided limit]] of the function for the given value of the main function variable.
:Returns left [[w:Limit of a function#One-sided limits|one-sided limit]] of the function for given value of variable.
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:{{example|1=<code><nowiki>LimitBelow(1 / x, 0)</nowiki></code> yields <math>-\infty</math> .}}
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:{{note| 1=Not all limits can be calculated by GeoGebra, so ''undefined'' will be returned in those cases (as well as when the correct result is undefined).}}
 
==CAS Syntax==
 
==CAS Syntax==
;LimitBelow[ <Expression f>, <Value t> ]
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;LimitBelow( <Expression>, <Value> )
:Computes the left one-sided limit of the function ''f'' for the given value ''t''.
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:Computes the left one-sided limit of the function for the given value of the main function variable.
:{{example|1=<div><code><nowiki>LimitBelow[1 / x, 0]</nowiki></code> yields <math>-\infty</math> .</div>}}
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:{{example|1=<code><nowiki>LimitBelow(1 / x, 0)</nowiki></code> yields <math>-\infty</math> .}}
;LimitBelow[ <Expression f>, <Variable v>, <Value t> ]
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;LimitBelow( <Expression>, <Variable>, <Value> )
:Computes the left one-sided limit of the multivariate function ''f'' for the given value ''t'' of the given variable ''v''.
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:Computes the left one-sided limit of the multivariate function for the given value of the given function variable.
:{{example|1=<div><code><nowiki>LimitBelow[1 / a, a, 0]</nowiki></code>  yields  <math>-\infty</math> .</div>}}
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:{{example|1=<code><nowiki>LimitBelow(1 / a, a, 0)</nowiki></code>  yields  <math>-\infty</math> .}}
{{note| 1=<div>See also [[Limit Command]] and [[LimitAbove Command]].</div>}}
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:{{note| 1=Not all limits can be calculated by GeoGebra, so ''?'' will be returned in those cases (as well as when the correct result is undefined).}}
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{{note| 1=See also [[Limit Command]] and [[LimitAbove Command]].}}

Latest revision as of 09:35, 9 October 2017


LimitBelow( <Function>, <Value> )
Computes the left one-sided limit of the function for the given value of the main function variable.
Example: LimitBelow(1 / x, 0) yields -\infty .
Note: Not all limits can be calculated by GeoGebra, so undefined will be returned in those cases (as well as when the correct result is undefined).

CAS Syntax

LimitBelow( <Expression>, <Value> )
Computes the left one-sided limit of the function for the given value of the main function variable.
Example: LimitBelow(1 / x, 0) yields -\infty .
LimitBelow( <Expression>, <Variable>, <Value> )
Computes the left one-sided limit of the multivariate function for the given value of the given function variable.
Example: LimitBelow(1 / a, a, 0) yields -\infty .
Note: Not all limits can be calculated by GeoGebra, so ? will be returned in those cases (as well as when the correct result is undefined).
Note: See also Limit Command and LimitAbove Command.
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