Difference between revisions of "LimitBelow Command"

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<noinclude>{{Manual Page|version=4.2}}</noinclude>
 
<noinclude>{{Manual Page|version=4.2}}</noinclude>
 
{{command|cas=true|function}}
 
{{command|cas=true|function}}
;LimitBelow[ <Function f>, <Value t> ]
+
;LimitBelow[ <Function>, <Value> ]
:Computes the left [[w:Limit of a function#One-sided limits|one-sided limit]] of the function ''f'' for given value ''t'' of the main function variable.
+
: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.
 
:{{example|1=<div><code><nowiki>LimitBelow[1 / x, 0]</nowiki></code> yields <math>-\infty</math> .</div>}}
 
:{{example|1=<div><code><nowiki>LimitBelow[1 / x, 0]</nowiki></code> yields <math>-\infty</math> .</div>}}
 
{{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).}}
 
{{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> ]
+
;LimitBelow[ <Expression>, <Value> ]
:Computes the left one-sided limit of the function ''f'' for the given value ''t'' of the main function variable.
+
: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>}}
 
:{{example|1=<div><code><nowiki>LimitBelow[1 / x, 0]</nowiki></code> yields <math>-\infty</math> .</div>}}
;LimitBelow[ <Expression f>, <Variable v>, <Value t> ]
+
;LimitBelow[ <Expression>, <Variable>, <Value> ]
:Computes the left one-sided limit of the multivariate function ''f'' for the given value ''t'' of the given function variable ''v''.
+
: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>}}
 
:{{example|1=<div><code><nowiki>LimitBelow[1 / a, a, 0]</nowiki></code>  yields  <math>-\infty</math> .</div>}}
 
{{note| 1=<div>
 
{{note| 1=<div>
 
* Not all limits can be calculated by GeoGebra, so ''?'' will be returned in those cases (as well as when the correct result is undefined).
 
* Not all limits can be calculated by GeoGebra, so ''?'' will be returned in those cases (as well as when the correct result is undefined).
 
* See also [[Limit Command]] and [[LimitAbove Command]].</div>}}
 
* See also [[Limit Command]] and [[LimitAbove Command]].</div>}}

Revision as of 09:46, 26 March 2013



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).
  • See also Limit Command and LimitAbove Command.
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