Difference between revisions of "LimitBelow Command"
From GeoGebra Manual
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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 | + | ;LimitBelow[ <Function>, <Value> ] |
| − | :Computes the left [[w:Limit of a function#One-sided limits|one-sided limit]] of the function | + | :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 | + | ;LimitBelow[ <Expression>, <Value> ] |
| − | :Computes the left one-sided limit of the function | + | :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 | + | ;LimitBelow[ <Expression>, <Variable>, <Value> ] |
| − | :Computes the left one-sided limit of the multivariate function | + | :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.
