Difference between revisions of "LimitBelow Command"
From GeoGebra Manual
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{{command|cas=true|function}} | {{command|cas=true|function}} | ||
;LimitBelow[ <Function f>, <Value t> ] | ;LimitBelow[ <Function f>, <Value t> ] | ||
− | : | + | :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. |
− | {{note| Not all limits can be calculated by GeoGebra, so | + | :{{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).}} | ||
==CAS Syntax== | ==CAS Syntax== | ||
;LimitBelow[ <Expression f>, <Value t> ] | ;LimitBelow[ <Expression f>, <Value t> ] | ||
: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 ''f'' for the given value ''t'' of the main function variable. | ||
− | :{{example|1=<div><code><nowiki>LimitBelow[1 / x, 0]</nowiki></code> | + | :{{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 f>, <Variable v>, <Value t> ] | ||
: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 ''f'' for the given value ''t'' of the given function variable ''v''. | ||
:{{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>See also [[Limit Command]] and [[LimitAbove Command]].</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). | ||
+ | * See also [[Limit Command]] and [[LimitAbove Command]].</div>}} |
Revision as of 12:15, 18 September 2012
- LimitBelow[ <Function f>, <Value t> ]
- Computes the left one-sided limit of the function f for given value t 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 f>, <Value t> ]
- Computes the left one-sided limit of the function f for the given value t of the main function variable.
- Example:
LimitBelow[1 / x, 0]
yields -\infty .
- LimitBelow[ <Expression f>, <Variable v>, <Value t> ]
- Computes the left one-sided limit of the multivariate function f for the given value t of the given function variable v.
- 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.