Difference between revisions of "Limit Command"

From GeoGebra Manual
Jump to: navigation, search
(command syntax: changed [ ] into ( ))
 
(25 intermediate revisions by 11 users not shown)
Line 1: Line 1:
<noinclude>{{Manual Page|version=4.0}}</noinclude>
+
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}}
{{command|function}}
+
;Limit( <Function>, <Value> )
;Limit[ <Function f>, <Value or Infinity> ]
+
:Computes the [[w:Limit_of_a_function|limit]] of the function for the given value of the main function variable. (This may also yield infinity.)
:Computes [[w:Limit_of_a_function|limit]] of function ''f'' for given value of function variable (may be infinity).
+
:{{example|1=<code><nowiki>Limit((x^2 + x) /  x^2, +∞)</nowiki></code> yields ''1''.}}
==CAS Specific syntaxes==
+
{{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).}}
Following syntaxes are available only in [[CAS View]].
+
==CAS Syntax==
;Limit[ <Expression f>, <Variable v>, <Value or Infinity t> ]
+
;Limit( <Expression>, <Value> )
:Computes limit of multivariate function ''f'' for ''v=t''.
+
:Computes the limit of the expression for the given value of the main function variable.
;Limit[ <Expression f>, <Variable v>, <Value or Infinity t>, <Direction Left or Right> ]
+
:{{example|1=<code><nowiki>Limit(a sin(x) / x, 0)</nowiki></code> yields ''a''.}}
:Computes left or right limit (depending on last parameter) of multivariate function ''f'' for ''v=t''.
+
;Limit( <Expression>, <Variable>, <Value> )
{{description}}
+
:Computes the limit of the expression for the given value of the given function variable.
{{Note|See also [[Limit Command]] and [[LimitBelow Command]].}}
+
:{{example|1=<code><nowiki>Limit(a sin(v) / v, v, 0)</nowiki></code> yields ''a''.}}
 +
{{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).
 +
* If you want the limit of a [[If Command|piecewise-defined function]] you need to use [[LimitAbove Command|LimitAbove]] or [[LimitBelow Command|LimitBelow]], for example <code><nowiki>LimitAbove(If(x>1, x^2, -2x), 1)</nowiki></code>
 +
* See also [[Asymptote Command]], [[LimitAbove Command]] and [[LimitBelow Command]].
 +
</div>}}

Latest revision as of 09:32, 9 October 2017


Limit( <Function>, <Value> )
Computes the limit of the function for the given value of the main function variable. (This may also yield infinity.)
Example: Limit((x^2 + x) / x^2, +∞) yields 1.
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

Limit( <Expression>, <Value> )
Computes the limit of the expression for the given value of the main function variable.
Example: Limit(a sin(x) / x, 0) yields a.
Limit( <Expression>, <Variable>, <Value> )
Computes the limit of the expression for the given value of the given function variable.
Example: Limit(a sin(v) / v, v, 0) yields a.
Note:
© 2021 International GeoGebra Institute