Difference between revisions of "Limit Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | ||
| − | ;Limit | + | ;Limit( <Function>, <Value> ) |
: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 the [[w:Limit_of_a_function|limit]] of the function for the given value of the main function variable. (This may also yield infinity.) | ||
:{{example|1=<div><code><nowiki>Limit[(x^2 + x) / x^2, +∞]</nowiki></code> yields ''1''.</div>}} | :{{example|1=<div><code><nowiki>Limit[(x^2 + x) / x^2, +∞]</nowiki></code> yields ''1''.</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== | ||
| − | ;Limit | + | ;Limit( <Expression>, <Value> ) |
:Computes the limit of the expression for the given value of the main function variable. | :Computes the limit of the expression for the given value of the main function variable. | ||
:{{example|1=<div><code><nowiki>Limit[a sin(x) / x, 0]</nowiki></code> yields ''a''.</div>}} | :{{example|1=<div><code><nowiki>Limit[a sin(x) / x, 0]</nowiki></code> yields ''a''.</div>}} | ||
| − | ;Limit | + | ;Limit( <Expression>, <Variable>, <Value> ) |
:Computes the limit of the expression for the given value of the given function variable. | :Computes the limit of the expression for the given value of the given function variable. | ||
:{{example|1=<div><code><nowiki>Limit[a sin(v) / v, v, 0]</nowiki></code> yields ''a''.</div>}} | :{{example|1=<div><code><nowiki>Limit[a sin(v) / v, v, 0]</nowiki></code> yields ''a''.</div>}} | ||
Revision as of 17:15, 7 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:
- 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 piecewise-defined function you need to use LimitAbove or LimitBelow, for example
LimitAbove[If[x>1, x^2, -2x], 1] - See also Asymptote Command, LimitAbove Command and LimitBelow Command.
