Difference between revisions of "NSolve Command"

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<noinclude>{{Manual Page|version=4.0}}</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geogebra}}
{{command|CAS}}
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==CAS Syntax==
;NSolve[ <Equation> ]
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This command is only available in the [[File:Menu view cas.svg|link=|16px]] [[CAS View]].
:Finds a numeric solution for a given equation (or a set of equations) for the variable x.
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:{{example|1=<div><code><nowiki>NSolve[sin(x) = x]</nowiki></code> gives you ''{x = 0}''.</div>}}
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;NSolve( <Equation> )
;NSolve[ <Equation>, <Variable> ]
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:Attempts (numerically) to find a solution for the equation for the main variable. For non-polynomials you should always specify a starting value (see below).
:Finds a numeric solution to an equation (or a set of equations) for a given unknown variable (or set of variables).
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:{{example|1=<div><code><nowiki>NSolve(x^6 - 2x + 1 = 0)</nowiki></code> yields ''{x = 0.51, x = 1}''.</div>}}
:{{example|1=<div><code><nowiki>NSolve[a^4 + 34a^3 - 34, a]</nowiki></code> gives you ''{a = 0.99}''.</div>}}
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;NSolve( <Equation>, <Variable> )
;NSolve[ <Equation>, <Variable> ]
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:Attempts (numerically) to find a solution of the equation for the given unknown variable. For non-polynomials you should always specify a starting value (see below).
:Finds a numeric solution to an equation (or a set of equations) for a given unknown variable (or set of variables).
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:{{example|1=<div><code><nowiki>NSolve(a^4 + 34a^3 = 34, a)</nowiki></code> yields '' {a =  -34, a = 0.99}''.</div>}}
:{{example|1=<div><code><nowiki>NSolve[{π / x = cos(x - 2y), 2 y - π = sin(x)}, {x=3, y=1.5}]</nowiki></code> yields ''{x = 3.141592651686591, y = 1.570796327746508}''.</div>}}
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;NSolve( <Equation>, <Variable = starting value> )
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:Finds numerically the list of solutions to the given equation for the given unknown variable with its starting value.
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:{{examples|1=<div>
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:*<code><nowiki>NSolve(cos(x) = x, x = 0)</nowiki></code> yields ''{x = 0.74}''
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:*<code><nowiki>NSolve(a^4 + 34a^3 = 34, a = 3)</nowiki></code> yields ''{a = 0.99}''.</div>}}
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;NSolve( <List of Equations>, <List of Variables> )
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:Attempts (numerically) to find a solution of the set of equations for the given set of unknown variables.
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:{{example|1=<div><code><nowiki>NSolve({pi / x = cos(x - 2y), 2 y - pi = sin(x)}, {x = 3, y = 1.5})</nowiki></code> yields ''{x = 3.14, y = 1.57}''.</div>}}
 
{{note| 1=<div>
 
{{note| 1=<div>
* It is optional to give the starting point like ''{x=3, y=1.5}''.
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* If you don't give a starting point like ''a=3'' or ''{x = 3, y = 1.5}'' the numerical algorithm may find it hard to find a solution (and giving a starting point doesn't guarantee that a solution will be found)
* See also [[Solve Command]].
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* The number of decimals depends on the choosen in [[Options Menu#Runding|global rounding]].
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* NSolve won't work for functions that are asymptotic to the x-axis or other extreme examples. They can often be reformulated though.
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* NSolve will work only if the function is continuous!
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* See also [[Solve Command]] and [[NSolutions Command]].
 
</div>}}
 
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Latest revision as of 09:58, 12 October 2017


CAS Syntax

This command is only available in the Menu view cas.svg CAS View.

NSolve( <Equation> )
Attempts (numerically) to find a solution for the equation for the main variable. For non-polynomials you should always specify a starting value (see below).
Example:
NSolve(x^6 - 2x + 1 = 0) yields {x = 0.51, x = 1}.
NSolve( <Equation>, <Variable> )
Attempts (numerically) to find a solution of the equation for the given unknown variable. For non-polynomials you should always specify a starting value (see below).
Example:
NSolve(a^4 + 34a^3 = 34, a) yields {a = -34, a = 0.99}.
NSolve( <Equation>, <Variable = starting value> )
Finds numerically the list of solutions to the given equation for the given unknown variable with its starting value.
Examples:
  • NSolve(cos(x) = x, x = 0) yields {x = 0.74}
  • NSolve(a^4 + 34a^3 = 34, a = 3) yields {a = 0.99}.
NSolve( <List of Equations>, <List of Variables> )
Attempts (numerically) to find a solution of the set of equations for the given set of unknown variables.
Example:
NSolve({pi / x = cos(x - 2y), 2 y - pi = sin(x)}, {x = 3, y = 1.5}) yields {x = 3.14, y = 1.57}.
Note:
  • If you don't give a starting point like a=3 or {x = 3, y = 1.5} the numerical algorithm may find it hard to find a solution (and giving a starting point doesn't guarantee that a solution will be found)
  • The number of decimals depends on the choosen in global rounding.
  • NSolve won't work for functions that are asymptotic to the x-axis or other extreme examples. They can often be reformulated though.
  • NSolve will work only if the function is continuous!
  • See also Solve Command and NSolutions Command.
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