Difference between revisions of "N-th root"

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This example shows the various possibilities to plot the graph of the function
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:<math> \mathbb{R} \to \mathbb{R}, x \mapsto x^{1/3}</math> 
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also for negative values of <math>x</math>.
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There are the following choices:
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* "Math.pow(x, 1/3)": this built-in JavaScript function is restricted to positive values of <math>x</math>.
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* "JXG.Math.cbrt(x)": cube root function which is able to compute the real cube root of <math>x</math>. It is available in most browsers as built-in "Math.cbrt()". The JSXGraph makes cbrt available also on old browsers.
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* "JXG.Math.nthroot(x, 3)": general method in JSXGraph to compute the real <math>n</math>-th root of a real number.
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<jsxgraph width="500" height="500">
 
<jsxgraph width="500" height="500">
 
var board = JXG.JSXGraph.initBoard('jxgbox', {
 
var board = JXG.JSXGraph.initBoard('jxgbox', {
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var plot1 = board.create('functiongraph', ["nthroot(x, 3)"], {withLabel: true, name:'nthroot(x,3)'});
 
var plot1 = board.create('functiongraph', ["nthroot(x, 3)"], {withLabel: true, name:'nthroot(x,3)'});
 
var plot2 = board.create('functiongraph', ["cbrt(x) + 1"], {withLabel: true, name:'cbrt(x)+1', strokeColor: 'black'});
 
var plot2 = board.create('functiongraph', ["cbrt(x) + 1"], {withLabel: true, name:'cbrt(x)+1', strokeColor: 'black'});
var plot3 = board.create('functiongraph', [(x) => Math.pow(x, 1/3) - 1], {withLabel: true, name:'Math.pow(x, 1/3) - 1', strokeColor: 'red'});
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var plot3 = board.create('functiongraph', [(x) => Math.pow(x, 1/3) - 1], {
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        withLabel: true,  
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        name:'Math.pow(x, 1/3) - 1',  
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        strokeColor: 'red',
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        label: {position: 'rt', offset:[-100,-20]}
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    });
 
</jsxgraph>
 
</jsxgraph>
  
 
===The underlying JavaScript code===
 
===The underlying JavaScript code===
 
<source lang="javascript">
 
<source lang="javascript">
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var board = JXG.JSXGraph.initBoard('jxgbox', {
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        axis:true,
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        boundingbox:[-5, 5, 5, -5],
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        showFullscreen: true
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});
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var plot1 = board.create('functiongraph', ["nthroot(x, 3)"], {withLabel: true, name:'nthroot(x,3)'});
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var plot2 = board.create('functiongraph', ["cbrt(x) + 1"], {withLabel: true, name:'cbrt(x)+1', strokeColor: 'black'});
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var plot3 = board.create('functiongraph', [(x) => Math.pow(x, 1/3) - 1], {
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        withLabel: true,
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        name:'Math.pow(x, 1/3) - 1',
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        strokeColor: 'red',
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        label: {position: 'rt', offset:[-100,-20]}
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    });
 
</source>
 
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Calculus]]
 
[[Category:Calculus]]

Latest revision as of 14:14, 2 April 2020

This example shows the various possibilities to plot the graph of the function

[math] \mathbb{R} \to \mathbb{R}, x \mapsto x^{1/3}[/math]

also for negative values of [math]x[/math].

There are the following choices:

  • "Math.pow(x, 1/3)": this built-in JavaScript function is restricted to positive values of [math]x[/math].
  • "JXG.Math.cbrt(x)": cube root function which is able to compute the real cube root of [math]x[/math]. It is available in most browsers as built-in "Math.cbrt()". The JSXGraph makes cbrt available also on old browsers.
  • "JXG.Math.nthroot(x, 3)": general method in JSXGraph to compute the real [math]n[/math]-th root of a real number.

The underlying JavaScript code

var board = JXG.JSXGraph.initBoard('jxgbox', {
        axis:true, 
        boundingbox:[-5, 5, 5, -5],
        showFullscreen: true
});

var plot1 = board.create('functiongraph', ["nthroot(x, 3)"], {withLabel: true, name:'nthroot(x,3)'});
var plot2 = board.create('functiongraph', ["cbrt(x) + 1"], {withLabel: true, name:'cbrt(x)+1', strokeColor: 'black'});
var plot3 = board.create('functiongraph', [(x) => Math.pow(x, 1/3) - 1], {
        withLabel: true, 
        name:'Math.pow(x, 1/3) - 1', 
        strokeColor: 'red',
        label: {position: 'rt', offset:[-100,-20]}
    });