N-th root: Difference between revisions

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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.
<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'});
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], {strokeColor: 'red', withLabel: true, name:'Math.pow(x, 1/3) - 1'});
var plot3 = board.create('functiongraph', [(x) => Math.pow(x, 1/3) - 1], {
var plot4 = board.create('functiongraph', [(x) => JXG.Math.pow(x, 1/3) - 2], {strokeColor: 'red', withLabel: true, name:'JXG.Math.pow(x, 1/3) - 2'});
        withLabel: true,  
        name:'Math.pow(x, 1/3) - 1',
        strokeColor: 'red',
        label: {position: 'rt', offset:[-100,-20]}
    });
</jsxgraph>
 
===The underlying JavaScript code===
<source lang="javascript">
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]}
    });
</source>


</jsxgraph>
[[Category:Examples]]
[[Category:Calculus]]

Latest revision as of 12:14, 2 April 2020

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

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

also for negative values of [math]\displaystyle{ x }[/math].

There are the following choices:

  • "Math.pow(x, 1/3)": this built-in JavaScript function is restricted to positive values of [math]\displaystyle{ x }[/math].
  • "JXG.Math.cbrt(x)": cube root function which is able to compute the real cube root of [math]\displaystyle{ 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]\displaystyle{ 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]}
    });