Power series - pointwise: Difference between revisions
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Approximate the value of | |||
:<math> \sum_{n=0}^\infty a_n\cdot x^n</math> | |||
for various values of <math>x</math>. | |||
Drag the point 'x', the blue point shows the value of the above series. | |||
<html> | <html> | ||
nth-coefficient: <input type="text" id="input" value="1 / factorial(n)"> | <p> | ||
<input type=" | nth-coefficient: <input type="text" id="input" value="x^n * 1 / factorial(n)">, | ||
start summation at n = <input type="number" id="startval" value="0" style="width:2em"><br /> | |||
</html> | </html> | ||
<jsxgraph width="600" height="600"> | <jsxgraph width="600" height="600"> | ||
var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-8,8,8,-8], axis:true}); | var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-8,8,8,-8], axis:true, showClearTraces: true}); | ||
var p = board.create('glider', [0, 0, board.defaultAxes.x] , {name: 'x'}); | var p = board.create('glider', [0, 0, board.defaultAxes.x] , {name: 'x'}); | ||
var q = board.create('point', [0, 1], {name: '', color: 'blue', trace: true}); | var q = board.create('point', [0, 1], {name: '', color: 'blue', trace: true, fixed: true}); | ||
p.on('up', function(evt) { | p.on('up', function(evt) { | ||
var x, n, m = 50; | var x, n, s, m = 50; | ||
var txtraw = document.getElementById('input').value; | var txtraw = document.getElementById('input').value; | ||
var a_n = board.jc.snippet(txtraw, true, 'n', true); | var a_n = board.jc.snippet(txtraw, true, 'x, n', true); | ||
var n_0 = parseInt(document.getElementById('startval').value); | |||
x = p.X(); | x = p.X(); | ||
for (n = 0; n < m; n++) { | for (n = n_0, s = 0; n < m; n++) { | ||
s += a_n | s += a_n(x, n); | ||
} | } | ||
q.moveTo([x, s], 0); | q.moveTo([x, s], 0); | ||
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</jsxgraph> | </jsxgraph> | ||
===The underlying JavaScript code=== | |||
<source lang="javascript"> | |||
var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-8,8,8,-8], axis:true, showClearTraces: true}); | |||
var p = board.create('glider', [0, 0, board.defaultAxes.x] , {name: 'x'}); | |||
var q = board.create('point', [0, 1], {name: '', color: 'blue', trace: true, fixed: true}); | |||
p.on('up', function(evt) { | |||
var x, n, s, m = 50; | |||
var txtraw = document.getElementById('input').value; | |||
var a_n = board.jc.snippet(txtraw, true, 'x, n', true); | |||
var n_0 = parseInt(document.getElementById('startval').value); | |||
x = p.X(); | |||
for (n = n_0, s = 0; n < m; n++) { | |||
s += a_n(x, n); | |||
} | |||
q.moveTo([x, s], 0); | |||
}); | |||
</source> | |||
[[Category:Examples]] | |||
[[Category:Calculus]] | |||
Latest revision as of 18:01, 7 January 2019
Approximate the value of
- [math]\displaystyle{ \sum_{n=0}^\infty a_n\cdot x^n }[/math]
for various values of [math]\displaystyle{ x }[/math]. Drag the point 'x', the blue point shows the value of the above series.
nth-coefficient: ,
start summation at n =
The underlying JavaScript code
var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-8,8,8,-8], axis:true, showClearTraces: true});
var p = board.create('glider', [0, 0, board.defaultAxes.x] , {name: 'x'});
var q = board.create('point', [0, 1], {name: '', color: 'blue', trace: true, fixed: true});
p.on('up', function(evt) {
var x, n, s, m = 50;
var txtraw = document.getElementById('input').value;
var a_n = board.jc.snippet(txtraw, true, 'x, n', true);
var n_0 = parseInt(document.getElementById('startval').value);
x = p.X();
for (n = n_0, s = 0; n < m; n++) {
s += a_n(x, n);
}
q.moveTo([x, s], 0);
});
