Difference between revisions of "Power series - pointwise"
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<html> | <html> | ||
<p> | <p> | ||
| − | nth-coefficient: <input type="text" id="input" value="1 / factorial(n)"> | + | 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> | ||
| Line 16: | Line 17: | ||
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); | ||
| Line 39: | Line 40: | ||
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); | ||
}); | }); | ||
| + | |||
</source> | </source> | ||
[[Category:Examples]] | [[Category:Examples]] | ||
[[Category:Calculus]] | [[Category:Calculus]] | ||
Latest revision as of 20:01, 7 January 2019
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.
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);
});
