Power series - pointwise: Difference between revisions

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Approximate the value of
Approximate the value of
:<math> \sum_{n=0}^\infty a_n\cdot x^n</math>
:<math> \sum_{n=0}^\infty a_n\cdot x^n</math>
for various values of <math>x</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="button" value="clear all" onClick="clearAll()">
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 15: 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);


  var s = 0;
   x = p.X();
   x = p.X();
   for (n = 0; n < m; n++) {
   for (n = n_0, s = 0; n < m; n++) {
     s += a_n(n) * Math.pow(x, n);
     s += a_n(x, n);
   }
   }
   q.moveTo([x, s], 0);
   q.moveTo([x, s], 0);
Line 38: 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);


  var s = 0;
   x = p.X();
   x = p.X();
   for (n = 0; n < m; n++) {
   for (n = n_0, s = 0; n < m; n++) {
     s += a_n(n) * Math.pow(x, 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 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);
});