Difference between revisions of "Power series for the exponential function"

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<html>
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<jsxgraph width="600" height="400" box="jxgbox1">
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<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
+
board1 = JXG.JSXGraph.initBoard('jxgbox1', {boundingbox: [-6, 25, 6, -15], axis: true});
−
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
 
−
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 
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<div id="jxgbox1" class="jxgbox" style="width:600px; height:300px;"></div>
 
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<script language="JavaScript">
 
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// Board
 
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board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 250, unitX: 50, unitY: 10});
 
 
board1.suspendUpdate();
 
board1.suspendUpdate();
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// Axes and Properties
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board1.createElement('axis', [[0,0], [1,0]], {});
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board1.create('functiongraph',  
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board1.createElement('axis', [[0,0], [0,1]], {});
+
     [function(t){ return Math.exp(t); },-10, 10],
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//
 
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board1.createElement('curve',  
 
−
     [function(t){ return t; }, function(t){ return Math.exp(t); }, "t", -10, 10],
 
 
     {strokeColor: "#cccccc"});
 
     {strokeColor: "#cccccc"});
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//
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var s = board1.createElement('slider', [[0.75,-2],[5,-2.0],[0,0,15]], {name:'S'});
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var s = board1.create('slider', [[0.75,-2],[5,-2.0],[0,0,15]], {name:'S',snapWidth:1});
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board1.createElement('text',[-4,10, function() {
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board1.create('text',[-4,10, function() {
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board1.createElement('text',[-4,8, function() {
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board1.create('text',[-4,8, function() {
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var val = 0, i, sv = s.Value()+1;
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for(var i=0;i<= Math.floor(s.X()); i++) {
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for(i = 0; i < sv; i++) {
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   val+= 1.0/board1.factorial(i);
+
   val+= 1.0/JXG.Math.factorial(i);
 
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return 'e~'+board1.round(val,10);
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return 'e~'+(val).toFixed(10);
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board1.createElement('curve', [
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board1.create('functiongraph', [
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't',
 
 
function(t) {
 
function(t) {
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var val = 0, i, sv = s.Value()+1;
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for(var i=0;i<= Math.floor(s.X()); i++) {
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for(i = 0; i < sv; i++) {
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   val+= Math.pow(t,i)/board1.factorial(i);
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   val+= Math.pow(t,i)/JXG.Math.factorial(i);
 
}
 
}
 
return val;
 
return val;
 
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},
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"t", -10, 10], {strokeColor: "#bb0000", curveType:'plot'});
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-10, 10], {strokeColor: "#bb0000", curveType:'plot'});
 
board1.unsuspendUpdate();
 
board1.unsuspendUpdate();
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</script>
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</jsxgraph>  
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</html>
 
  
 
=== References ===
 
=== References ===
Line 48: Line 37:
  
 
=== The underlying JavaScript code ===
 
=== The underlying JavaScript code ===
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<source lang="html4strict">
 
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<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
 
−
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
 
−
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 
−
<div id="jxgbox1" class="jxgbox" style="width:600px; height:300px;"></div>
 
−
</source>
 
  
 
<source lang="javascript">
 
<source lang="javascript">
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// Board
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board1 = JXG.JSXGraph.initBoard('jxgbox1', {boundingbox: [-6, 25, 6, -15], axis: true});
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board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 250, unitX: 50, unitY: 10});
 
 
board1.suspendUpdate();
 
board1.suspendUpdate();
−
// Axes and Properties
+
 
−
board1.createElement('axis', [[0,0], [1,0]], {});
+
board1.create('functiongraph',  
−
board1.createElement('axis', [[0,0], [0,1]], {});
+
    [function(t){ return Math.exp(t); },-10, 10],
−
//
+
    {strokeColor: "#cccccc"});
−
board1.createElement('curve',
+
 
−
        [function(t){ return t; }, function(t){ return Math.exp(t); }, "t", -10, 10],
+
var s = board1.create('slider', [[0.75,-2],[5,-2.0],[0,0,15]], {name:'S',snapWidth:1});
−
        {strokeColor: "#cccccc"});
+
board1.create('text',[-4,10, function() {
−
var s = board1.createElement('slider', [0.75,-2.0,5,0,15,0], {name:'S'});
+
return 'n='+s.Value();
−
board1.createElement('text',[-4,10, function() {
+
}
−
return 'n='+Math.floor(s.X());
 
−
},
 
 
     ]);
 
     ]);
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board1.createElement('text',[-4,8, function() {
+
board1.create('text',[-4,8, function() {
−
var val = 0;
+
var val = 0, i, sv = s.Value()+1;
−
for(var i=0;i<= Math.floor(s.X()); i++) {
+
for(i = 0; i < sv; i++) {
−
   val+= 1.0/board1.factorial(i);
+
   val+= 1.0/JXG.Math.factorial(i);
 
}
 
}
−
return 'e~'+board1.round(val,10);
+
return 'e~'+(val).toFixed(10);
−
},
+
}
−
]);
+
    ]);
−
board1.createElement('curve', [
+
 
−
't',
+
board1.create('functiongraph', [
 
function(t) {
 
function(t) {
−
var val = 0;
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var val = 0, i, sv = s.Value()+1;
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for(var i=0;i<= Math.floor(s.X()); i++) {
+
for(i = 0; i < sv; i++) {
−
   val+= Math.pow(t,i)/board1.factorial(i);
+
   val+= Math.pow(t,i)/JXG.Math.factorial(i);
 
}
 
}
 
return val;
 
return val;
 
},
 
},
−
"t", -10, 10], {strokeColor: "#bb0000", curveType:'plot'});
+
-10, 10], {strokeColor: "#bb0000", curveType:'plot'});
 
board1.unsuspendUpdate();
 
board1.unsuspendUpdate();
 
</source>
 
</source>
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[[Category:Examples]]
 
[[Category:Examples]]
 +
[[Category:Calculus]]

Latest revision as of 16:44, 20 February 2013

References

The underlying JavaScript code

board1 = JXG.JSXGraph.initBoard('jxgbox1', {boundingbox: [-6, 25, 6, -15], axis: true});
board1.suspendUpdate();

board1.create('functiongraph', 
    [function(t){ return Math.exp(t); },-10, 10],
    {strokeColor: "#cccccc"});

var s = board1.create('slider', [[0.75,-2],[5,-2.0],[0,0,15]], {name:'S',snapWidth:1});
board1.create('text',[-4,10, function() {
		return 'n='+s.Value();
	}
     ]);
board1.create('text',[-4,8, function() {
		var val = 0, i, sv = s.Value()+1;
		for(i = 0; i < sv; i++) {
   			val+= 1.0/JXG.Math.factorial(i);
		}
		return 'e~'+(val).toFixed(10);
	}
     ]);

board1.create('functiongraph', [
	function(t) {
		var val = 0, i, sv = s.Value()+1;
		for(i = 0; i < sv; i++) {
   			val+= Math.pow(t,i)/JXG.Math.factorial(i);
		}
		return val;
	},
-10, 10], {strokeColor: "#bb0000", curveType:'plot'});
board1.unsuspendUpdate();
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