Power series for the exponential function: Difference between revisions

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<html>
<jsxgraph width="600" height="400" box="jxgbox1">
<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>
<div id="jxgbox1" class="jxgbox" style="width:600px; height:300px;"></div>
<script language="JavaScript">
// Board
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],
//
board1.createElement('curve',  
     [function(t){ return t; }, function(t){ return Math.exp(t); }, "t", -10, 10],
     {strokeColor: "#cccccc"});
     {strokeColor: "#cccccc"});
//
 
var s = board1.createElement('slider', [[0.75,-2],[5,-2.0],[0,0,15]], {name:'S'});
var s = board1.create('slider', [[0.75,-2],[5,-2.0],[0,0,15]], {name:'S',snapWidth:1});
board1.createElement('text',[-4,10, function() {
board1.create('text',[-4,10, function() {
return 'n='+Math.floor(s.X());
return 'n='+s.Value();
},
}
     ]);
     ]);
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', [
board1.create('functiongraph', [
't',
function(t) {
function(t) {
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+= 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();
</script>
</jsxgraph>  
</html>


=== References ===
=== References ===
Line 48: Line 37:


=== The underlying JavaScript code ===
=== The underlying JavaScript code ===
<source lang="html4strict">
<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">
// Board
board1 = JXG.JSXGraph.initBoard('jxgbox1', {boundingbox: [-6, 25, 6, -15], axis: true});
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());
},
     ]);
     ]);
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;
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+= 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>
Line 95: Line 74:


[[Category:Examples]]
[[Category:Examples]]
[[Category:Calculus]]

Latest revision as of 15:44, 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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