Power series for the exponential function: Difference between revisions

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Line 1: Line 1:
<jsxgraph width="600" height="400" box="jxgbox1">
<jsxgraph width="600" height="400" box="jxgbox1">
board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 250, unitX: 50, unitY: 10});
board1 = JXG.JSXGraph.initBoard('jxgbox1', {boundingbox: [-6, 25, 6, -15], axis: true});
board1.suspendUpdate();
board1.suspendUpdate();
board1.create('axis', [[0,0], [1,0]], {});
board1.create('axis', [[0,0], [0,1]], {});


board1.create('functiongraph',  
board1.create('functiongraph',  
Line 17: Line 15:
var val = 0, i, sv = s.Value()+1;
var val = 0, i, sv = s.Value()+1;
for(i = 0; i < sv; 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);
}
}
     ]);
     ]);
Line 27: Line 25:
var val = 0, i, sv = s.Value()+1;
var val = 0, i, sv = s.Value()+1;
for(i = 0; i < sv; 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;
Line 41: Line 39:


<source lang="javascript">
<source lang="javascript">
board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 250, unitX: 50, unitY: 10});
board1 = JXG.JSXGraph.initBoard('jxgbox1', {boundingbox: [-6, 25, 6, -15], axis: true});
board1.suspendUpdate();
board1.suspendUpdate();
board1.create('axis', [[0,0], [1,0]], {});
board1.create('axis', [[0,0], [0,1]], {});


board1.create('functiongraph',  
board1.create('functiongraph',  
Line 58: Line 54:
var val = 0, i, sv = s.Value()+1;
var val = 0, i, sv = s.Value()+1;
for(i = 0; i < sv; 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);
}
}
     ]);
     ]);
Line 68: Line 64:
var val = 0, i, sv = s.Value()+1;
var val = 0, i, sv = s.Value()+1;
for(i = 0; i < sv; 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;

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();