Power Series for sine - Revision history

A WASSERMANN at 15:41, 20 February 2013

2013-02-20T15:41:38Z

← Older revision		Revision as of 15:41, 20 February 2013
Line 22:		Line 22:
	a = -Math.cos(x0.X());		a = -Math.cos(x0.X());
	}		}
	val = val + a*Math.pow(t-x0.X(), i) / ~~brd~~.factorial(i);		val = val + a*Math.pow(t-x0.X(), i) / JXG.Math.factorial(i);
	}		}
	return val;		return val;
Line 53:		Line 53:
	a = -Math.cos(x0.X());		a = -Math.cos(x0.X());
	}		}
	val = val + a*Math.pow(t-x0.X(), i) / ~~brd~~.factorial(i);		val = val + a*Math.pow(t-x0.X(), i) / JXG.Math.factorial(i);
	}		}
	return val;		return val;

A WASSERMANN at 10:53, 28 May 2010

2010-05-28T10:53:47Z

← Older revision		Revision as of 10:53, 28 May 2010
Line 7:		Line 7:
	brd.suspendUpdate();		brd.suspendUpdate();
	brd.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});		brd.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
	var s = brd.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});		var s = brd.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,1,10]], {name:'S',snapWidth:1});
	var x0 = brd.create('glider', [0,0,axx], {name:'x_0'});		var x0 = brd.create('glider', [0,0,axx], {name:'x_0'});
	brd.create('functiongraph', [		brd.create('functiongraph', [

A WASSERMANN at 10:52, 28 May 2010

2010-05-28T10:52:26Z

@@ Line 1: / Line 1: @@
 == Power Series for Sine ==
-:<math>x</math>
+<jsxgraph with="700" height="400">
-<jsxgraph with="700" height="400">
+brd.suspendUpdate();
 var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-7,3,8,-3]});
 var axx = brd.create('axis',[[0,0],[1,0]]);
@@ Line 30: / Line 59: @@
 -10, 10], {strokeColor: "#bb0000"});
 brd.unsuspendUpdate();
-</jsxgraph>
+[[Category:Calculus]]

A WASSERMANN at 10:39, 28 May 2010

2010-05-28T10:39:25Z

← Older revision		Revision as of 10:39, 28 May 2010
Line 1:		Line 1:
	== Power Series for Sine ==		== Power Series for Sine ==
	:<math>~~\sum_{k=0}^n a_k (~~x~~-x_0)^k~~</math>		:<math>x</math>

	<jsxgraph with="700" height="400">		<jsxgraph with="700" height="400">

A WASSERMANN at 10:38, 28 May 2010

2010-05-28T10:38:52Z

← Older revision		Revision as of 10:38, 28 May 2010
Line 1:		Line 1:
	== Power Series for Sine ==		== Power Series for Sine ==
	:<math>\sum_{k=0}^n a_k(x-x_0)^{k}</math>		:<math>\sum_{k=0}^n a_k (x-x_0)^k</math>

	<jsxgraph with="700" height="400">		<jsxgraph with="700" height="400">

A WASSERMANN at 10:37, 28 May 2010

2010-05-28T10:37:45Z

← Older revision		Revision as of 10:37, 28 May 2010
Line 1:		Line 1:
	== Power Series for Sine ==		== Power Series for Sine ==
	:<math>\sum_{k=0}^n (-1)^k~~\frac{1}{(2k+1)!}x^{2k+1~~}</math>		:<math>\sum_{k=0}^n a_k(x-x_0)^{k}</math>

	<jsxgraph with="700" height="400">		<jsxgraph with="700" height="400">
Line 11:		Line 11:
	var s = brd.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});		var s = brd.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
	var x0 = brd.create('glider', [0,0,axx], {name:'x_0'});		var x0 = brd.create('glider', [0,0,axx], {name:'x_0'});
	/*
	brd.create('functiongraph', [		brd.create('functiongraph', [
	function(t) {		function(t) {
	var val = 0, i, sv = s.Value()+1;		var val = 0, i, sv = s.Value()+1, a;
	for(i = 0; i < sv; i++) {		for(i = 0; i < sv; i++) {
	~~val~~ = ~~val +~~ Math.~~pow~~(-1, i) * Math.pow(t, 2 * i ~~+ 1~~) / ~~board1~~.factorial(2*i+1);		if (i%4==0) {
			a = Math.sin(x0.X());
			} else if (i%4==1) {
			a = Math.cos(x0.X());
			} else if (i%4==2) {
			a = -Math.sin(x0.X());
			} else if (i%4==3) {
			a = -Math.cos(x0.X());
			}
			val = val + a*Math.pow(t-x0.X(), i) / brd.factorial(i);
	}		}
	return val;		return val;
	},		},
	-10, 10], {strokeColor: "#bb0000"});		-10, 10], {strokeColor: "#bb0000"});
	*/
	brd.unsuspendUpdate();		brd.unsuspendUpdate();

	</jsxgraph>		</jsxgraph>

A WASSERMANN at 10:32, 28 May 2010

2010-05-28T10:32:25Z

← Older revision		Revision as of 10:32, 28 May 2010
Line 3:		Line 3:

	<jsxgraph with="700" height="400">		<jsxgraph with="700" height="400">
	var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-7,3,7,-3]});		var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-7,3,8,-3]});
	var axx = brd.create('axis',[[0,0],[1,0]]);		var axx = brd.create('axis',[[0,0],[1,0]]);
	var axy = brd.create('axis',[[0,0],[0,1]]);		var axy = brd.create('axis',[[0,0],[0,1]]);
Line 10:		Line 10:
	brd.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});		brd.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
	var s = brd.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});		var s = brd.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
	var x0 = brd.create('glider', [0,0,ax], {name:'x_0'});		var x0 = brd.create('glider', [0,0,axx], {name:'x_0'});
	/*		/*
	brd.create('functiongraph', [		brd.create('functiongraph', [

A WASSERMANN at 10:31, 28 May 2010

2010-05-28T10:31:56Z

← Older revision		Revision as of 10:31, 28 May 2010
Line 9:		Line 9:
	brd.suspendUpdate();		brd.suspendUpdate();
	brd.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});		brd.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
	var s = ~~board1~~.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});		var s = brd.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
	var x0 = ~~board1~~.create('glider', [0,0,ax], {name:'x_0'});		var x0 = brd.create('glider', [0,0,ax], {name:'x_0'});
	/*		/*
	brd.create('functiongraph', [		brd.create('functiongraph', [

A WASSERMANN: New page: == Power Series for Sine == : $\sum_{k=0}^n (-1)^k\frac{1}{(2k+1)!}x^{2k+1}$ var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-7,3,7,-...

2010-05-28T10:31:27Z

New page: == Power Series for Sine == :<math>\sum_{k=0}^n (-1)^k\frac{1}{(2k+1)!}x^{2k+1}</math> <jsxgraph with="700" height="400"> var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-7,3,7,-...

New page

== Power Series for Sine ==
:<math>\sum_{k=0}^n (-1)^k\frac{1}{(2k+1)!}x^{2k+1}</math>

<jsxgraph with="700" height="400">
var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-7,3,7,-3]});
var axx = brd.create('axis',[[0,0],[1,0]]);
var axy = brd.create('axis',[[0,0],[0,1]]);

brd.suspendUpdate();
brd.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
var s = board1.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
var x0 = board1.create('glider', [0,0,ax], {name:'x_0'});
/*
brd.create('functiongraph', [
function(t) {
var val = 0, i, sv = s.Value()+1;
for(i = 0; i < sv; i++) {
val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / board1.factorial(2*i+1);
}
return val;
},
-10, 10], {strokeColor: "#bb0000"});
*/
brd.unsuspendUpdate();

</jsxgraph>