Cauchy's mean value theorem - Revision history

Michael at 19:06, 18 January 2013

2013-01-18T19:06:24Z

← Older revision		Revision as of 19:06, 18 January 2013
Line 11:		Line 11:
	p[3] = board.create('point', [3,2], {style:4});		p[3] = board.create('point', [3,2], {style:4});
	p[4] = board.create('point', [4,1], {style:4});		p[4] = board.create('point', [4,1], {style:4});
	var fArray = JXG.Math.Numerics.~~neville~~(p);		var fArray = JXG.Math.Numerics.Neville(p);
	var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});		var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});
	/*		/*

Michael at 19:05, 18 January 2013

2013-01-18T19:05:11Z

← Older revision		Revision as of 19:05, 18 January 2013
Line 11:		Line 11:
	p[3] = board.create('point', [3,2], {style:4});		p[3] = board.create('point', [3,2], {style:4});
	p[4] = board.create('point', [4,1], {style:4});		p[4] = board.create('point', [4,1], {style:4});
	var fArray = ~~board~~.neville(p);		var fArray = JXG.Math.Numerics.neville(p);
	var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});		var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});
	/*		/*

	var g = function(t) {		var g = function(t) {
	return ~~board~~.D(fArray[0])(t)/~~board~~.D(fArray[1])(t)-(p[4].X()-p[0].X())/(p[4].Y()-p[0].Y());		return JXG.Math.Numerics.D(fArray[0])(t)/JXG.Math.Numerics.D(fArray[1])(t)-(p[4].X()-p[0].X())/(p[4].Y()-p[0].Y());
	};		};

A WASSERMANN at 12:58, 27 January 2010

2010-01-27T12:58:43Z

← Older revision		Revision as of 12:58, 27 January 2010
Line 13:		Line 13:
	var fArray = board.neville(p);		var fArray = board.neville(p);
	var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});		var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});
			/*

	var g = function(t) {		var g = function(t) {
Line 23:		Line 24:
	graph], {name:' ',style:6,fixed:true});		graph], {name:' ',style:6,fixed:true});
	board.create('tangent', [r], {strokeColor:'#ff0000'});		board.create('tangent', [r], {strokeColor:'#ff0000'});
	/*
	*/		*/
	line = board.create('line',[p[0],p[4]],{strokeColor:'#ff0000',dash:1});		line = board.create('line',[p[0],p[4]],{strokeColor:'#ff0000',dash:1});

A WASSERMANN at 12:56, 27 January 2010

2010-01-27T12:56:57Z

← Older revision		Revision as of 12:56, 27 January 2010
Line 6:		Line 6:
	board.suspendUpdate();		board.suspendUpdate();
	var p = [];		var p = [];
	p[0] = board.create('point', [-2,1], {style:4});		p[0] = board.create('point', [0,1], {style:4});
	p[1] = board.create('point', [-1,2], {style:4});		p[1] = board.create('point', [1,2], {style:4});
	p[2] = board.create('point', [0.5,3], {style:4});		p[2] = board.create('point', [2.5,3], {style:4});
	p[3] = board.create('point', [1,2], {style:4});		p[3] = board.create('point', [3,2], {style:4});
	p[4] = board.create('point', [2,1], {style:4});		p[4] = board.create('point', [4,1], {style:4});
	var fArray = board.neville(p);		var fArray = board.neville(p);
	var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});		var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});

A WASSERMANN at 12:54, 27 January 2010

2010-01-27T12:54:02Z

A WASSERMANN at 12:53, 27 January 2010

2010-01-27T12:53:37Z

← Older revision		Revision as of 12:53, 27 January 2010
Line 6:		Line 6:
	board.suspendUpdate();		board.suspendUpdate();
	var p = [];		var p = [];
	p[0] = board.create('point', [-1~~,-2~~], {style:4});		p[0] = board.create('point', [-2,1], {style:4});
	p[1] = board.create('point', [1,4], {style:4});		p[1] = board.create('point', [-1,2], {style:4});
	p[2] = board.create('point', [-0.5,1], {style:4});		p[2] = board.create('point', [0,3], {style:4});
	p[3] = board.create('point', [3,3], {style:4});		p[3] = board.create('point', [1,2], {style:4});
	p[4] = board.create('point', [-2,5], {style:4});		p[4] = board.create('point', [2,1], {style:4});
	var fArray = board.neville(p);		var fArray = board.neville(p);
	var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});		var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});

A WASSERMANN at 10:46, 27 January 2010

2010-01-27T10:46:30Z

← Older revision		Revision as of 10:46, 27 January 2010
Line 14:		Line 14:
	var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});		var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});

			/*
	var g = function(t) {		var g = function(t) {
	return board.D(fArray[0])(t)/board.D(fArray[1])(t)-(p[4].X()-p[0].X())/(p[4].Y()-p[0].Y());		return board.D(fArray[0])(t)/board.D(fArray[1])(t)-(p[4].X()-p[0].X())/(p[4].Y()-p[0].Y());
Line 23:		Line 24:
	graph], {name:' ',style:6,fixed:true});		graph], {name:' ',style:6,fixed:true});
	board.create('tangent', [r], {strokeColor:'#ff0000'});		board.create('tangent', [r], {strokeColor:'#ff0000'});
	/*
	*/		*/
	line = board.create('line',[p[0],p[4]],{strokeColor:'#ff0000',dash:1});		line = board.create('line',[p[0],p[4]],{strokeColor:'#ff0000',dash:1});

A WASSERMANN at 10:46, 27 January 2010

2010-01-27T10:46:12Z

← Older revision		Revision as of 10:46, 27 January 2010
Line 14:		Line 14:
	var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});		var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});

	/*
	var g = function(t) {		var g = function(t) {
	return board.D(fArray[0])(t)/board.D(fArray[1])(t)-(p[4].X()-p[0].X())/(p[4].Y()-p[0].Y());		return board.D(fArray[0])(t)/board.D(fArray[1])(t)-(p[4].X()-p[0].X())/(p[4].Y()-p[0].Y());
Line 24:		Line 23:
	graph], {name:' ',style:6,fixed:true});		graph], {name:' ',style:6,fixed:true});
	board.create('tangent', [r], {strokeColor:'#ff0000'});		board.create('tangent', [r], {strokeColor:'#ff0000'});
			/*
	*/		*/
	line = board.create('line',[p[0],p[4]],{strokeColor:'#ff0000',dash:1});		line = board.create('line',[p[0],p[4]],{strokeColor:'#ff0000',dash:1});

A WASSERMANN at 10:45, 27 January 2010

2010-01-27T10:45:58Z

← Older revision		Revision as of 10:45, 27 January 2010
Line 16:		Line 16:
	/*		/*
	var g = function(t) {		var g = function(t) {
	return board.D(fArray[1])(t)/board.D(fArray[0])(t)-(p[4].Y()-p[0].Y())/(p[4].X()-p[0].X());		return board.D(fArray[0])(t)/board.D(fArray[1])(t)-(p[4].X()-p[0].X())/(p[4].Y()-p[0].Y());
	};		};

A WASSERMANN at 10:45, 27 January 2010

2010-01-27T10:45:02Z

← Older revision		Revision as of 12:54, 27 January 2010
Line 8:		Line 8:
	p[0] = board.create('point', [-2,1], {style:4});		p[0] = board.create('point', [-2,1], {style:4});
	p[1] = board.create('point', [-1,2], {style:4});		p[1] = board.create('point', [-1,2], {style:4});
	p[2] = board.create('point', [0,3], {style:4});		p[2] = board.create('point', [0.5,3], {style:4});
	p[3] = board.create('point', [1,2], {style:4});		p[3] = board.create('point', [1,2], {style:4});
	p[4] = board.create('point', [2,1], {style:4});		p[4] = board.create('point', [2,1], {style:4});
Line 14:		Line 14:
	var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});		var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});

	/*
	var g = function(t) {		var g = function(t) {
	return board.D(fArray[0])(t)/board.D(fArray[1])(t)-(p[4].X()-p[0].X())/(p[4].Y()-p[0].Y());		return board.D(fArray[0])(t)/board.D(fArray[1])(t)-(p[4].X()-p[0].X())/(p[4].Y()-p[0].Y());
Line 24:		Line 23:
	graph], {name:' ',style:6,fixed:true});		graph], {name:' ',style:6,fixed:true});
	board.create('tangent', [r], {strokeColor:'#ff0000'});		board.create('tangent', [r], {strokeColor:'#ff0000'});
			/*
	*/		*/
	line = board.create('line',[p[0],p[4]],{strokeColor:'#ff0000',dash:1});		line = board.create('line',[p[0],p[4]],{strokeColor:'#ff0000',dash:1});

← Older revision		Revision as of 10:45, 27 January 2010
Line 1:		Line 1:
	''Cauchy's mean value theorem'' is also known as ''extended mean value theorem''. In Germany it is called ''Zweiter Mittelwertsatz''.		''Cauchy's mean value theorem'' is also known as ''extended mean value theorem''. In Germany it is called ''Zweiter Mittelwertsatz''.

			DRAFT
	<jsxgraph width="600" height="400">		<jsxgraph width="600" height="400">
	var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5,8,7,-8], axis:true});		var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5,8,7,-8], axis:true});
Line 11:		Line 13:
	var fArray = board.neville(p);		var fArray = board.neville(p);
	var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});		var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});

			/*
	var g = function(t) {		var g = function(t) {
	return board.D(fArray[1])(t)/board.D(fArray[0])(t)-(p[4].Y()-p[0].Y())/(p[4].X()-p[0].X());		return board.D(fArray[1])(t)/board.D(fArray[0])(t)-(p[4].Y()-p[0].Y())/(p[4].X()-p[0].X());
Line 20:		Line 24:
	graph], {name:' ',style:6,fixed:true});		graph], {name:' ',style:6,fixed:true});
	board.create('tangent', [r], {strokeColor:'#ff0000'});		board.create('tangent', [r], {strokeColor:'#ff0000'});
	/*
	*/		*/
	line = board.create('line',[p[0],p[4]],{strokeColor:'#ff0000',dash:1});		line = board.create('line',[p[0],p[4]],{strokeColor:'#ff0000',dash:1});