Secant and tangent - Revision history

A WASSERMANN at 08:26, 17 January 2024

2024-01-17T08:26:30Z

← Older revision		Revision as of 08:26, 17 January 2024
Line 1:		Line 1:
	<jsxgraph box="box" width="600" height="400">		<jsxgraph box="box" width="600" height="400">
	board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});		board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces:true});

	var p = [];		var p = [];
Line 20:		Line 20:

	<jsxgraph box="box2" width="600" height="400">		<jsxgraph box="box2" width="600" height="400">
	board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});		board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces:true});

	var f = function(x) { return (Math.abs(x)); };		var f = function(x) { return (Math.abs(x)); };
Line 35:		Line 35:

	<jsxgraph box="box3" width="600" height="400">		<jsxgraph box="box3" width="600" height="400">
	board = JXG.JSXGraph.initBoard('box3', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});		board = JXG.JSXGraph.initBoard('box3', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces:true});

	var g = function(x) { return (x<=0)?0:1; };		var g = function(x) { return (x<=0)?0:1; };
Line 54:		Line 54:
	Construction 1:		Construction 1:
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});		board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces:true});

	var p = [];		var p = [];
Line 75:		Line 75:
	Construction 2:		Construction 2:
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});		board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces:true});

	var f = function(x) { return (Math.abs(x)); };		var f = function(x) { return (Math.abs(x)); };
Line 91:		Line 91:
	Construction 3:		Construction 3:
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('box3', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});		board = JXG.JSXGraph.initBoard('box3', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces:true});

	var g = function(x) { return (x<=0)?0:1; };		var g = function(x) { return (x<=0)?0:1; };

A WASSERMANN at 08:25, 17 January 2024

2024-01-17T08:25:56Z

← Older revision		Revision as of 08:25, 17 January 2024
Line 1:		Line 1:
	<jsxgraph box="box" width="600" height="400">		<jsxgraph box="box" width="600" height="400">
	board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});		board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});

	var p = [];		var p = [];
Line 20:		Line 20:

	<jsxgraph box="box2" width="600" height="400">		<jsxgraph box="box2" width="600" height="400">
	board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 10, 7, -6], axis: true});		board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});

	var f = function(x) { return (Math.abs(x)); };		var f = function(x) { return (Math.abs(x)); };
Line 35:		Line 35:

	<jsxgraph box="box3" width="600" height="400">		<jsxgraph box="box3" width="600" height="400">
	board = JXG.JSXGraph.initBoard('box3', {boundingbox: [-5, 10, 7, -6], axis: true});		board = JXG.JSXGraph.initBoard('box3', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});

	var g = function(x) { return (x<=0)?0:1; };		var g = function(x) { return (x<=0)?0:1; };
Line 54:		Line 54:
	Construction 1:		Construction 1:
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});		board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});

	var p = [];		var p = [];
Line 75:		Line 75:
	Construction 2:		Construction 2:
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 10, 7, -6], axis: true});		board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});

	var f = function(x) { return (Math.abs(x)); };		var f = function(x) { return (Math.abs(x)); };
Line 91:		Line 91:
	Construction 3:		Construction 3:
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('box3', {boundingbox: [-5, 10, 7, -6], axis: true});		board = JXG.JSXGraph.initBoard('box3', {boundingbox: [-5, 10, 7, -6], axis: true, showClearTraces});

	var g = function(x) { return (x<=0)?0:1; };		var g = function(x) { return (x<=0)?0:1; };

A WASSERMANN at 08:24, 17 January 2024

2024-01-17T08:24:49Z

← Older revision		Revision as of 08:24, 17 January 2024
Line 75:		Line 75:
	Construction 2:		Construction 2:
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('~~box3~~', {boundingbox: [-5, 10, 7, -6], axis: true});		board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 10, 7, -6], axis: true});

	var g = function(x) { return (x~~<=0~~)~~?0:1~~; };		var f = function(x) { return (Math.abs(x)); };
	graph = board.create('functiongraph', [g,-10, 10]);		graph = board.create('functiongraph', [f, -10, 10], {strokeWidth:3});

	qg = board.create('glider', [0,0,graph], {size:4});		qf = board.create('glider', [0,0,graph], {size:5});
	sg = board.create('slider', [[0,-3],[4,-3],[0.001,1,1]]);		sf = board.create('slider', [[0,-3],[4,-3],[0.001,1,1]]);
	~~qg2~~ = board.create('point', [function(){ return qg.X()+sg.Value();},		qf2 = board.create('point', [function(){ return qf.X()+sf.Value();},
	function(){ return g(qg.X()+sg.Value());}], {face:'[]',size:2});		function(){ return f(qf.X()+sf.Value());}], {face:'[]',size:2});
	eg = board.create('point', [function(){ return ~~qg2~~.X()-qg.X();},		ef = board.create('point', [function(){ return qf2.X()-qf.X();},
	function(){ return (~~qg2~~.Y()-qg.Y())/(~~qg2~~.X()-qg.X());}], {face:'[]',size:2,name:'Sekantensteigung',trace:true});		function(){ return (qf2.Y()-qf.Y())/(qf2.X()-qf.X());}], {face:'[]',size:2,name:'Sekantensteigung',trace:true});
	line = board.create('line',[qg,~~qg2~~],{strokeColor:'#ff0000',dash:2});		line = board.create('line',[qf,qf2],{strokeColor:'#ff0000',dash:2});
	</source>		</source>

Line 94:		Line 94:

	var g = function(x) { return (x<=0)?0:1; };		var g = function(x) { return (x<=0)?0:1; };
	graph = board.create('functiongraph', [g,-10, 10]);		graph = board.create('functiongraph', [g,-10, 10], {strokeWidth:3});

	qg = board.create('glider', [0,0,graph], {size:4});		qg = board.create('glider', [0,0,graph], {size:4});

A WASSERMANN at 08:22, 17 January 2024

2024-01-17T08:22:32Z

A WASSERMANN at 08:21, 17 January 2024

2024-01-17T08:21:18Z

@@ Line 1: / Line 1: @@
 <jsxgraph box="box" width="600" height="400">
 board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});
 var p = [];
@@ Line 18: / Line 17: @@
          function(){ return (q2.Y()-q.Y())/(q2.X()-q.X());}], {style:7,name:'Sekantensteigung',trace:true});
 line = board.create('line',[q,q2],{strokeColor:'#ff0000',dash:2});
 </jsxgraph>
 <jsxgraph box="box2" width="600" height="400">
 board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 10, 7, -6], axis: true});
 var f = function(x) { return (Math.abs(x)); };
@@ Line 35: / Line 32: @@
             function(){ return (qf2.Y()-qf.Y())/(qf2.X()-qf.X());}], {face:'[]',size:2,name:'Sekantensteigung',trace:true});
 line = board.create('line',[qf,qf2],{strokeColor:'#ff0000',dash:2});
 </jsxgraph>
 <jsxgraph box="box3" width="600" height="400">
 board = JXG.JSXGraph.initBoard('box3', {boundingbox: [-5, 10, 7, -6], axis: true});
 var g = function(x) { return (x<=0)?0:1; };
@@ Line 52: / Line 47: @@
              function(){ return (qg2.Y()-qg.Y())/(qg2.X()-qg.X());}], {face:'[]',size:2,name:'Sekantensteigung',trace:true});
 line = board.create('line',[qg,qg2],{strokeColor:'#ff0000',dash:2});
 </jsxgraph>
 [[Category:Examples]]
 [[Category:Calculus]]

A WASSERMANN at 15:55, 20 February 2013

2013-02-20T15:55:22Z

← Older revision		Revision as of 15:55, 20 February 2013
Line 8:		Line 8:
	p[2] = board.create('point', [2,0.5], {size:2});		p[2] = board.create('point', [2,0.5], {size:2});
	p[3] = board.create('point', [6,5], {size:2});		p[3] = board.create('point', [6,5], {size:2});
	var pol = ~~board~~.lagrangePolynomial(p);		var pol = JXG.Math.Numerics.lagrangePolynomial(p);
	graph = board.create('functiongraph', [pol, -10, 10]);		graph = board.create('functiongraph', [pol, -10, 10]);

Michael at 13:14, 8 June 2011

2011-06-08T13:14:08Z

Show changes

A WASSERMANN at 17:27, 29 October 2009

2009-10-29T17:27:30Z

← Older revision		Revision as of 17:27, 29 October 2009
Line 1:		Line 1:
	<html>		<html>
	<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />		<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>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>		<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>

A WASSERMANN at 13:36, 4 June 2009

2009-06-04T13:36:29Z

A WASSERMANN at 14:14, 23 March 2009

2009-03-23T14:14:54Z

← Older revision		Revision as of 08:22, 17 January 2024
Line 8:		Line 8:
	p[3] = board.create('point', [6,5], {size:2});		p[3] = board.create('point', [6,5], {size:2});
	var pol = JXG.Math.Numerics.lagrangePolynomial(p);		var pol = JXG.Math.Numerics.lagrangePolynomial(p);
	graph = board.create('functiongraph', [pol, -10, 10]);		graph = board.create('functiongraph', [pol, -10, 10], {strokeWidth:3});

	q = board.create('glider', [4.5,0,graph], {size:5});		q = board.create('glider', [4.5,0,graph], {size:5});
Line 23:		Line 23:

	var f = function(x) { return (Math.abs(x)); };		var f = function(x) { return (Math.abs(x)); };
	graph = board.create('functiongraph', [f, -10, 10]);		graph = board.create('functiongraph', [f, -10, 10], {strokeWidth:3});

	qf = board.create('glider', [0,0,graph], {size:5});		qf = board.create('glider', [0,0,graph], {size:5});
Line 38:		Line 38:

	var g = function(x) { return (x<=0)?0:1; };		var g = function(x) { return (x<=0)?0:1; };
	graph = board.create('functiongraph', [g,-10, 10]);		graph = board.create('functiongraph', [g,-10, 10], {strokeWidth:3});

	qg = board.create('glider', [0,0,graph], {size:4});		qg = board.create('glider', [0,0,graph], {size:4});
Line 62:		Line 62:
	p[3] = board.create('point', [6,5], {size:2});		p[3] = board.create('point', [6,5], {size:2});
	var pol = JXG.Math.Numerics.lagrangePolynomial(p);		var pol = JXG.Math.Numerics.lagrangePolynomial(p);
	graph = board.create('functiongraph', [pol, -10, 10]);		graph = board.create('functiongraph', [pol, -10, 10], {strokeWidth:3});

	q = board.create('glider', [4.5,0,graph], {size:5});		q = board.create('glider', [4.5,0,graph], {size:5});

← Older revision		Revision as of 13:36, 4 June 2009
Line 21:		Line 21:
	q = board.createElement('glider', [4.5,0,graph], {style:6});		q = board.createElement('glider', [4.5,0,graph], {style:6});
	s = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);		s = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);
	q2 = board.createElement('point', [function(){ return q.X()+Math.max(s.X(),0.01);},		q2 = board.createElement('point', [function(){ return q.X()+Math.max(s.Value(),0.01);},
	function(){ return pol(q.X()+Math.max(s.X(),0.01));}], {style:7});		function(){ return pol(q.X()+Math.max(s.Value(),0.01));}], {style:7});
	e = board.createElement('point', [function(){ return q2.X()-q.X();},		e = board.createElement('point', [function(){ return q2.X()-q.X();},
	function(){ return (q2.Y()-q.Y())/(q2.X()-q.X());}], {style:7,name:'Sekantensteigung',trace:true});		function(){ return (q2.Y()-q.Y())/(q2.X()-q.X());}], {style:7,name:'Sekantensteigung',trace:true});
Line 44:		Line 44:
	qf = board.createElement('glider', [0,0,graph], {style:6});		qf = board.createElement('glider', [0,0,graph], {style:6});
	sf = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);		sf = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);
	qf2 = board.createElement('point', [function(){ return qf.X()+sf.X();},		qf2 = board.createElement('point', [function(){ return qf.X()+sf.Value();},
	function(){ return f(qf.X()+sf.X());}], {style:7});		function(){ return f(qf.X()+sf.Value());}], {style:7});
	ef = board.createElement('point', [function(){ return qf2.X()-qf.X();},		ef = board.createElement('point', [function(){ return qf2.X()-qf.X();},
	function(){ return (qf2.Y()-qf.Y())/(qf2.X()-qf.X());}], {style:7,name:'Sekantensteigung',trace:true});		function(){ return (qf2.Y()-qf.Y())/(qf2.X()-qf.X());}], {style:7,name:'Sekantensteigung',trace:true});
Line 67:		Line 67:
	qg = board.createElement('glider', [0,0,graph], {style:6});		qg = board.createElement('glider', [0,0,graph], {style:6});
	sg = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);		sg = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);
	qg2 = board.createElement('point', [function(){ return qg.X()+sg.X();},		qg2 = board.createElement('point', [function(){ return qg.X()+sg.Value();},
	function(){ return g(qg.X()+sg.X());}], {style:7});		function(){ return g(qg.X()+sg.Value());}], {style:7});
	eg = board.createElement('point', [function(){ return qg2.X()-qg.X();},		eg = board.createElement('point', [function(){ return qg2.X()-qg.X();},
	function(){ return (qg2.Y()-qg.Y())/(qg2.X()-qg.X());}], {style:7,name:'Sekantensteigung',trace:true});		function(){ return (qg2.Y()-qg.Y())/(qg2.X()-qg.X());}], {style:7,name:'Sekantensteigung',trace:true});

← Older revision		Revision as of 14:14, 23 March 2009
Line 20:		Line 20:

	q = board.createElement('glider', [4.5,0,graph], {style:6});		q = board.createElement('glider', [4.5,0,graph], {style:6});
	s = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]~~,{name:' '}~~);		s = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);
	q2 = board.createElement('point', [function(){ return q.X()+Math.max(s.X(),0.01);},		q2 = board.createElement('point', [function(){ return q.X()+Math.max(s.X(),0.01);},
	function(){ return pol(q.X()+Math.max(s.X(),0.01));}], {style:7});		function(){ return pol(q.X()+Math.max(s.X(),0.01));}], {style:7});
Line 43:		Line 43:

	qf = board.createElement('glider', [0,0,graph], {style:6});		qf = board.createElement('glider', [0,0,graph], {style:6});
	sf = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]~~,{name:' '}~~);		sf = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);
	qf2 = board.createElement('point', [function(){ return qf.X()+sf.X();},		qf2 = board.createElement('point', [function(){ return qf.X()+sf.X();},
	function(){ return f(qf.X()+sf.X());}], {style:7});		function(){ return f(qf.X()+sf.X());}], {style:7});
Line 66:		Line 66:

	qg = board.createElement('glider', [0,0,graph], {style:6});		qg = board.createElement('glider', [0,0,graph], {style:6});
	sg = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]~~,{name:' '}~~);		sg = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);
	qg2 = board.createElement('point', [function(){ return qg.X()+sg.X();},		qg2 = board.createElement('point', [function(){ return qg.X()+sg.X();},
	function(){ return g(qg.X()+sg.X());}], {style:7});		function(){ return g(qg.X()+sg.X());}], {style:7});