Differentiability - Revision history

A WASSERMANN at 19:38, 22 January 2019

2019-01-22T19:38:52Z

← Older revision		Revision as of 19:38, 22 January 2019
Line 60:		Line 60:

	var x0 = board.create('glider', [1, 0, board.defaultAxes.x], {name: 'x_0', size:4});		var x0 = board.create('glider', [1, 0, board.defaultAxes.x], {name: 'x_0', size:4});
	var fx0 = board.create('point', [function() { return x0.X(); }, function() { return pol(x0.X()); }], {name: '', color: 'grey', fixed: true, size:3});		var fx0 = board.create('point', [
			function() { return x0.X(); },
			function() { return pol(x0.X()); }
			], {name: '', color: 'grey', fixed: true, size:3});
	var x = board.create('glider', [5, 0, board.defaultAxes.x], {name: 'x', size:4});		var x = board.create('glider', [5, 0, board.defaultAxes.x], {name: 'x', size:4});
	var fx = board.create('point', [function() { return x.X(); }, function() { return pol(x.X()); }], {name: '', color: 'grey', fixed: true, size:3});		var fx = board.create('point', [
			function() { return x.X(); },
			function() { return pol(x.X()); }
			], {name: '', color: 'grey', fixed: true, size:3});
	var line = board.create('line',[fx0, fx],{strokeColor:'#ff0000',dash:2});		var line = board.create('line',[fx0, fx],{strokeColor:'#ff0000',dash:2});

2019-01-22T19:36:47Z

@@ Line 5: / Line 5: @@
 :<math> f(x) = f(x_0) + (x-x_0) f_1(x) \,.</math>
+Drag the point <math>x</math> to draw the function <math>f_1</math>.
 <jsxgraph box="box" width="600" height="400">
 board = JXG.JSXGraph.initBoard('box', {
@@ Line 45: / Line 45: @@
 ===The underlying JavaScript code===
 <source lang="javascript">
 </source>
 [[Category:Examples]]
 [[Category:Calculus]]

2019-01-22T19:35:14Z

← Older revision		Revision as of 19:35, 22 January 2019
Line 3:		Line 3:
	<math>f_1: D \to {\mathbb R}</math> that is continuous in <math>x_0</math> such that		<math>f_1: D \to {\mathbb R}</math> that is continuous in <math>x_0</math> such that

	:<math> f(x) = f(x_0) + (x-x_0) f_1(x) </math>		:<math> f(x) = f(x_0) + (x-x_0) f_1(x) \,.</math>


Line 32:		Line 32:
	{ size: 1, name: 'f_1', color: 'black', fixed: true, trace: true});		{ size: 1, name: 'f_1', color: 'black', fixed: true, trace: true});

	var txt = board.create('text', [2, 7, function() {		var txt = board.create('text', [0.5, 7, function() {
	return '( ' +		return '( ' +
	fx.Y().toFixed(2) + ' - (' + fx0.Y().toFixed(2) +		fx.Y().toFixed(2) + ' - (' + fx0.Y().toFixed(2) +
	') ) / (' +		') ) / ( ' +
	fx.X().toFixed(2) + ' - (' + fx0.X().toFixed(2) +		fx.X().toFixed(2) + ' - (' + fx0.X().toFixed(2) +
	') ) = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3);		') ) = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3);

2019-01-22T19:34:36Z

← Older revision		Revision as of 19:34, 22 January 2019
Line 33:		Line 33:

	var txt = board.create('text', [2, 7, function() {		var txt = board.create('text', [2, 7, function() {
	return '(' +		return '( ' +
	fx.Y().toFixed(2) + '-(' + fx0.Y().toFixed(2) +		fx.Y().toFixed(2) + ' - (' + fx0.Y().toFixed(2) +
	'))(' +		') ) / (' +
	fx.X().toFixed(2) + '-(' + fx0.X().toFixed(2) +		fx.X().toFixed(2) + ' - (' + fx0.X().toFixed(2) +
	')) = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3);		') ) = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3);
	}]);		}]);

2019-01-22T19:33:34Z

← Older revision		Revision as of 19:33, 22 January 2019
Line 7:		Line 7:

	<jsxgraph box="box" width="600" height="400">		<jsxgraph box="box" width="600" height="400">
	~~//JXG.Options.text.useMathJax = true;~~
	board = JXG.JSXGraph.initBoard('box', {		board = JXG.JSXGraph.initBoard('box', {
	boundingbox: [-5, 10, 7, -6],		boundingbox: [-5, 10, 7, -6],
Line 34:		Line 33:

	var txt = board.create('text', [2, 7, function() {		var txt = board.create('text', [2, 7, function() {
	return '~~:<math>\\frac{~~' +		return '(' +
	fx.Y().toFixed(2) + '-(' + fx0.Y().toFixed(2) +		fx.Y().toFixed(2) + '-(' + fx0.Y().toFixed(2) +
	')}{' +		'))(' +
	fx.X().toFixed(2) + '-(' + fx0.X().toFixed(2) +		fx.X().toFixed(2) + '-(' + fx0.X().toFixed(2) +
	')} = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3) ~~+ '</math>'~~;		')) = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3);
	}]);		}]);

2019-01-22T19:32:03Z

← Older revision		Revision as of 19:32, 22 January 2019
Line 34:		Line 34:

	var txt = board.create('text', [2, 7, function() {		var txt = board.create('text', [2, 7, function() {
	return '<math>~~\\[~~ \\frac{' +		return ':<math>\\frac{' +
	fx.Y().toFixed(2) + '-(' + fx0.Y().toFixed(2) +		fx.Y().toFixed(2) + '-(' + fx0.Y().toFixed(2) +
	')}{' +		')}{' +
	fx.X().toFixed(2) + '-(' + fx0.X().toFixed(2) +		fx.X().toFixed(2) + '-(' + fx0.X().toFixed(2) +
	')} = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3) + '~~\\]~~</math>';		')} = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3) + '</math>';
	}]);		}]);

2019-01-22T19:31:14Z

← Older revision		Revision as of 19:31, 22 January 2019
Line 7:		Line 7:

	<jsxgraph box="box" width="600" height="400">		<jsxgraph box="box" width="600" height="400">
	JXG.Options.text.useMathJax = true;		//JXG.Options.text.useMathJax = true;
	board = JXG.JSXGraph.initBoard('box', {		board = JXG.JSXGraph.initBoard('box', {
	boundingbox: [-5, 10, 7, -6],		boundingbox: [-5, 10, 7, -6],
Line 34:		Line 34:

	var txt = board.create('text', [2, 7, function() {		var txt = board.create('text', [2, 7, function() {
	return '\\[ \\frac{' +		return '<math>\\[ \\frac{' +
	fx.Y().toFixed(2) + '-(' + fx0.Y().toFixed(2) +		fx.Y().toFixed(2) + '-(' + fx0.Y().toFixed(2) +
	')}{' +		')}{' +
	fx.X().toFixed(2) + '-(' + fx0.X().toFixed(2) +		fx.X().toFixed(2) + '-(' + fx0.X().toFixed(2) +
	')} = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3) + '\\]';		')} = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3) + '\\]</math>';
	}]);		}]);

2019-01-22T19:28:25Z

← Older revision		Revision as of 19:28, 22 January 2019
Line 1:		Line 1:

	If the function <math>f: D \to R</math> is differentiable in <math>x_0\in D</math> then there is a function		If the function <math>f: D \to {\mathbb R}</math> is differentiable in <math>x_0\in D</math> then there is a function
	<math>f_1: D \to R</math> that is continuous in <math>x_0</math> such that		<math>f_1: D \to {\mathbb R}</math> that is continuous in <math>x_0</math> such that

	:<math> f(x) = f(x_0) + (x-x_0) f_1(x) </math>		:<math> f(x) = f(x_0) + (x-x_0) f_1(x) </math>

2019-01-22T19:26:40Z

← Older revision		Revision as of 19:26, 22 January 2019
Line 1:		Line 1:
	~~<html>~~
	~~<script type="text/javascript" src="/distrib/MathJax/MathJax.js"></script>~~
	~~</html>~~

	If the function <math>f: D \to R</math> is differentiable in <math>x_0\in D</math> then there is a function		If the function <math>f: D \to R</math> is differentiable in <math>x_0\in D</math> then there is a function

2019-01-22T19:26:18Z

← Older revision		Revision as of 19:26, 22 January 2019
Line 1:		Line 1:
			<html>
			<script type="text/javascript" src="/distrib/MathJax/MathJax.js"></script>
			</html>

	If the function <math>f: D \to R</math> is differentiable in <math>x_0\in D</math> then there is a function		If the function <math>f: D \to R</math> is differentiable in <math>x_0\in D</math> then there is a function
	<math>f_1: D \to R</math> that is continuous in <math>x_0</math> such that		<math>f_1: D \to R</math> that is continuous in <math>x_0</math> such that
Line 4:		Line 8:
	:<math> f(x) = f(x_0) + (x-x_0) f_1(x) </math>		:<math> f(x) = f(x_0) + (x-x_0) f_1(x) </math>

	~~<html>~~
	~~<script type="text/javascript" src="/distrib/MathJax/MathJax.js"></script>~~
	~~</html>~~
	<jsxgraph box="box" width="600" height="400">		<jsxgraph box="box" width="600" height="400">
	JXG.Options.text.useMathJax = true;		JXG.Options.text.useMathJax = true;