Difference between revisions of "Continuous function II"

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<html>
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<jsxgraph width="600" height="500" box="box">
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<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
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  var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-1, 10, 2, -2], axis: true});
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<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
 
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<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 
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<div id="box" class="jxgbox" style="width:600px; height:500px;"></div>
 
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<script language="JavaScript">
 
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  board = JXG.JSXGraph.initBoard('box', {originX: 50, originY: 400, unitX: 50, unitY: 50});
 
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board.suspendUpdate();
 
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b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
 
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b1axisy = board.createElement('axis', [[0,0], [0,1]], {});
 
  
 
  var f = function(x) { return 1.0/x; };
 
  var f = function(x) { return 1.0/x; };
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  graph = board.createElement('functiongraph', [f,0.00001, 15], {strokeColor:'#00ff00'});
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  var graph = board.create('functiongraph', [f,0.00001, 15], {strokeColor:'#0000ff'});
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var s = board.create('slider', [[0,-1],[1.5,-1],[0,1,1]],{name:'&epsilon;'});
  
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  s = board.createElement('slider', [[0,-1],[4,-1],[0,1,1]],{name:'&epsilon;'});
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  var x1 = board.create('glider', [1/2, 0, board.defaultAxes.x],{name:'a'});
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board.suspendUpdate();
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var y1 = board.create('point', [0,function(){return f(x1.X());}],{size:2,face:'[]',name:'f(a)'});
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var y2 = board.create('point', [0,function(){return f(x1.X())-s.Value();}],{size:2,face:'[]',name:' '});
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var y3 = board.create('point', [0,function(){return f(x1.X())+s.Value();}],{size:2,face:'[]',name:' '});
  
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  y1 = board.createElement('glider', [0,3,b1axisy],{name:'f(a)'});
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  var z1 = board.create('point', [function(){return f(y1.Y());},function(){return y1.Y();}],{size:2,face:'[]',name:' '});
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  y2 = board.createElement('point', [0,function(){return y1.Y()-s.Value();}],{style:7,name:' '});
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  var z2 = board.create('point', [function(){return f(y2.Y());},function(){return y2.Y();}],{size:2,face:'[]',name:' '});
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  y3 = board.createElement('point', [0,function(){return y1.Y()+s.Value();}],{style:7,name:' '});
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  var z3 = board.create('point', [function(){return f(y3.Y());},function(){return y3.Y();}],{size:2,face:'[]',name:' '});
  
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  z1 = board.createElement('point', [function(){return f(y1.Y());},function(){return y1.Y();}],{style:7,name:'f(a)'});
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  var v1 = board.create('segment', [z1,y1],{strokeColor:'gray',dash:2,strokeWidth:1});
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  z2 = board.createElement('point', [function(){return f(y2.Y());},function(){return y2.Y();}],{style:7,name:' '});
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  var v2 = board.create('line', [z2,y2],{strokeColor:'gray',dash:2,strokeWidth:1});
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  z3 = board.createElement('point', [function(){return f(y3.Y());},function(){return y3.Y();}],{style:7,name:' '});
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  var v3 = board.create('line', [z3,y3],{strokeColor:'gray',dash:2,strokeWidth:1});
  
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  v1 = board.createElement('line', [z1,y1],{strokeColor:'gray',dash:2,strokeWidth:1,straightFirst:false,straightLast:false});
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  var h1 = board.create('curve', [function(t){return z1.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});
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  v2 = board.createElement('line', [z2,y2],{strokeColor:'gray',dash:2,strokeWidth:1});
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  var h2 = board.create('curve', [function(t){return z2.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});
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  v3 = board.createElement('line', [z3,y3],{strokeColor:'gray',dash:2,strokeWidth:1});
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  var h3 = board.create('curve', [function(t){return z3.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});
  
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  h1 = board.createElement('curve', [function(t){return z1.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});
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  var txt = board.create('text', [1.2, 4.3, function() {  
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h2 = board.createElement('curve', [function(t){return z2.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});
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            return '&delta; = ' + Math.min(z1.X() - z3.X(), z2.X() - z1.X()).toFixed(5); }]);
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h3 = board.createElement('curve', [function(t){return z3.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});
 
 
  board.unsuspendUpdate();
 
  board.unsuspendUpdate();
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</jsxgraph>
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</script>
 
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</html>
 
  
 
=== References ===
 
=== References ===
  
 
* [http://en.wikipedia.org/wiki/Continuous_function http://en.wikipedia.org/wiki/Continuous_function]
 
* [http://en.wikipedia.org/wiki/Continuous_function http://en.wikipedia.org/wiki/Continuous_function]
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=== The underlying JavaScript code ===
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 +
<source lang="javascript">
 +
var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-1, 10, 2, -2], axis: true});
 +
 +
var f = function(x) { return 1.0/x; };
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var graph = board.create('functiongraph', [f,0.00001, 15], {strokeColor:'#0000ff'});
 +
 +
var s = board.create('slider', [[0,-1],[1.5,-1],[0,1,1]],{name:'&epsilon;'});
 +
 +
var x1 = board.create('glider', [1/2, 0, board.defaultAxes.x],{name:'a'});
 +
board.suspendUpdate();
 +
var y1 = board.create('point', [0,function(){return f(x1.X());}],{size:2,face:'[]',name:'f(a)'});
 +
var y2 = board.create('point', [0,function(){return f(x1.X())-s.Value();}],{size:2,face:'[]',name:' '});
 +
var y3 = board.create('point', [0,function(){return f(x1.X())+s.Value();}],{size:2,face:'[]',name:' '});
 +
 +
var z1 = board.create('point', [function(){return f(y1.Y());},function(){return y1.Y();}],{size:2,face:'[]',name:' '});
 +
var z2 = board.create('point', [function(){return f(y2.Y());},function(){return y2.Y();}],{size:2,face:'[]',name:' '});
 +
var z3 = board.create('point', [function(){return f(y3.Y());},function(){return y3.Y();}],{size:2,face:'[]',name:' '});
 +
 +
var v1 = board.create('segment', [z1,y1],{strokeColor:'gray',dash:2,strokeWidth:1});
 +
var v2 = board.create('line', [z2,y2],{strokeColor:'gray',dash:2,strokeWidth:1});
 +
var v3 = board.create('line', [z3,y3],{strokeColor:'gray',dash:2,strokeWidth:1});
 +
 +
var h1 = board.create('curve', [function(t){return z1.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});
 +
var h2 = board.create('curve', [function(t){return z2.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});
 +
var h3 = board.create('curve', [function(t){return z3.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});
 +
 +
var txt = board.create('text', [1.2, 4.3, function() {
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            return '&delta; = ' + Math.min(z1.X() - z3.X(), z2.X() - z1.X()).toFixed(5); }]);
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board.unsuspendUpdate();
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</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Calculus]]
 
[[Category:Calculus]]

Latest revision as of 19:23, 7 January 2019

References

The underlying JavaScript code

 var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-1, 10, 2, -2], axis: true});

 var f = function(x) { return 1.0/x; };
 var graph = board.create('functiongraph', [f,0.00001, 15], {strokeColor:'#0000ff'});

 var s = board.create('slider', [[0,-1],[1.5,-1],[0,1,1]],{name:'&epsilon;'});

 var x1 = board.create('glider', [1/2, 0, board.defaultAxes.x],{name:'a'});
 board.suspendUpdate();
 var y1 = board.create('point', [0,function(){return f(x1.X());}],{size:2,face:'[]',name:'f(a)'});
 var y2 = board.create('point', [0,function(){return f(x1.X())-s.Value();}],{size:2,face:'[]',name:' '});
 var y3 = board.create('point', [0,function(){return f(x1.X())+s.Value();}],{size:2,face:'[]',name:' '});

 var z1 = board.create('point', [function(){return f(y1.Y());},function(){return y1.Y();}],{size:2,face:'[]',name:' '});
 var z2 = board.create('point', [function(){return f(y2.Y());},function(){return y2.Y();}],{size:2,face:'[]',name:' '});
 var z3 = board.create('point', [function(){return f(y3.Y());},function(){return y3.Y();}],{size:2,face:'[]',name:' '});

 var v1 = board.create('segment', [z1,y1],{strokeColor:'gray',dash:2,strokeWidth:1});
 var v2 = board.create('line', [z2,y2],{strokeColor:'gray',dash:2,strokeWidth:1});
 var v3 = board.create('line', [z3,y3],{strokeColor:'gray',dash:2,strokeWidth:1});

 var h1 = board.create('curve', [function(t){return z1.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});
 var h2 = board.create('curve', [function(t){return z2.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});
 var h3 = board.create('curve', [function(t){return z3.X();},function(t){return t},0,20], {strokeColor:'gray',dash:2,strokeWidth:1});

 var txt = board.create('text', [1.2, 4.3, function() { 
            return '&delta; = ' + Math.min(z1.X() - z3.X(), z2.X() - z1.X()).toFixed(5); }]);
 board.unsuspendUpdate();
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