Difference between revisions of "Continuous functions"

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<html>
+
<jsxgraph width="600" height="500" box="box">
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
+
  var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-4, 6, 6, -4], axis: true});
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
+
  board.suspendUpdate();
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
+
 
<div id="box" class="jxgbox" style="width:600px; height:200px;"></div>
+
  var f = function(x) {
<script language="JavaScript">
 
  board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25});
 
b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
 
  b1axisy = board.createElement('axis', [[0,0], [0,1]], {});
 
  graph = board.createElement('curve', ['x', #
 
    function(x) {
 
 
       if (x<1) {
 
       if (x<1) {
 
           return 0.5*x*x;
 
           return 0.5*x*x;
Line 15: Line 9:
 
         return x+1;
 
         return x+1;
 
       }
 
       }
       }, 'x'], {curveType:'graph'});
+
       };
 +
var graph = board.create('functiongraph', [f], {strokeColor:'#0000ff'});
 +
 
 +
var s = board.create('slider', [[0,-1],[4,-1],[0,1,1]],{name:'&delta;'});
 +
 
 +
var x1 = board.create('glider', [-2,0,board.defaultAxes.x],{name:'a'});
 +
board.suspendUpdate();
 +
var x2 = board.create('point', [function(){return x1.X()-s.Value();},0],{size:2,face:'[]',name:' '});
 +
var x3 = board.create('point', [function(){return x1.X()+s.Value();},0],{size:2,face:'[]',name:' '});
 +
var y1 = board.create('point', [function(){return x1.X();},function(){return f(x1.X());}],{size:2,face:'[]',name:'f(a)'});
 +
var y2 = board.create('point', [function(){return x2.X();},function(){return f(x2.X());}],{size:2,face:'[]',name:' '});
 +
var y3 = board.create('point', [function(){return x3.X();},function(){return f(x3.X());}],{size:2,face:'[]',name:' '});
 +
var v1 = board.create('segment', [x1,y1],{strokeColor:'gray',dash:2,strokeWidth:1});
 +
var v2 = board.create('line', [x2,y2],{strokeColor:'gray',dash:2,strokeWidth:1});
 +
var v3 = board.create('line', [x3,y3],{strokeColor:'gray',dash:2,strokeWidth:1});
 +
 
 +
var h1 = board.create('curve', [function(t){return t},function(t){return y1.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});
 +
var h2 = board.create('curve', [function(t){return t},function(t){return y2.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});
 +
var h3 = board.create('curve', [function(t){return t},function(t){return y3.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});
  
</script>
+
var txt = board.create('text', [4.2, -1.5, function() {
</html>
+
            return '&epsilon; = ' + Math.max(Math.abs(y2.Y() - y1.Y()), Math.abs(y1.Y() - y3.Y())).toFixed(5);
 +
          }], {strokeColor: 'blue'});
 +
board.unsuspendUpdate();
 +
</jsxgraph>
  
 
=== References ===
 
=== References ===
 +
 +
* [http://en.wikipedia.org/wiki/Continuous_function http://en.wikipedia.org/wiki/Continuous_function]
  
 
=== The underlying JavaScript source code ===
 
=== The underlying JavaScript source code ===
  
 
<source lang="javascript">
 
<source lang="javascript">
 +
var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-4, 6, 6, -4], axis: true});
 +
board.suspendUpdate();
 +
 +
var f = function(x) {
 +
      if (x<1) {
 +
          return 0.5*x*x;
 +
      } else {
 +
        return x+1;
 +
      }
 +
      };
 +
var graph = board.create('functiongraph', [f], {strokeColor:'#0000ff'});
 +
 +
var s = board.create('slider', [[0,-1],[4,-1],[0,1,1]],{name:'&delta;'});
 +
 +
var x1 = board.create('glider', [-2,0,board.defaultAxes.x],{name:'a'});
 +
board.suspendUpdate();
 +
var x2 = board.create('point', [function(){return x1.X()-s.Value();},0],{size:2,face:'[]',name:' '});
 +
var x3 = board.create('point', [function(){return x1.X()+s.Value();},0],{size:2,face:'[]',name:' '});
 +
var y1 = board.create('point', [function(){return x1.X();},function(){return f(x1.X());}],{size:2,face:'[]',name:'f(a)'});
 +
var y2 = board.create('point', [function(){return x2.X();},function(){return f(x2.X());}],{size:2,face:'[]',name:' '});
 +
var y3 = board.create('point', [function(){return x3.X();},function(){return f(x3.X());}],{size:2,face:'[]',name:' '});
 +
var v1 = board.create('segment', [x1,y1],{strokeColor:'gray',dash:2,strokeWidth:1});
 +
var v2 = board.create('line', [x2,y2],{strokeColor:'gray',dash:2,strokeWidth:1});
 +
var v3 = board.create('line', [x3,y3],{strokeColor:'gray',dash:2,strokeWidth:1});
 +
 +
var h1 = board.create('curve', [function(t){return t},function(t){return y1.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});
 +
var h2 = board.create('curve', [function(t){return t},function(t){return y2.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});
 +
var h3 = board.create('curve', [function(t){return t},function(t){return y3.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});
 +
 +
var txt = board.create('text', [4.2, -1.5, function() {
 +
            return '&epsilon; = ' + Math.max(Math.abs(y2.Y() - y1.Y()), Math.abs(y1.Y() - y3.Y())).toFixed(5);
 +
          }], {strokeColor: 'blue'});
 +
board.unsuspendUpdate();
 
</source>
 
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 +
[[Category:Calculus]]

Latest revision as of 20:02, 7 January 2019

References

The underlying JavaScript source code

 var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-4, 6, 6, -4], axis: true});
 board.suspendUpdate();

 var f = function(x) {
       if (x<1) {
          return 0.5*x*x;
       } else {
         return x+1;
       }
      };
 var graph = board.create('functiongraph', [f], {strokeColor:'#0000ff'});

 var s = board.create('slider', [[0,-1],[4,-1],[0,1,1]],{name:'&delta;'});

 var x1 = board.create('glider', [-2,0,board.defaultAxes.x],{name:'a'});
 board.suspendUpdate();
 var x2 = board.create('point', [function(){return x1.X()-s.Value();},0],{size:2,face:'[]',name:' '});
 var x3 = board.create('point', [function(){return x1.X()+s.Value();},0],{size:2,face:'[]',name:' '});
 var y1 = board.create('point', [function(){return x1.X();},function(){return f(x1.X());}],{size:2,face:'[]',name:'f(a)'});
 var y2 = board.create('point', [function(){return x2.X();},function(){return f(x2.X());}],{size:2,face:'[]',name:' '});
 var y3 = board.create('point', [function(){return x3.X();},function(){return f(x3.X());}],{size:2,face:'[]',name:' '});
 var v1 = board.create('segment', [x1,y1],{strokeColor:'gray',dash:2,strokeWidth:1});
 var v2 = board.create('line', [x2,y2],{strokeColor:'gray',dash:2,strokeWidth:1});
 var v3 = board.create('line', [x3,y3],{strokeColor:'gray',dash:2,strokeWidth:1});

 var h1 = board.create('curve', [function(t){return t},function(t){return y1.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});
 var h2 = board.create('curve', [function(t){return t},function(t){return y2.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});
 var h3 = board.create('curve', [function(t){return t},function(t){return y3.Y();}], {strokeColor:'gray',dash:2,strokeWidth:1});

 var txt = board.create('text', [4.2, -1.5, function() {
            return '&epsilon; = ' + Math.max(Math.abs(y2.Y() - y1.Y()), Math.abs(y1.Y() - y3.Y())).toFixed(5); 
           }], {strokeColor: 'blue'});
 board.unsuspendUpdate();