Difference between revisions of "Secant and tangent"

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Line 1: Line 1:
<html>
+
<jsxgraph box="box" width="600" height="400">
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
+
board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});
<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>
 
<script language="JavaScript">
 
        board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25});
 
 
board.suspendUpdate();
 
board.suspendUpdate();
        // Axes
 
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
 
        b1axisy = board.createElement('axis', [[0,0], [0,1]], {});
 
  
        var p = [];
+
var p = [];
        p[0] = board.createElement('point', [-1,0], {style:4});
+
p[0] = board.create('point', [-1,0], {size:2});
        p[1] = board.createElement('point', [-0.5,1], {style:4});
+
p[1] = board.create('point', [-0.5,1], {size:2});
        p[2] = board.createElement('point', [2,0.5], {style:4});
+
p[2] = board.create('point', [2,0.5], {size:2});
        p[3] = board.createElement('point', [6,5], {style:4});
+
p[3] = board.create('point', [6,5], {size:2});
        var pol = board.lagrangePolynomial(p);
+
var pol = board.lagrangePolynomial(p);
        graph = board.createElement('functiongraph', [pol, -10, 10]);
+
graph = board.create('functiongraph', [pol, -10, 10]);
  
q = board.createElement('glider', [4.5,0,graph], {style:6});
+
q = board.create('glider', [4.5,0,graph], {size:5});
s = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);
+
s = board.create('slider', [[0,-3],[4,-3],[0.001,1,1]]);
q2 = board.createElement('point', [function(){ return q.X()+Math.max(s.Value(),0.01);},
+
q2 = board.create('point', [function(){ return q.X()+Math.max(s.Value(),0.01);},
      function(){ return pol(q.X()+Math.max(s.Value(),0.01));}], {style:7});
+
        function(){ return pol(q.X()+Math.max(s.Value(),0.01));}], {face:'[]',size:2});
e = board.createElement('point', [function(){ return q2.X()-q.X();},
+
e = board.create('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 = board.createElement('line',[q,q2],{strokeColor:'#ff0000',dash:2});
+
line = board.create('line',[q,q2],{strokeColor:'#ff0000',dash:2});
 
board.unsuspendUpdate();
 
board.unsuspendUpdate();
</script>
+
</jsxgraph>
</html>
 
  
<html>
+
<jsxgraph box="box2" width="600" height="400">
<div id="box2" class="jxgbox" style="width:600px; height:400px;"></div>
+
board = JXG.JSXGraph.initBoard('box2', {boundingbox: [-5, 10, 7, -6], axis: true});
<script language="JavaScript">
 
        board = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 50, unitY: 25});
 
 
board.suspendUpdate();
 
board.suspendUpdate();
        // Axes
 
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
 
        b1axisy = board.createElement('axis', [[0,0], [0,1]], {});
 
  
        var f = function(x) { return (Math.abs(x)); };
+
var f = function(x) { return (Math.abs(x)); };
        graph = board.createElement('functiongraph', [f, -10, 10]);
+
graph = board.create('functiongraph', [f, -10, 10]);
  
        qf = board.createElement('glider', [0,0,graph], {style:6});
+
qf = board.create('glider', [0,0,graph], {size:5});
        sf = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);
+
sf = board.create('slider', [[0,-3],[4,-3],[0.001,1,1]]);
        qf2 = board.createElement('point', [function(){ return qf.X()+sf.Value();},
+
qf2 = board.create('point', [function(){ return qf.X()+sf.Value();},
                            function(){ return f(qf.X()+sf.Value());}], {style:7});
+
          function(){ return f(qf.X()+sf.Value());}], {face:'[]',size:2});
        ef = board.createElement('point', [function(){ return qf2.X()-qf.X();},
+
ef = board.create('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());}], {face:'[]',size:2,name:'Sekantensteigung',trace:true});
        line = board.createElement('line',[qf,qf2],{strokeColor:'#ff0000',dash:2});
+
line = board.create('line',[qf,qf2],{strokeColor:'#ff0000',dash:2});
 
board.unsuspendUpdate();
 
board.unsuspendUpdate();
</script>
+
</jsxgraph>
</html>
 
  
<html>
+
<jsxgraph box="box3" width="600" height="400">
<div id="box3" class="jxgbox" style="width:600px; height:400px;"></div>
+
board = JXG.JSXGraph.initBoard('box3', {boundingbox: [-5, 10, 7, -6], axis: true});
<script language="JavaScript">
 
        board = JXG.JSXGraph.initBoard('box3', {originX: 250, originY: 250, unitX: 50, unitY: 25});
 
 
board.suspendUpdate();
 
board.suspendUpdate();
        // Axes
 
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
 
        b1axisy = board.createElement('axis', [[0,0], [0,1]], {});
 
  
        var g = function(x) { return (x<=0)?0:1; };
+
var g = function(x) { return (x<=0)?0:1; };
        graph = board.createElement('functiongraph', [g,-10, 10]);
+
graph = board.create('functiongraph', [g,-10, 10]);
  
        qg = board.createElement('glider', [0,0,graph], {style:6});
+
qg = board.create('glider', [0,0,graph], {size:4});
        sg = board.createElement('slider', [[0,-3],[4,-3],[0.001,1,1]]);
+
sg = board.create('slider', [[0,-3],[4,-3],[0.001,1,1]]);
        qg2 = board.createElement('point', [function(){ return qg.X()+sg.Value();},
+
qg2 = board.create('point', [function(){ return qg.X()+sg.Value();},
                            function(){ return g(qg.X()+sg.Value());}], {style:7});
+
            function(){ return g(qg.X()+sg.Value());}], {face:'[]',size:2});
        eg = board.createElement('point', [function(){ return qg2.X()-qg.X();},
+
eg = board.create('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());}], {face:'[]',size:2,name:'Sekantensteigung',trace:true});
        line = board.createElement('line',[qg,qg2],{strokeColor:'#ff0000',dash:2});
+
line = board.create('line',[qg,qg2],{strokeColor:'#ff0000',dash:2});
 
board.unsuspendUpdate();
 
board.unsuspendUpdate();
</script>
+
</jsxgraph>
</html>
 
  
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Calculus]]
 
[[Category:Calculus]]

Revision as of 15:14, 8 June 2011