Difference between revisions of "Sequences of functions"

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Line 1: Line 1:
====Pointwise convergence====
+
==Pointwise convergence==
 +
 
 
<jsxgraph width="650" height="400" box="box">
 
<jsxgraph width="650" height="400" box="box">
 
var brd = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
 
var brd = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
Line 11: Line 12:
 
</jsxgraph>
 
</jsxgraph>
  
====Uniform convergence====
+
===The underlying JavaScript code===
 +
<source lang="javascript">
 +
var brd = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
 +
brd.suspendUpdate();
 +
var n = brd.create('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n',snapWidth:1});
 +
var f = function(x){ return Math.pow(x,n.Value()); }
 +
var plot = brd.create('functiongraph',[f,0,1], {strokeWidth:2});
 +
brd.createElement('text',[0.2,0.7,function(){return 'f<sub>'+Math.floor(n.Value())+'</sub>(x)=x<sup>'+Math.floor(n.Value())+'</sup>';}],
 +
  {fontSize:'20px'});
 +
brd.unsuspendUpdate();
 +
</source>
 +
 
 +
==Uniform convergence==
 
<jsxgraph width="650" height="400" box="box2">
 
<jsxgraph width="650" height="400" box="box2">
 
var brd2 = JXG.JSXGraph.initBoard('box2', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
 
var brd2 = JXG.JSXGraph.initBoard('box2', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
Line 21: Line 34:
 
   {fontSize:'20px'});
 
   {fontSize:'20px'});
 
brd2.unsuspendUpdate();
 
brd2.unsuspendUpdate();
</jsxgraph>
 
 
<jsxgraph width="650" height="400" box="box3">
 
var brd3 = JXG.JSXGraph.initBoard('box3', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
 
brd3.suspendUpdate();
 
var n3 = brd3.create('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n',snapWidth:1});
 
var f3 = function(x){ return x*x+x/n3.Value(); }
 
var plot3 = brd3.create('functiongraph',[f3,0,1], {strokeWidth:2});
 
brd3.createElement('text',[0.2,0.7,function(){return 'f<sub>'+Math.floor(n3.Value())+'</sub>(x)=x<sup>2</sup>+x/'+n3.Value().toFixed(0);}],
 
  {fontSize:'20px'});
 
brd3.unsuspendUpdate();
 
 
</jsxgraph>
 
</jsxgraph>
  
 
===The underlying JavaScript code===
 
===The underlying JavaScript code===
<source lang="xml">
+
<source lang="javascript">
<jsxgraph width="650" height="400" box="box">
 
var brd = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
 
brd.suspendUpdate();
 
var n = brd.create('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n',snapWidth:1});
 
var f = function(x){ return Math.pow(x,n.Value()); }
 
var plot = brd.create('functiongraph',[f,0,1], {strokeWidth:2});
 
brd.createElement('text',[0.2,0.7,function(){return 'f<sub>'+Math.floor(n.Value())+'</sub>(x)=x<sup>'+Math.floor(n.Value())+'</sup>';}],
 
  {fontSize:'20px'});
 
brd.unsuspendUpdate();
 
</jsxgraph>
 
 
 
<jsxgraph width="650" height="400" box="box2">
 
 
var brd2 = JXG.JSXGraph.initBoard('box2', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
 
var brd2 = JXG.JSXGraph.initBoard('box2', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
 
brd2.suspendUpdate();
 
brd2.suspendUpdate();
Line 56: Line 46:
 
   {fontSize:'20px'});
 
   {fontSize:'20px'});
 
brd2.unsuspendUpdate();
 
brd2.unsuspendUpdate();
</jsxgraph>
+
</source>
  
 
<jsxgraph width="650" height="400" box="box3">
 
<jsxgraph width="650" height="400" box="box3">
Line 69: Line 59:
 
</jsxgraph>
 
</jsxgraph>
  
 +
===The underlying JavaScript code===
 +
<source lang="javascript">
 +
var brd3 = JXG.JSXGraph.initBoard('box3', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
 +
brd3.suspendUpdate();
 +
var n3 = brd3.create('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n',snapWidth:1});
 +
var f3 = function(x){ return x*x+x/n3.Value(); }
 +
var plot3 = brd3.create('functiongraph',[f3,0,1], {strokeWidth:2});
 +
brd3.createElement('text',[0.2,0.7,function(){return 'f<sub>'+Math.floor(n3.Value())+'</sub>(x)=x<sup>2</sup>+x/'+n3.Value().toFixed(0);}],
 +
  {fontSize:'20px'});
 +
brd3.unsuspendUpdate();
 
</source>
 
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Calculus]]
 
[[Category:Calculus]]

Revision as of 15:32, 8 June 2011

Pointwise convergence

The underlying JavaScript code

var brd = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
brd.suspendUpdate();
var n = brd.create('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n',snapWidth:1});
var f = function(x){ return Math.pow(x,n.Value()); }
var plot = brd.create('functiongraph',[f,0,1], {strokeWidth:2});
brd.createElement('text',[0.2,0.7,function(){return 'f<sub>'+Math.floor(n.Value())+'</sub>(x)=x<sup>'+Math.floor(n.Value())+'</sup>';}],
  {fontSize:'20px'});
brd.unsuspendUpdate();

Uniform convergence

The underlying JavaScript code

var brd2 = JXG.JSXGraph.initBoard('box2', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
brd2.suspendUpdate();
var n2 = brd2.create('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n',snapWidth:1});
var f2 = function(x){ return 4*(1-x)*x/n2.Value(); }
var plot2 = brd2.create('functiongraph',[f2,0,1], {strokeWidth:2});
brd2.createElement('text',[0.2,0.7,function(){return 'f<sub>'+Math.floor(n2.Value())+'</sub>(x)=4*(1-x)*x/'+n2.Value().toFixed(0);}],
  {fontSize:'20px'});
brd2.unsuspendUpdate();

The underlying JavaScript code

var brd3 = JXG.JSXGraph.initBoard('box3', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
brd3.suspendUpdate();
var n3 = brd3.create('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n',snapWidth:1});
var f3 = function(x){ return x*x+x/n3.Value(); }
var plot3 = brd3.create('functiongraph',[f3,0,1], {strokeWidth:2});
brd3.createElement('text',[0.2,0.7,function(){return 'f<sub>'+Math.floor(n3.Value())+'</sub>(x)=x<sup>2</sup>+x/'+n3.Value().toFixed(0);}],
  {fontSize:'20px'});
brd3.unsuspendUpdate();