Sequences of functions: Difference between revisions

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==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 5: Line 7:
var f = function(x){ return Math.pow(x,n.Value()); }
var f = function(x){ return Math.pow(x,n.Value()); }
var plot = brd.create('functiongraph',[f,0,1], {strokeWidth:2});
var plot = brd.create('functiongraph',[f,0,1], {strokeWidth:2});
brd.createElement('text',[0.2,0.7,function(){return 'f(x)=x<sup>'+Math.floor(n.Value())+'</sup>';}],
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'});
   {fontSize:20});
brd.unsuspendUpdate();
brd.unsuspendUpdate();
</jsxgraph>
</jsxgraph>


<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:20});
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]});
brd2.suspendUpdate();
brd2.suspendUpdate();
var n2 = brd2.create('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n',snapWidth:1});
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 (1-x)*x/n2.Value(); }
var f2 = function(x){ return 4*(1-x)*x/n2.Value(); }
var plot2 = brd2.create('functiongraph',[f2,0,1], {strokeWidth:2});
var plot2 = brd2.create('functiongraph',[f2,0,1], {strokeWidth:2});
brd2.createElement('text',[0.2,0.7,function(){return 'f(x)=(1-x)*x/'+n2.Value().toFixed(0);}],
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'});
   {fontSize:20});
brd2.unsuspendUpdate();
brd2.unsuspendUpdate();
</jsxgraph>
</jsxgraph>


 
<source lang="javascript">
===The underlying JavaScript code===
<source lang="xml">
<jsxgraph width="600" 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(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();
var n2 = brd2.create('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n',snapWidth:1});
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 x*x/n2.Value(); }
var f2 = function(x){ return 4*(1-x)*x/n2.Value(); }
var plot2 = brd2.create('functiongraph',[f2,0,1], {strokeWidth:2});
var plot2 = brd2.create('functiongraph',[f2,0,1], {strokeWidth:2});
brd2.createElement('text',[0.2,0.7,function(){return 'f(x)=x<sup>2</sup>/'+n2.Value().toFixed(0);}],
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'});
   {fontSize:20});
brd2.unsuspendUpdate();
brd2.unsuspendUpdate();
</source>
<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:20});
brd3.unsuspendUpdate();
</jsxgraph>
</jsxgraph>
<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:20});
brd3.unsuspendUpdate();
</source>
</source>


[[Category:Examples]]
[[Category:Examples]]
[[Category:Calculus]]
[[Category:Calculus]]

Revision as of 15:57, 20 February 2013

Pointwise convergence

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:20});
brd.unsuspendUpdate();

Uniform convergence

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:20});
brd2.unsuspendUpdate();

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:20});
brd3.unsuspendUpdate();