Sequences of functions: Difference between revisions

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<jsxgraph width="600" height="450" box="box">
==Pointwise convergence==
var brd = JXG.JSXGraph.initBoard('box', {axis:true, originX: 100, originY: 340, unitX: 400, unitY: 200});
 
var n = brd.createElement('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n'});
<jsxgraph width="650" height="400" box="box">
var f = function(x){ return Math.pow(x,Math.floor(n.Value())); }
var brd = JXG.JSXGraph.initBoard('box', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
var plot = brd.createElement('functiongraph',[f,0,1], {strokeWidth:1});
brd.suspendUpdate();
brd.createElement('text',[0.2,0.7,function(){return 'f(x)=x<sup>'+Math.floor(n.Value())+'</sup>';}],
var n = brd.create('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n',snapWidth:1});
   {fontSize:'20px'});
var f = function(x){ return Math.pow(x,n.Value()); }
var plot = brd.create('functiongraph',[f,0,1], {strokeWidth:2});
brd.create('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();
</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.create('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">
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.create('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();
</jsxgraph>
</jsxgraph>


===The underlying JavaScript code===
<source lang="javascript">
<source lang="xml">
var brd2 = JXG.JSXGraph.initBoard('box2', {axis:true, boundingbox:[-0.25,1.7,1.25,-0.5]});
<jsxgraph width="600" height="400" box="box">
brd2.suspendUpdate();
var brd = JXG.JSXGraph.initBoard('box', {axis:true, originX: 100, originY: 340, unitX: 400, unitY: 200});
var n2 = brd2.create('slider',[[0.1,1.5],[1.1,1.5],[1,1,100]],{name:'n',snapWidth:1});
var n = brd.createElement('slider',[[0.1,1.5],[0.9,1.5],[1,1,100]],{name:'n'});
var f2 = function(x){ return 4*(1-x)*x/n2.Value(); }
var f = function(x){ return Math.pow(x,Math.floor(n.Value())); }
var plot2 = brd2.create('functiongraph',[f2,0,1], {strokeWidth:2});
var plot = brd.createElement('functiongraph',[f,0,1], {strokeWidth:1});
brd2.create('text',[0.2,0.7,function(){return 'f<sub>'+Math.floor(n2.Value())+'</sub>(x)=4*(1-x)*x/'+n2.Value().toFixed(0);}],
brd.createElement('text',[0.2,0.7,function(){return 'f(x)=x<sup>'+Math.floor(n.Value())+'</sup>';}],
  {fontSize:20});
   {fontSize:'20px'});
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.create('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.create('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]]

Latest revision as of 13:23, 3 March 2021

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.create('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.create('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.create('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();