1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
|
<html>
<head>
<title>JSXGraph example</title>
<link rel="stylesheet" type="text/css" href="../distrib/jsxgraph.css" />
<script type="text/javascript" src="/javascript/prototype/prototype.js"></script>
<script type="text/javascript" src="../distrib/jsxgraphcore.js"></script>
</head>
<body>
<h2>Power Series for Sine</h2>
<div id="jxgbox1" class="jxgbox" style="width:600px; height:300px;"></div>
<br clear=all>
<div id="debug" style="display:block;"></div>
<script language="JavaScript">
// Board
board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 200, originY: 150, unitX: 5, unitY: 5});
board1.suspendUpdate();
// Axes and Properties
board1.createElement('axis', [[0,0], [1,0]], {});
board1.createElement('axis', [[0,0], [0,1]], {});
board1.snapToGrid = true;
//
board1.createElement('functiongraph', [function(t){ return Math.sin(t); }, -10, 10],{strokeColor: "#cccccc"});
var s = board1.createElement('slider', [[2,-4],[7,-4],[0,1,10]], {name:'S',snapWidth:1});
board1.createElement('curve', [
function(t){ return t; },
function(t) {
var val = 0;
for(var i = 0; i < s.Value() + 1; i++) {
var f = JXG.Math.factorial(2*i+1); // sin
val += Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / f;
}
return val;
},
-10, 10], {strokeColor: "#bb0000"});
board1.unsuspendUpdate();
</script>
<h2>Power Series for Cosine</h2>
<div id="jxgbox2" class="jxgbox" style="width:600px; height:300px;"></div>
<script language="JavaScript">
// Board
board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 25, unitY: 25});
board2.suspendUpdate();
// Axes and Properties
board2.createElement('axis', [[0,0], [1,0]], {});
board2.createElement('axis', [[0,0], [0,1]], {});
board2.snapToGrid = true;
//
board2.createElement('functiongraph', [function(t){ return Math.cos(t); }, -10, 10],{strokeColor: "#cccccc"});
var s2 = board2.createElement('slider', [[2,-4],[7,-4],[0,0,10]], {name:'S2',snapWidth:1});
board2.createElement('curve', [
function(t){ return t; },
function(t) {
var val = 0;
for(var i = 0; i < s2.Value() + 1; i++) {
//var f = 1;
//var n = 1;
//while (n <= 2 * i) { f = f * n++; }
var f = JXG.Math.factorial(2*i);
val += Math.pow(-1, i) * Math.pow(t, 2 * i) / f;
}
return val;
},
-10, 10],{strokeColor: "#009900"});
board2.unsuspendUpdate();
</script>
<h2>Binomial theorem</h2>
<div id="jxgbox3" class="jxgbox" style="width:600px; height:300px;"></div>
<script language="JavaScript">
board3 = JXG.JSXGraph.initBoard('jxgbox3', {originX: 300, originY: 150, unitX: 25, unitY: 25, axis:true, grid:true});
board3.suspendUpdate();
board3.snapToGrid = true;
//
var s3 = board3.createElement('slider', [[2,-4],[7,-4],[0,0,10]], {name:'S3',snapWidth:1});
board3.createElement('functiongraph', [function(t){ return Math.pow(1+t,s3.Value()); }, -10, 10],{strokeColor: "#cccccc"});
board3.createElement('functiongraph', [
function(x) {
var val = 0;
var n = Math.round(s3.Value());
var z = 1;
for(var k=0; k<=n; k++) {
var f = JXG.Math.binomial(n,k);
val += z*f;
z *= x;
}
return val;
},
-3, 3],{strokeColor: "#009900"});
board3.unsuspendUpdate();
</script>
</body>
</html>
|
