Difference between revisions of "Extended mean value theorem"
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Jump to navigationJump to searchA WASSERMANN (talk | contribs) |
A WASSERMANN (talk | contribs) |
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Line 3: | Line 3: | ||
var p = []; | var p = []; | ||
− | |||
p[0] = board.create('point', [-2,-2], {size:2}); | p[0] = board.create('point', [-2,-2], {size:2}); | ||
p[1] = board.create('point', [-1.5, 5], {size:2}); | p[1] = board.create('point', [-1.5, 5], {size:2}); | ||
Line 19: | Line 18: | ||
var dg = JXG.Math.Numerics.D(fg[1]); | var dg = JXG.Math.Numerics.D(fg[1]); | ||
+ | // Usually, the extended mean value theorem is formulated as | ||
+ | // df(t) / dg(t) == (p[3].X() - p[0].X()) / (p[3].Y() - p[0].Y()) | ||
+ | // We can avoid division by zero with that formulation: | ||
var quot = function(t) { | var quot = function(t) { | ||
− | |||
return df(t) * (p[3].Y() - p[0].Y()) - dg(t) * (p[3].X() - p[0].X()); | return df(t) * (p[3].Y() - p[0].Y()) - dg(t) * (p[3].X() - p[0].X()); | ||
}; | }; | ||
− | |||
− | |||
var r = board.create('glider', [ | var r = board.create('glider', [ | ||
− | + | function() { return fg[0](JXG.Math.Numerics.root(quot, (fg[3]() + fg[2]) * 0.5)); }, | |
− | + | function() { return fg[1](JXG.Math.Numerics.root(quot, (fg[3]() + fg[2]) * 0.5)); }, | |
− | + | graph], {name: '', size: 4, fixed:true, color: 'blue'}); | |
board.create('tangent', [r], {strokeColor:'#ff0000'}); | board.create('tangent', [r], {strokeColor:'#ff0000'}); | ||
− | |||
</jsxgraph> | </jsxgraph> | ||
===The underlying JavaScript code=== | ===The underlying JavaScript code=== | ||
<source lang="javascript"> | <source lang="javascript"> | ||
+ | var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis:true}); | ||
+ | var p = []; | ||
+ | |||
+ | p[0] = board.create('point', [-2,-2], {size:2}); | ||
+ | p[1] = board.create('point', [-1.5, 5], {size:2}); | ||
+ | p[2] = board.create('point', [1,4], {size:2}); | ||
+ | p[3] = board.create('point', [3,-1], {size:2}); | ||
+ | |||
+ | // Curve | ||
+ | var fg = JXG.Math.Numerics.Neville(p); | ||
+ | var graph = board.create('curve', fg, {strokeWidth:3, strokeOpacity:0.5}); | ||
+ | |||
+ | // Secant | ||
+ | line = board.create('line', [p[0], p[3]], {strokeColor:'#ff0000', dash:1}); | ||
+ | |||
+ | var df = JXG.Math.Numerics.D(fg[0]); | ||
+ | var dg = JXG.Math.Numerics.D(fg[1]); | ||
+ | |||
+ | // Usually, the extended mean value theorem is formulated as | ||
+ | // df(t) / dg(t) == (p[3].X() - p[0].X()) / (p[3].Y() - p[0].Y()) | ||
+ | // We can avoid division by zero with that formulation: | ||
+ | var quot = function(t) { | ||
+ | return df(t) * (p[3].Y() - p[0].Y()) - dg(t) * (p[3].X() - p[0].X()); | ||
+ | }; | ||
+ | |||
+ | var r = board.create('glider', [ | ||
+ | function() { return fg[0](JXG.Math.Numerics.root(quot, (fg[3]() + fg[2]) * 0.5)); }, | ||
+ | function() { return fg[1](JXG.Math.Numerics.root(quot, (fg[3]() + fg[2]) * 0.5)); }, | ||
+ | graph], {name: '', size: 4, fixed:true, color: 'blue'}); | ||
+ | |||
+ | board.create('tangent', [r], {strokeColor:'#ff0000'}); | ||
</source> | </source> | ||
[[Category:Examples]] | [[Category:Examples]] | ||
[[Category:Calculus]] | [[Category:Calculus]] |
Revision as of 18:10, 29 January 2019
The underlying JavaScript code
var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis:true});
var p = [];
p[0] = board.create('point', [-2,-2], {size:2});
p[1] = board.create('point', [-1.5, 5], {size:2});
p[2] = board.create('point', [1,4], {size:2});
p[3] = board.create('point', [3,-1], {size:2});
// Curve
var fg = JXG.Math.Numerics.Neville(p);
var graph = board.create('curve', fg, {strokeWidth:3, strokeOpacity:0.5});
// Secant
line = board.create('line', [p[0], p[3]], {strokeColor:'#ff0000', dash:1});
var df = JXG.Math.Numerics.D(fg[0]);
var dg = JXG.Math.Numerics.D(fg[1]);
// Usually, the extended mean value theorem is formulated as
// df(t) / dg(t) == (p[3].X() - p[0].X()) / (p[3].Y() - p[0].Y())
// We can avoid division by zero with that formulation:
var quot = function(t) {
return df(t) * (p[3].Y() - p[0].Y()) - dg(t) * (p[3].X() - p[0].X());
};
var r = board.create('glider', [
function() { return fg[0](JXG.Math.Numerics.root(quot, (fg[3]() + fg[2]) * 0.5)); },
function() { return fg[1](JXG.Math.Numerics.root(quot, (fg[3]() + fg[2]) * 0.5)); },
graph], {name: '', size: 4, fixed:true, color: 'blue'});
board.create('tangent', [r], {strokeColor:'#ff0000'});