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Approximation of e
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<iframe 
    src="https://jsxgraph.uni-bayreuth.de/share/iframe/approximation-of-e" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Approximation of e" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution 4.0 International License.
    https://creativecommons.org/licenses/by/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    const board = JXG.JSXGraph.initBoard(BOARDID, {
        axis: true,
        boundingbox: [-3, 3, 50, 0.5]
    });
    
    var line = board.create('line', [
        [-10, Math.E],
        [100, Math.E]
    ], {
        strokeColor: 'red',
        strokeWidth: 2,
        layer: 4
    });
    var seq = board.create('curve', [
        [0],
        [1]
    ], {
        strokeColor: 'blue',
        strokeWidth: 2
    });
    
    var seq_add = function() {
        var n = seq.dataX.length,
            val = Math.pow(1 + 1 / n, n);
        seq.dataX.push(n);
        seq.dataY.push(val);
    };
    
    var series = board.create('curve', [
        [0],
        [1]
    ], {
        strokeColor: 'black',
        strokeWidth: 2
    });
    
    var series_add = function() {
        var n = series.dataX.length,
            val = series.dataY[n - 1] + 1 / JXG.Math.factorial(n);
        series.dataX.push(n);
        series.dataY.push(val);
    };
    
    var txt1 = board.create('text', [15, 1.6, function() {
        return 'n=' + (seq.dataX.length - 1) + ': value = ' + seq.dataY[seq.dataY.length - 1];
    }], {
        strokeColor: 'blue',
        fixed: true
    });
    var txt2 = board.create('text', [15, 1.8, function() {
        return 'n=' + (series.dataX.length - 1) + ': value = ' + series.dataY[series.dataY.length - 1];
    }], {
        strokeColor: 'black',
        fixed: true
    });
    
    var approx = function() {
        seq_add();
        series_add();
        board.update();
        if (seq.dataX.length <= 50) {
            setTimeout(approx, 500);
        }
    }
    
    approx();
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

const board = JXG.JSXGraph.initBoard(BOARDID, {
    axis: true,
    boundingbox: [-3, 3, 50, 0.5]
});

var line = board.create('line', [
    [-10, Math.E],
    [100, Math.E]
], {
    strokeColor: 'red',
    strokeWidth: 2,
    layer: 4
});
var seq = board.create('curve', [
    [0],
    [1]
], {
    strokeColor: 'blue',
    strokeWidth: 2
});

var seq_add = function() {
    var n = seq.dataX.length,
        val = Math.pow(1 + 1 / n, n);
    seq.dataX.push(n);
    seq.dataY.push(val);
};

var series = board.create('curve', [
    [0],
    [1]
], {
    strokeColor: 'black',
    strokeWidth: 2
});

var series_add = function() {
    var n = series.dataX.length,
        val = series.dataY[n - 1] + 1 / JXG.Math.factorial(n);
    series.dataX.push(n);
    series.dataY.push(val);
};

var txt1 = board.create('text', [15, 1.6, function() {
    return 'n=' + (seq.dataX.length - 1) + ': value = ' + seq.dataY[seq.dataY.length - 1];
}], {
    strokeColor: 'blue',
    fixed: true
});
var txt2 = board.create('text', [15, 1.8, function() {
    return 'n=' + (series.dataX.length - 1) + ': value = ' + series.dataY[series.dataY.length - 1];
}], {
    strokeColor: 'black',
    fixed: true
});

var approx = function() {
    seq_add();
    series_add();
    board.update();
    if (seq.dataX.length <= 50) {
        setTimeout(approx, 500);
    }
}

approx();
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Approximation of e" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution 4.0 International License.
   https://creativecommons.org/licenses/by/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   const board = JXG.JSXGraph.initBoard(BOARDID, {
       axis: true,
       boundingbox: [-3, 3, 50, 0.5]
   });
   
   var line = board.create('line', [
       [-10, Math.E],
       [100, Math.E]
   ], {
       strokeColor: 'red',
       strokeWidth: 2,
       layer: 4
   });
   var seq = board.create('curve', [
       [0],
       [1]
   ], {
       strokeColor: 'blue',
       strokeWidth: 2
   });
   
   var seq_add = function() {
       var n = seq.dataX.length,
           val = Math.pow(1 + 1 / n, n);
       seq.dataX.push(n);
       seq.dataY.push(val);
   };
   
   var series = board.create('curve', [
       [0],
       [1]
   ], {
       strokeColor: 'black',
       strokeWidth: 2
   });
   
   var series_add = function() {
       var n = series.dataX.length,
           val = series.dataY[n - 1] + 1 / JXG.Math.factorial(n);
       series.dataX.push(n);
       series.dataY.push(val);
   };
   
   var txt1 = board.create('text', [15, 1.6, function() {
       return 'n=' + (seq.dataX.length - 1) + ': value = ' + seq.dataY[seq.dataY.length - 1];
   }], {
       strokeColor: 'blue',
       fixed: true
   });
   var txt2 = board.create('text', [15, 1.8, function() {
       return 'n=' + (series.dataX.length - 1) + ': value = ' + series.dataY[series.dataY.length - 1];
   }], {
       strokeColor: 'black',
       fixed: true
   });
   
   var approx = function() {
       seq_add();
       series_add();
       board.update();
       if (seq.dataX.length <= 50) {
           setTimeout(approx, 500);
       }
   }
   
   approx();
</jsxgraph>
This little animation approximates $e$ (displayed by the horizontal red line) by the sequence (blue line) $$ (1+\frac{1}{n})^n $$ and by the series (black line) $$ \sum_{n=0}^\infty \frac{1}{n!} $$
// Define the id of your board in BOARDID

const board = JXG.JSXGraph.initBoard(BOARDID, {
    axis: true,
    boundingbox: [-3, 3, 50, 0.5]
});

var line = board.create('line', [
    [-10, Math.E],
    [100, Math.E]
], {
    strokeColor: 'red',
    strokeWidth: 2,
    layer: 4
});
var seq = board.create('curve', [
    [0],
    [1]
], {
    strokeColor: 'blue',
    strokeWidth: 2
});

var seq_add = function() {
    var n = seq.dataX.length,
        val = Math.pow(1 + 1 / n, n);
    seq.dataX.push(n);
    seq.dataY.push(val);
};

var series = board.create('curve', [
    [0],
    [1]
], {
    strokeColor: 'black',
    strokeWidth: 2
});

var series_add = function() {
    var n = series.dataX.length,
        val = series.dataY[n - 1] + 1 / JXG.Math.factorial(n);
    series.dataX.push(n);
    series.dataY.push(val);
};

var txt1 = board.create('text', [15, 1.6, function() {
    return 'n=' + (seq.dataX.length - 1) + ': value = ' + seq.dataY[seq.dataY.length - 1];
}], {
    strokeColor: 'blue',
    fixed: true
});
var txt2 = board.create('text', [15, 1.8, function() {
    return 'n=' + (series.dataX.length - 1) + ': value = ' + series.dataY[series.dataY.length - 1];
}], {
    strokeColor: 'black',
    fixed: true
});

var approx = function() {
    seq_add();
    series_add();
    board.update();
    if (seq.dataX.length <= 50) {
        setTimeout(approx, 500);
    }
}

approx();

license

This example is licensed under a Creative Commons Attribution 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.