数学 - JavaScript - 解析学 - 各種の初等関数 - 累乗関数、大きさの比較(ネイピア数(オイラー数、自然対数の底)、無限回微分可能性)

解析入門〈1〉

学習環境

• Surface 3 (4G LTE)、Surface 3 タイプ カバー、Surface ペン(端末)
• Windows 10 Pro (OS)
• 数式入力ソフト(TeX, MathML): MathType
• MathML対応ブラウザ: Firefox、Safari
• MathML非対応ブラウザ(Internet Explorer, Google Chrome...)用JavaScript Library: MathJax

解析入門〈1〉(松坂 和夫(著)、岩波書店)の第5章(各種の初等関数)、5.2(累乗関数、大きさの比較)、問題5.2-5.を取り組んでみる。

5. 
   $\begin{array}{l}\frac{A}{x-a}+\frac{B}{x-b}\\ =\frac{A\left(x-b\right)+B\left(x-a\right)}{\left(x-a\right)\left(x-b\right)}\\ A\left(x-b\right)+B\left(x-a\right)=1\\ A+B=0\\ B=-A\\ -Ab+Aa=1\\ A\left(a-b\right)=1\\ A=\frac{1}{a-b}=-\frac{1}{b-a}\\ B=\frac{1}{b-a}\\ a<x<b\\ f\left(x\right)=e^{\frac{-1}{\left(x-a\right)\left(b-a\right)}+\frac{1}{\left(x-b\right)\left(b-a\right)}}\\ =e^{\frac{-1}{\left(x-a\right)\left(b-a\right)}}{e}^{\frac{1}{\left(x-b\right)\left(b-a\right)}}\\ b-a>0\\ x-a>0\\ x-b<0\end{array}$

コード(Emacs)

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
<label for="a0">a = </label><input id="a0" type="number" value="5">
<br>
<label for="h0">h = </label><input id="h0" type="number" min="0.01" value="5">(h > 0)
<br>
b = a + h = <span id="b0"></span>
<br>
<button id="draw0">draw</button>
<button id="clear0">clear</button>

<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/d3/4.2.6/d3.min.js" integrity="sha256-5idA201uSwHAROtCops7codXJ0vja+6wbBrZdQ6ETQc=" crossorigin="anonymous"></script>
<script src="sample5.js"></script>    

JavaScript

let div0 = document.querySelector('#graph0'),
    pre0 = document.querySelector('#output0'),
    width = 600,
    height = 600,
    padding = 50,
    input_a = document.querySelector('#a0'),
    input_h = document.querySelector('#h0'),
    span_b = document.querySelector('#b0'),
    inputs = [input_a, input_h],
    btn0 = document.querySelector('#draw0'),
    btn1 = document.querySelector('#clear0'),
    p = (x) => pre0.textContent += x + '\n';

let draw = () => {
    pre0.textContent = '';    
    let a = parseFloat(input_a.value),
        h = parseFloat(input_h.value),
        b = a + h,
        points = [];

    span_b.textContent = b;
    
    let f = (x) => Math.exp(1 / ((x - a) * (x - b)));
    
    for (let x = a - 0.5; x <= b + 0.5; x += 0.001) {
        if (a < x && x < b) {
            points.push([x, f(x)]);
        } else {
            points.push([x, 0]);
        }
    }
    
    let xscale = d3.scaleLinear()
        .domain([a - 0.5, b + 0.5])
        .range([padding, width - padding]);
    let ys = points.map((a) => a[1]);
    let yscale = d3.scaleLinear()
        .domain([Math.min(...ys), Math.max(...ys)])
        .range([height - padding, padding]);

    let xaxis = d3.axisBottom().scale(xscale);
    let yaxis = d3.axisLeft().scale(yscale);
    div0.innerHTML = '';
    let svg = d3.select('#graph0')
        .append('svg')
        .attr('width', width)
        .attr('height', height);

    svg.selectAll('circle')
        .data(points)
        .enter()
        .append('circle')
        .attr('cx', (d) => xscale(d[0]))
        .attr('cy', (d) => yscale(d[1]))
        .attr('r', 1)
        .attr('fill', 'green');

    svg.append('g')
        .attr('transform', `translate(0, ${height - padding})`)
        .call(xaxis);

    svg.append('g')
        .attr('transform', `translate(${padding}, 0)`)
        .call(yaxis);
}

inputs.forEach((input) => input.onchange = draw);
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();

a =
h = (h > 0)
b = a + h =