数学 - JavaScript - 解析学 - 各種の初等関数 - 累乗関数、大きさの比較(指数関数、微分、接線)

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5.2-2.を取り組んでみる。

2. 
   $\begin{array}{l}\frac{d}{dx}{e}^x=e^x\\ x=1\\ e^1=e\\ y=ex+b\\ e=e1+b\\ b=0\\ y=ex\\ \\ m<0\\ 実数解1個\\ 0<m<e\\ 実数解0個\\ m=e\\ 実数解1個\\ e<m\\ 実数解2個\end{array}$

コード(Emacs)

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
m = <input id="m0" type="number">
<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="sample2.js"></script>    

JavaScript

let div0 = document.querySelector('#graph0'),
    input_m = document.querySelector('#m0'),
    pre0 = document.querySelector('#output0'),
    width = 600,
    height = 600,
    padding = 50,
    btn0 = document.querySelector('#draw0'),
    btn1 = document.querySelector('#clear0'),
    p = (x) => pre0.textContent += x + '\n';

input_m.value = Math.E;

let draw = () => {
    pre0.textContent = '';    
    
    let points = [],
        m = parseFloat(input_m.value),
        g = (x) => m * x;

    for (let x = -1; x <= 3; x += 0.01) {
        points.push([x, Math.exp(x)]);
    }
    for (let x = -1; x <= 3; x += 0.01) {
        points.push([x, m * x]);
    }
    
    let xscale = d3.scaleLinear()
        .domain([-1, 3])
        .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);

    let t = points.length / 2;
    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', (d, i) => i < t ? 'green' : 'blue');

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

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

input_m.onchange = draw;
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();

m =