2017年4月28日金曜日

学習環境

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5.2-3.を取り組んでみる。


    1. f'( x )=2x e x x 2 e x =x e x ( 2x ) f'( x )=0 x=0,x=2 f''( x )=2 e x 2x e x 2x e x + x 2 e x = e x ( x 2 4x+2 ) f''( x )=0 x=2± 42 =2± 2
      x02-√222+√2
      f'(x)-0+++0---
      f''(x)+++0---0+
      f(x)04 / e^2

    2. f'( x )= 1logx x 2 f'( x )=0 x=e f''( x )= 1 x x 2 ( 1logx )2x x 4 = 12+2logx x 3 = 3+2logx x 3 f''( x )=0 3+2logx=0 logx= 2 3 x= e 2 3

    3. f'( x )= e 1 x 1 x 2 = e 1 x x 2 f''( x )= e 1 x 1 x 2 x 2 e 1 x 2x x 4 = e 1 x e 1 x 2x x 4 = e 1 x + e 1 x 2x x 4 = e 1 x ( 1+2x ) x 4 f''( x )=0 x= 1 2

コード(Emacs)

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
<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="sample3.js"></script>    

JavaScript

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

let f = (x) => Math.pow(x, 2) * Math.exp(-x);

let draw = () => {
    pre0.textContent = '';    
    
    let points = [];

    for (let x = -0.5; x <= 4; x += 0.001) {
        points.push([x, f(x)]);
    }
    
    let xscale = d3.scaleLinear()
        .domain([-0.5, 4.5])
        .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);

    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', 'green');

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

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

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






  







 
						

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