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
- 参考書籍
数学読本〈4〉数列の極限,順列/順列・組合せ/確率/関数の極限と微分法(松坂 和夫(著)、岩波書店)の第17章(関数の変化をとらえる - 関数の極限と微分法)、17.1(関数と極限)、極限 lim_{x→+∞} f(x), 極限 lim_{x→-∞} f(x)、問6、7、8.を取り組んでみる。
-
−∞
−∞
limx→+∞x3(−1+2x2)=−∞
limx→−∞x3(−1+2x2)=∞
limx→+∞x4(1−6x)=∞
limx→−∞x4(1−6x)=∞
limx→+∞1x(x+1)=0
limx→−∞−2+1x26+5x=−13
limt→+∞2t+3t310t2−1=−∞
limt→−∞2t+3t310t2−1=∞
1
limt→−∞x+211x101−310x10=−∞
limx→+∞f(x)=+∞n=2klimx→−∞f(x)=+∞n=2k+1limx→−∞f(x)=−∞-
limx→∞x+1−x+1√x+1+√x−1=0
limx→∞1√1+1x2=1
limx→−∞1−√1+1x2=−1
limx→∞x√x2+x+x=limx→∞1√1+1x+1=12
limx→−∞x√x2+x+x=limx→∞1−√1+1x+1=∞
コード(Emacs)
Python 3
#!/usr/bin/env python3 # -*- coding: utf-8 -*- from sympy import Symbol, Limit, sqrt, S, pprint x = Symbol('x') exprs = [(sqrt(x + 1) - sqrt(x - 1), x, S.Infinity), (x / sqrt(x ** 2 + 1), x, S.Infinity), (x / sqrt(x ** 2 + 1), x, S.NegativeInfinity), (sqrt(x ** 2 + x) - x, x, S.Infinity), (sqrt(x ** 2 + x) - x, x, S.NegativeInfinity)] for t in exprs: pprint(Limit(*t).doit())
入出力結果(Terminal, IPython)
$ ./sample6.py 0 1 -1 1/2 ∞ $
コード(Emacs)
HTML5
<div id="graph0"></div> <pre id="output0"></pre> <label for="x1">x1 = </label> <input id="x1" type="number" value="-5"> <label for="x2">x2 = </label> <input id="x2" type="number" value="5"> <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="sample6.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'), input_x1 = document.querySelector('#x1'), input_x2 = document.querySelector('#x2'), inputs = [input_x1, input_x2], p = (x) => pre0.textContent += x + '\n'; let f1 = (x) => Math.sqrt(x + 1) - Math.sqrt(x - 1), f2 = (x) => x / Math.sqrt(x ** 2 + 1), f3 = (x) => Math.sqrt(x ** 2 + x) - x; let draw = () => { pre0.textContent = ''; let x1 = parseFloat(input_x1.value), x2 = parseFloat(input_x2.value); let points = []; for (let x = x1; x <= x2; x += 0.001) { if (x >= 1) { points.push([x, f1(x)]); } } let t1 = points.length; for (let x = x1; x <= x2; x += 0.001) { points.push([x, f2(x)]); } let t2 = points.length; for (let x = x1; x <= x2; x += 0.001) { if (x <= -1 || 0 <= x) { points.push([x, f3(x)]); } } let xscale = d3.scaleLinear() .domain([x1, x2]) .range([padding, width - padding]); let ys = points.map((a) => a[1]); let yscale = d3.scaleLinear() .domain([x1, x2]) .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', (d, i) => i < t1 ? 'red' : i < t2 ? 'green' : 'blue'); svg.append('g') .attr('transform', `translate(0, ${yscale(0)})`) .call(xaxis); svg.append('g') .attr('transform', `translate(${xscale(0)}, 0)`) .call(yaxis); } inputs.forEach((input) => input.onchange = draw); btn0.onclick = draw; btn1.onclick = () => pre0.textContent = ''; draw();
0 コメント:
コメントを投稿