{"id":17975,"date":"2016-12-23T00:00:43","date_gmt":"2016-12-22T15:00:43","guid":{"rendered":"http:\/\/yukisako.xsrv.jp\/entry\/napier-number"},"modified":"2016-12-23T00:00:43","modified_gmt":"2016-12-22T15:00:43","slug":"napier-number","status":"publish","type":"post","link":"https:\/\/skill-hacks.co.jp\/media\/napier-number\/","title":{"rendered":"\u30cd\u30a4\u30d4\u30a2\u6570e\u306e\u5b9a\u7fa9\u304c\u306a\u305c\u3042\u306e\u5f62\u304b\uff0c\u5148\u751f\u306f\u8aac\u660e\u3092\u3057\u3066\u304f\u308c\u306a\u304b\u3063\u305f"},"content":{"rendered":"<p><!-- [mathjax] --><\/p>\n<p>\u9ad8\u68213\u5e74\u751f\u306e\u590f\uff0c\u7a81\u5982\u3068\u3057\u3066\u73fe\u308c\u305f\u8b0e\u306e\u7121\u7406\u6570\\(e\\)<\/p>\n<p>\u30cd\u30a4\u30d4\u30a2\u6570\u3068\u547c\u3070\u308c\uff0c\u81ea\u7136\u5bfe\u6570\u306e\u5e95\u306b\u3088\u304f\u51fa\u3066\u304f\u308b\\(e\\)<\/p>\n<p>\u305d\u306e\\(e\\)\u306e\u5b9a\u7fa9\u306f\u9ad8\u68213\u5e74\u751f\u306e\u6570\u5b66\u2162\u306e\u6559\u79d1\u66f8\u306b\u3057\u308c\u3063\u3068\u3053\u3046\u66f8\u3044\u3066\u3042\u308a\u307e\u3059\uff0e<\/p>\n<p>$$e = \\displaystyle \\lim_{x \\to 0} \\bigl(1+x\\bigr)^{\\frac{1}{x}}$$<\/p>\n<p>\u3082\u3057\u304f\u306f<\/p>\n<p>$$e = \\displaystyle \\lim_{x \\to \\infty} \\bigl(1+\\frac{1}{x}\\bigr)^x$$<\/p>\n<p><!--more--><\/p>\n<p>\u79c1\u306f\u521d\u3081\u3066\u3053\u308c\u3092\u7fd2\u3063\u305f\u6642\uff0c\u300c\u306f\uff1f\u3069\u3063\u304b\u3089\u3067\u3066\u304d\u305f\u3053\u308c\u300d\u3063\u3066\u306a\u308a\u307e\u3057\u305f\u304c\uff0c\u5148\u751f\u306f\u2026<\/p>\n<div class=\"entry-talk-box\">\n<div class=\"entry-talk-img\"><img decoding=\"async\" src=\"http:\/\/yukisako.github.io\/blog\/teacher.png\" alt=\"\u8feb\"><\/div>\n<div class=\"entry-talk-txt-left entry-talk-txt\">\n<p>\u3053\u308c\u306f\u5b9a\u7fa9\u3060\u304b\u3089\u3053\u3046\u3044\u3046\u3082\u306e\u3067\u3059<\/p>\n<p>\u899a\u3048\u307e\u3057\u3087\u3046<\/p>\n<\/div>\n<\/div>\n<p>\u307e\u3041\u305f\u3057\u304b\u306b\u305d\u3046\u306a\u3093\u3067\u3059\u304c\uff0c\u5b9a\u7fa9\u306e\u80cc\u666f\u306b\u306f\uff0c<strong>\u305d\u3046\u5b9a\u7fa9\u3059\u308c\u3070\u90fd\u5408\u306e\u826f\u3044\u7406\u7531\u304c\u3042\u308b<\/strong>\u306f\u305a\u306a\u3093\u3067\u3059\u3088\u306d\uff0e<\/p>\n<p>\u3068\u3044\u3046\u3053\u3068\u3067\uff0c\u3053\u306e\\(e\\)\u306e\u5b9a\u7fa9\u306b\u3064\u3044\u3066\u4eca\u65e5\u306f\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\uff0e<\/p>\n<p><\/p>\n<p><!--more--><\/p>\n<h2 id=\"e\u304c\u3088\u304f\u51fa\u3066\u304f\u308b\u6240\">e\u304c\u3088\u304f\u51fa\u3066\u304f\u308b\u6240<\/h2>\n<p>\u3055\u3066\uff0ce\u304c\u3088\u304f\u51fa\u3066\u304f\u308b\u3068\u3053\u308d\u3063\u3066\u3069\u3053\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n<p>\u305d\u3046\u3067\u3059\uff0c<b>\u5fae\u5206<\/b>\u3067\u3059\u306d\uff0e<\/p>\n<p>\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u3044\u308b\u3068\uff0c\u5fc5\u305a\u3068\u884c\u3063\u3066\u3044\u3044\u307b\u3069\\(e\\)\u304c\u51fa\u3066\u304d\u307e\u3059\uff0e<\/p>\n<p>\u3057\u304b\u3082\uff0c\u7406\u7cfb\u306e\u65b9\u306a\u3089\u304a\u306a\u3058\u307f\uff0c\\(e\\)<b>\u306b\u306f\uff0c\u6307\u6570\u95a2\u6570\\(e^x\\)\u3092\u5fae\u5206\u3057\u305f\u7d50\u679c\u306f\uff0c\\(e^x\\)<\/b>\u3068\u3068\u3044\u3046\u7d20\u6674\u3089\u3057\u3044\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\uff0e<\/p>\n<p>\u307e\u305f\uff0c<b>\u5e95\u3092\\(e\\)\u3068\u3059\u308b\u5bfe\u6570\u95a2\u6570\\(log(x)\\)\u306e\u5fae\u5206\u306f\\(\\frac{1}{x}\\)<\/b>\u3068\u3068\u3066\u3082\u304d\u308c\u3044\u306b\u306a\u308a\u307e\u3059\u306d\uff0e<\/p>\n<p>\u3055\u3066\uff0c\u3053\u308c\u3063\u3066\uff0c\u672c\u5f53\u306b\u305f\u307e\u305f\u307e<b>\\(e^x\\)<\/b>\u3084<b>\\(log(x)\\)<\/b>\u3092\u5fae\u5206\u3057\u305f\u7d50\u679c\u3053\u3046\u306a\u3063\u305f\u306e\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n<p>\u3044\u3084\uff0c<strong>\u304d\u308c\u3044\u306b\u306a\u308b\u3088\u3046\u306b\u81ea\u7136\u5bfe\u6570<b>\\(e\\)<\/b>\u3092\u5b9a\u7fa9\u3057\u305f<\/strong>\u3068\u8003\u3048\u308b\u307b\u3046\u304c\u81ea\u7136\u3058\u3083\u306a\u3044\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n<p>\u3068\u3044\u3046\u3053\u3068\u3067\uff0c\u4eca\u56de\u306f\uff0c\u6307\u6570\u95a2\u6570\u3084\u5bfe\u6570\u95a2\u6570\u306e\u5fae\u5206\u3068\u3044\u3046\u89b3\u70b9\u304b\u3089\uff0c\u30cd\u30a4\u30d4\u30a2\u6570<b>\\(e\\)<\/b>\u306e\u5b9a\u7fa9\u3092\u898b\u76f4\u3057\u3066\u307f\u307e\u3057\u3087\u3046\uff0e<\/p>\n<h2 id=\"\u5fae\u5206\u306e\u5b9a\u7fa9\u3092\u78ba\u8a8d\u3057\u3066\u307f\u308b\">\u5fae\u5206\u306e\u5b9a\u7fa9\u3092\u78ba\u8a8d\u3057\u3066\u307f\u308b<\/h2>\n<p>\u3055\u3066\uff0c\u5fae\u5206\u3068\u3044\u3046\u89b3\u70b9\u304b\u3089<b>\\(e\\)<\/b>\u306e\u5b9a\u7fa9\u3092\u898b\u76f4\u3057\u3066\u307f\u308b\u306e\u306f\u826f\u3044\u306e\u3067\u3059\u304c\uff0c\u305d\u306e\u524d\u306b\u5fae\u5206\u306e\u5b9a\u7fa9\u3060\u3051\u78ba\u8a8d\u3057\u3066\u304a\u304d\u307e\u3059\uff0e<\/p>\n<p>\u95a2\u6570<b>\\(f(x)\\)<\/b>\u304c\u4e0e\u3048\u3089\u308c\u305f\u6642\uff0c\u5c0e\u95a2\u6570<b>\\(f'(x)\\)<\/b>\u306f\uff0c\\( \\displaystyle \\lim_{h \\to 0} \\frac{f(x+h) \u2013 f(x)}{h}\\)\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e<\/p>\n<p>\u5fae\u5206\u306e\u5b9a\u7fa9\u306b\u95a2\u3057\u3066\u306f\uff0c\u8a73\u3057\u304f\u306f\u6271\u3044\u307e\u305b\u3093\uff0e<\/p>\n<p>\u6c17\u304c\u5411\u3044\u305f\u3089\u307e\u305f\u66f8\u304d\u307e\u3059\uff0e<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-686\" src=\"https:\/\/www.yukisako.xyz\/wp-content\/uploads\/2016\/12\/2018-06-13-08-45-31-300x156.png\" alt=\"\" width=\"1006\" height=\"523\"><\/p>\n<h2 id=\"\u6307\u6570\u95a2\u6570\u306e\u5fae\u5206\u304b\u3089e\u3092\u898b\u76f4\u3057\u3066\u307f\u308b\">\u6307\u6570\u95a2\u6570\u306e\u5fae\u5206\u304b\u3089e\u3092\u898b\u76f4\u3057\u3066\u307f\u308b<\/h2>\n<p>\u3055\u3066\uff0c\u6307\u6570\u95a2\u6570\u306e\u5fae\u5206\u3092\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\uff0e<\/p>\n<p>\u6307\u6570\u95a2\u6570\uff0c\\(f(x)=a^x\\)\u3092\u8003\u3048\u3066\u307f\u307e\u3059\uff0e<\/p>\n<p>\u5148\u7a0b\u306e\u5fae\u5206\u306e\u5b9a\u7fa9\u306b\u3057\u305f\u304c\u3063\u3066\u6307\u6570\u95a2\u6570\u3092\u5fae\u5206\u3057\u3066\u307f\u307e\u3057\u3087\u3046\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20f%27%28x%29%20%3D%5Cdisplaystyle%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Bf%28x%2Bh%29%20-%20f%28x%29%7D%7Bh%7D\" alt=\" f'(x) =\\displaystyle \\lim_{h \\to 0} \\frac{f(x+h) - f(x)}{h}\"><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20%3D%20%5Cdisplaystyle%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Ba%5E%7B%28x%2Bh%29%7D%20-%20a%5Ex%7D%7Bh%7D\" alt=\" = \\displaystyle \\lim_{h \\to 0} \\frac{a^{(x+h)} - a^x}{h}\"><\/p>\n<p>\u3055\u3066\uff0c\u6307\u6570\u95a2\u6570\u306e\u7279\u5fb4\u3092\u4f7f\u3046\u3068\uff0c\\(a^{(x+h)}\\)\u3068\u3044\u3046\u306e\u306f\uff0c\\(a^x a^h\\)\u3068\u66f8\u304f\u3053\u3068\u304c\u51fa\u6765\u307e\u3059\uff0e<\/p>\n<p>\u306a\u306e\u3067\uff0c\u4e0a\u306e\u5f0f\u306f<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20%3D%20%5Cdisplaystyle%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Ba%5Ex%20a%5Eh%20-%20a%5Ex%7D%7Bh%7D\" alt=\" = \\displaystyle \\lim_{h \\to 0} \\frac{a^x a^h - a^x}{h}\"><\/p>\n<p>\u3068\u304b\u3051\u307e\u3059\uff0e<\/p>\n<p>\u304a\uff0c\u90fd\u5408\u306e\u826f\u3044\u3053\u3068\u306b\uff0c\u5206\u5b50\u304b\u3089\\(a^x\\)\u3092\u304f\u304f\u308a\u3060\u3059\u3053\u3068\u304c\u51fa\u6765\u307e\u3059\uff0e<\/p>\n<p>\u3055\u3089\u306b\uff0c\\(a^x\\)\u306f\\(h\\)\u306b\u95a2\u4fc2\u306a\u3044\u306e\u3067\uff0clim\u306e\u524d\u306b\u51fa\u305b\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20%3D%20%5Cdisplaystyle%20%20a%5Ex%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Ba%5Eh%20-%201%7D%7Bh%7D\" alt=\" = \\displaystyle a^x \\lim_{h \\to 0} \\frac{a^h - 1}{h}\"><\/p>\n<p>\u304a\u3049\uff1f<\/p>\n<p>\u3053\u308c\u3063\u3066\uff0c\u3082\u3068\u306e\\(f(x) = a^x\\)\u306b\\(\\displaystyle \\lim_{h \\to 0} \\frac{a^h \u2013 1}{h}\\)\u304c\u304b\u304b\u3063\u305f\u3082\u306e\u3067\u3059\u306d\uff0e<\/p>\n<p>\u3064\u307e\u308a\uff0c\\(\\displaystyle \\lim_{h \\to 0} \\frac{a^h \u2013 1}{h}\\)<strong>\u304c1\u306b\u306a\u308b\u3088\u3046\u306a\u5024\\(a\\)\u3092\u5e95\u3068\u3059\u308b\u6307\u6570\u95a2\u6570\u306f\uff0c\u5fae\u5206\u3057\u3066\u3082\u305d\u306e\u307e\u307e\u3067\u90fd\u5408\u304c\u3044\u3044<\/strong>\u306b\u306a\u308b\u308f\u3051\u3067\u3059\uff0e<\/p>\n<p>\u3055\u3066\uff0c\u305d\u308c\u3067\u306f\\(\\displaystyle \\lim_{h \\to 0} \\frac{a^h \u2013 1}{h}=1\\)\u306b\u306a\u308b\u3088\u3046\u306a\\(a\\)\u3092\u8003\u3048\u3066\u307f\u307e\u3059\uff0e<\/p>\n<p>\\(\\displaystyle \\lim_{h \\to 0} \\frac{a^h \u2013 1}{h}=1\\)\u3092\uff0c\\(a\\)\u306b\u3064\u3044\u3066\u89e3\u3051\u3070\u3044\u3044\u3060\u3051\u3067\u3059\u306e\u3067\u307e\u305a\u306f\uff0c\u4e21\u8fba\u306b\\(h\\)\u3092\u304b\u3051\u3066\u3042\u3052\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%5Cdisplaystyle%20%5Clim_%7Bh%20%5Cto%200%7D%20a%5Eh%20-%201%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%20%5Cto%200%7D%20h\" alt=\"\\displaystyle \\lim_{h \\to 0} a^h - 1 = \\displaystyle \\lim_{h \\to 0} h\"><\/p>\n<p>\u305d\u3057\u3066\uff0c\u5de6\u8fba\u306e1\u3092\u53f3\u8fba\u3078\u79fb\u884c<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%5Cdisplaystyle%20%5Clim_%7Bh%20%5Cto%200%7D%20a%5Eh%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%20%5Cto%200%7D%20h%20%2B%201\" alt=\"\\displaystyle \\lim_{h \\to 0} a^h = \\displaystyle \\lim_{h \\to 0} h + 1\"><\/p>\n<p>\u305d\u3057\u3066\uff0c\u4e21\u8fba\\(\\frac{1}{h}\\)\u4e57\u3057\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%5Cdisplaystyle%20a%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%20%5Cto%200%7D%20%281%20%2B%20h%29%5E%7B%5Cfrac%7B1%7D%7Bh%7D%7D\" alt=\"\\displaystyle a = \\displaystyle \\lim_{h \\to 0} (1 + h)^{\\frac{1}{h}}\"><\/p>\n<p>\u3067\u307e\u3057\u305f\uff0c \\(e = \\displaystyle \\lim_{x \\to 0} \\bigl(1+x\\bigr)^{\\frac{1}{x}}\\)\u3067\u3059\uff0e<\/p>\n<p>\u3053\u306e\\(a\\)\u304c\u30cd\u30a4\u30d4\u30a2\u6570\\(e\\)\u306e\u5b9a\u7fa9\u3067\u3042\u308a\uff0c\u3053\u3046\u5b9a\u7fa9\u3059\u308b\u3068\u6307\u6570\u95a2\u6570\u306e\u5fae\u5206\u304c\u3068\u3066\u3082\u6271\u3044\u3084\u3059\u3044\u3068\u3044\u3046\u306e\u304c\u308f\u304b\u3063\u3066\u3082\u3089\u3048\u305f\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n<h2 id=\"\u5bfe\u6570\u95a2\u6570\u306e\u5fae\u5206\u304b\u3089e\u3092\u898b\u76f4\u3057\u3066\u307f\u308b\">\u5bfe\u6570\u95a2\u6570\u306e\u5fae\u5206\u304b\u3089e\u3092\u898b\u76f4\u3057\u3066\u307f\u308b<\/h2>\n<p>\u3055\u3066\uff0c\u6307\u6570\u95a2\u6570\u306e\u5fae\u5206\u306e\u6642\u306b\u90fd\u5408\u306e\u826f\u3044\u306e\u304c\\(e\\)\u3060\u3068\u3044\u3046\u306e\u304c\u4e0a\u306e\u8a71\u3067\u308f\u304b\u308a\u307e\u3057\u305f\uff0e<\/p>\n<p>\u5e8f\u76e4\u306b\u8003\u3048\u305f\uff0c\u300c\\(log(x)\\)\u306e\u5fae\u5206\u304c<b>\\(\\frac{1}{x}\\)<\/b>\u3068\u304d\u308c\u3044\u306b\u306a\u308b\u300d\u306b\u3064\u3044\u3066\u3082\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046<\/p>\n<p>\u6307\u6570\u95a2\u6570\u306e\u3068\u304d\u306f\uff0c\u5e95\u304ca\u306e\u6307\u6570\u95a2\u6570\u3092\u8003\u3048\u307e\u3057\u305f\uff0e<\/p>\n<p>\u540c\u69d8\u306b\u5e95\u304ca\u306e\u5bfe\u6570\u95a2\u6570\\(f(x) = log_a(x)\\)\u3092\u8003\u3048\u3066\u307f\u307e\u3059\uff0e<\/p>\n<p>\u3053\u308c\u3092\uff0c\u5b9a\u7fa9\u306b\u5f93\u3063\u3066\u5fae\u5206\u3057\u3066\u307f\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20f%27%28x%29%20%3D%20%5Cdisplaystyle%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Bf%28x%2Bh%29%20-%20f%28x%29%7D%7Bh%7D\" alt=\" f'(x) = \\displaystyle \\lim_{h \\to 0} \\frac{f(x+h) - f(x)}{h}\"><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20%3D%20%5Cdisplaystyle%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Blog_a%28x%2Bh%29%20-%20log_a%28x%29%7D%7Bh%7D\" alt=\" = \\displaystyle \\lim_{h \\to 0} \\frac{log_a(x+h) - log_a(x)}{h}\"><\/p>\n<p>\u5bfe\u6570\u95a2\u6570\u306e\u6027\u8cea\u3088\u308a\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20log_a%28x%2Bh%29%20-%20log_a%28x%29%20%3D%20log_a%28%5Cfrac%7Bx%2Bh%7D%7Bx%7D%29\" alt=\" log_a(x+h) - log_a(x) = log_a(\\frac{x+h}{x})\"><\/p>\n<p>\u305d\u308c\u3092\u4f7f\u3046\u3068\uff0c\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Blog_a%28%5Cfrac%7Bx%2Bh%7D%7Bx%7D%29%7D%7Bh%7D\" alt=\" = \\displaystyle \\lim_{h \\to 0} \\frac{log_a(\\frac{x+h}{x})}{h}\"><\/p>\n<p>\u3061\u3087\u3063\u3068\u898b\u306b\u304f\u3044\u306e\u3067\uff0c\u5206\u6570\u3092\u524d\u306b\u51fa\u3057\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B1%7D%7Bh%7D%20log_a%5Cbigl%28%5Cfrac%7Bx%2Bh%7D%7Bx%7D%5Cbigr%29\" alt=\" = \\displaystyle \\lim_{h \\to 0} \\frac{1}{h} log_a\\bigl(\\frac{x+h}{x}\\bigr)\"><\/p>\n<p>\u5bfe\u6570\u95a2\u6570\u306e\u6027\u8cea\u3088\u308a\uff0c\\(\\alpha log(x) = log(x)^{\\alpha}\\)\u3068\u304b\u3051\u307e\u3059\u306e\u3067\uff0c\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%20%5Cto%200%7D%20log_a%5Cbigl%28%5Cfrac%7Bx%2Bh%7D%7Bx%7D%5Cbigr%29%5E%7B%5Cfrac%7B1%7D%7Bh%7D%7D\" alt=\" = \\displaystyle \\lim_{h \\to 0} log_a\\bigl(\\frac{x+h}{x}\\bigr)^{\\frac{1}{h}}\"><\/p>\n<p>\\(log\\)\u306e\u4e2d\u8eab\u3092\u8a08\u7b97\u3057\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%20%5Cto%200%7D%20log_a%5Cbigl%281%2B%5Cfrac%7Bh%7D%7Bx%7D%5Cbigr%29%5E%7B%5Cfrac%7B1%7D%7Bh%7D%7D\" alt=\" = \\displaystyle \\lim_{h \\to 0} log_a\\bigl(1+\\frac{h}{x}\\bigr)^{\\frac{1}{h}}\"><\/p>\n<p>log\u306e\u4e2d\u306b\u5206\u6570\u304c\u3042\u308b\u306e\u304c\u5acc\u306a\u306e\u3067\uff0c\\(\\frac{h}{x})\\)\u3092\u306a\u3093\u304b\u306e\u5909\u6570\u3067\u7f6e\u304d\u63db\u3048\u307e\u3057\u3087\u3046\uff0e<\/p>\n<p>\u4eca\u56de\u306f\uff0c\\(\\frac{h}{x})\\)\u3092\\(t\\)\u3068\u7f6e\u3044\u3066\u3042\u3052\u307e\u3059\uff0e<\/p>\n<p>\u3059\u308b\u3068\uff0c\\(h=xt\\)\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n<p>\u307e\u305f\uff0ch\u304c0\u306b\u8fd1\u3065\u304f\u6642\uff0c\u540c\u3058\u304ft\u30820\u306b\u8fd1\u3065\u304f\u306e\u3067\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3059\u308b\u3053\u3068\u304c\u51fa\u6765\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bt%20%5Cto%200%7D%20log_a%281%2Bt%29%5E%7B%5Cfrac%7B1%7D%7Bxt%7D%7D\" alt=\" = \\displaystyle \\lim_{t \\to 0} log_a(1+t)^{\\frac{1}{xt}}\"><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bt%20%5Cto%200%7D%20log_a%281%2Bt%29%5E%7B%5Cfrac%7B1%7D%7Bx%7D%5Cfrac%7B1%7D%7Bt%7D%7D\" alt=\" = \\displaystyle \\lim_{t \\to 0} log_a(1+t)^{\\frac{1}{x}\\frac{1}{t}}\"><\/p>\n<p>\u3053\u3053\u3067\uff0c\\(\\frac{1}{x}\\)\u3092\u5bfe\u6570\u306e\u524d\u306b\u51fa\u3057\uff0c\\(lim\\)\u306e\u524d\u306b\u51fa\u3057\u3066\u3042\u3052\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%20%3D%20%5Cdisplaystyle%20%5Cfrac%7B1%7D%7Bx%7D%20%5Clim_%7Bt%20%5Cto%200%7D%20log_a%281%2Bt%29%5E%7B%5Cfrac%7B1%7D%7Bt%7D%7D\" alt=\" = \\displaystyle \\frac{1}{x} \\lim_{t \\to 0} log_a(1+t)^{\\frac{1}{t}}\"><\/p>\n<p>\u3055\u3041\uff0c\u898b\u3048\u3066\u304d\u307e\u3057\u305f\uff0e<\/p>\n<p>\u3064\u307e\u308a\uff0c\u4e0a\u306e\u5f0f\u306e\u5f8c\u534a\u306e\\(\\displaystyle \\lim_{t \\to 0} log_a(1+t)^{\\frac{1}{t}}\\)\u304c1\u306b\u306a\u308c\u3070\uff0c\u5bfe\u6570\u95a2\u6570\u306e\u5fae\u5206\u304c\u3068\u3066\u3082\u304d\u308c\u3044\u306a\u5f62\u306b\u306a\u308b\u3068\u3044\u3046\u8a71\u3067\u3059\uff0e<\/p>\n<p>\u5bfe\u6570\u306e\u5e95\u3068\u771f\u6570\u90e8\u5206\u304c\u540c\u3058\u306a\u3089\uff0c\u305d\u306e\u5024\u306f1\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n<p>\u3064\u307e\u308a\uff0c<strong>\u5bfe\u6570\u306e\u5e95\\(a\\)\u3092\\(\\displaystyle \\lim_{t \\to 0}(1+t)^{\\frac{1}{t}}\\)\u3068\u3059\u308c\u3070\uff0c\u5c0e\u95a2\u6570\u304c\\(\\frac{1}{x}\\)\u306b\u306a\u3063\u3066\u90fd\u5408\u304c\u826f\u3044<\/strong>\u3068\u3044\u3046\u308f\u3051\uff0e<\/p>\n<p>\u3068\u3044\u3046\u3053\u3068\u3067\uff0c\u5bfe\u6570\u306e\u5fae\u5206\u3092\u7dba\u9e97\u306b\u3059\u308b\u305f\u3081\u306e\u5e95e\u3068\u3057\u3066\uff0c\\(e = \\displaystyle \\lim_{t \\to 0} (1+t)^{\\frac{1}{t}}\\)\u3068\u5b9a\u7fa9\u3059\u308c\u3070\u90fd\u5408\u304c\u826f\u3044\uff0e<\/p>\n<h2 id=\"\u307e\u3068\u3081\">\u307e\u3068\u3081<\/h2>\n<p>\u3044\u304b\u304c\u3060\u3063\u305f\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n<p>\u9ad8\u6821\u3067\u30cd\u30a4\u30d4\u30a2\u6570\\(e\\)\u304c\u521d\u3081\u3066\u51fa\u73fe\u3057\u305f\u3068\u304d\u306f\u8ab0\u3082\u304c\u611f\u3058\u305f\u3067\u3042\u308d\u3046\u3053\u306e\u7591\u554f\uff0e<\/p>\n<p>\u5b9a\u7fa9\u306e\u88cf\u306b\u306f\u3057\u3063\u304b\u308a\u80cc\u666f\u304c\u3042\u308b\u3093\u3067\u3059\uff0e<\/p>\n<p>\u300c\u5b9a\u7fa9\u3060\u304b\u3089\u899a\u3048\u308d!!\u300d\u3068\u3044\u3046\u524d\u306b\uff0c\u5c11\u3057\u3053\u306e\u3088\u3046\u306a\u8a71\u3092\u307e\u305c\u308b\u3068\uff0c\u3082\u3084\u3082\u3084\u304c\u306a\u304f\u306a\u308a\u307e\u3059\uff0e<\/p>\n<div class=\"date-box\">\n<div class=\"date-midashi\">\u5f53\u30d6\u30ed\u30b0\u304c\u66f8\u7c4d\u5316\u3055\u308c\u307e\u3057\u305f!!<\/div>\n<div class=\"date-content\">\n<p><a href=\"https:\/\/www.yukisako.xyz\/entry\/no-meorize-math-publishing\" target=\"_blank\" rel=\"noopener\">\u5f53\u30d6\u30ed\u30b0\u3067\u5927\u597d\u8a55\u306e\u3010\u6697\u8a18\u3057\u306a\u3044\u6570\u5b66\u3011\u30b7\u30ea\u30fc\u30ba\u304c\u66f8\u7c4d\u5316\u3055\u308c\u307e\u3057\u305f!!<\/a><\/p>\n<div class=\"booklink-box\" style=\"text-align: left; padding-bottom: 20px; font-size: small; \/zoom: 1; overflow: hidden; background-color: white; border-radius: 5px;\">\n<div class=\"booklink-image\" style=\"float: left; margin: 0 15px 10px 0;\"><a href=\"http:\/\/www.amazon.co.jp\/exec\/obidos\/asin\/B06X9LJLPH\/m035f-22\/\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" style=\"border: none;\" src=\"https:\/\/images-fe.ssl-images-amazon.com\/images\/I\/51pJLaN8DNL._SL160_.jpg\"><\/a><\/div>\n<div class=\"booklink-info\" style=\"line-height: 120%; \/zoom: 1; overflow: hidden;\">\n<div class=\"booklink-name\" style=\"margin-bottom: 10px; line-height: 120%;\">\n<p><a href=\"http:\/\/www.amazon.co.jp\/exec\/obidos\/asin\/B06X9LJLPH\/m035f-22\/\" target=\"_blank\" rel=\"noopener\">\u6697\u8a18\u3057\u306a\u3044\u6570\u5b66: 30\u4e07\u4eba\u306b\u8aad\u307e\u308c\u305f\u30d6\u30ed\u30b0\u304c\u3064\u3044\u306b\u66f8\u7c4d\u5316[Kindle\u7248]<\/a><\/p>\n<div class=\"booklink-powered-date\" style=\"font-size: 8pt; margin-top: 5px; font-family: verdana; line-height: 120%;\">posted with <a href=\"http:\/\/yomereba.com\" target=\"_blank\" rel=\"nofollow noopener\">\u30e8\u30e1\u30ec\u30d0<\/a><\/div>\n<\/div>\n<div class=\"booklink-detail\" style=\"margin-bottom: 5px;\">\u8feb \u4f51\u6a39 \u8feb \u4f51\u6a39 2017-02-22<\/div>\n<div class=\"booklink-link2\" style=\"margin-top: 10px;\">\n<div class=\"shoplinkkindle\" style=\"display: inline; margin-right: 5px;\"><a href=\"http:\/\/www.amazon.co.jp\/exec\/obidos\/ASIN\/B06X9LJLPH\/m035f-22\/\" target=\"_blank\" rel=\"noopener\">Kindle<\/a><\/div>\n<\/div>\n<\/div>\n<div class=\"booklink-footer\" style=\"clear: left;\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<h2 id=\"\u6570\u5b66\u95a2\u9023\u30aa\u30b9\u30b9\u30e1\">\u6570\u5b66\u95a2\u9023\u30aa\u30b9\u30b9\u30e1<\/h2>\n<p>\u3053\u308c\u3092\u8aad\u3093\u3067\u304f\u308c\u305f\u65b9\u306b\u306f\u3053\u3061\u3089\u306e\u8a18\u4e8b\u3082\u30aa\u30b9\u30b9\u30e1\u3067\u3059\uff01<\/p>\n<div class=\"date-box\">\n<div class=\"date-midashi\">\u95a2\u9023\u304a\u3059\u3059\u3081\u8a18\u4e8b<\/div>\n<div class=\"date-content\"><a href=\"https:\/\/www.yukisako.xyz\/entry\/kahouteiri\">\u6298\u308a\u7d19\u3067\u5c0e\u51fa\u3059\u308b\u52a0\u6cd5\u5b9a\u7406<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u9ad8\u68213\u5e74\u751f\u306e\u590f\uff0c\u7a81\u5982\u3068\u3057\u3066\u73fe\u308c\u305f\u8b0e\u306e\u7121\u7406\u6570\\(e\\) \u30cd\u30a4\u30d4\u30a2\u6570\u3068\u547c\u3070\u308c\uff0c\u81ea\u7136\u5bfe\u6570\u306e\u5e95\u306b\u3088\u304f\u51fa\u3066\u304f\u308b\\(e\\) \u305d\u306e\\(e\\)\u306e\u5b9a\u7fa9\u306f\u9ad8\u68213\u5e74\u751f\u306e\u6570\u5b66\u2162\u306e\u6559\u79d1\u66f8\u306b\u3057\u308c\u3063\u3068\u3053\u3046\u66f8\u3044\u3066\u3042\u308a\u307e\u3059\uff0e $$e = \\display &#8230; <\/p>\n","protected":false},"author":1,"featured_media":16930,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[],"class_list":{"0":"post-17975","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-15","8":"entry"},"_links":{"self":[{"href":"https:\/\/skill-hacks.co.jp\/media\/wp-json\/wp\/v2\/posts\/17975","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/skill-hacks.co.jp\/media\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/skill-hacks.co.jp\/media\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/skill-hacks.co.jp\/media\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/skill-hacks.co.jp\/media\/wp-json\/wp\/v2\/comments?post=17975"}],"version-history":[{"count":0,"href":"https:\/\/skill-hacks.co.jp\/media\/wp-json\/wp\/v2\/posts\/17975\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/skill-hacks.co.jp\/media\/wp-json\/wp\/v2\/media\/16930"}],"wp:attachment":[{"href":"https:\/\/skill-hacks.co.jp\/media\/wp-json\/wp\/v2\/media?parent=17975"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/skill-hacks.co.jp\/media\/wp-json\/wp\/v2\/categories?post=17975"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/skill-hacks.co.jp\/media\/wp-json\/wp\/v2\/tags?post=17975"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}