{"id":376,"date":"2023-07-04T01:25:58","date_gmt":"2023-07-04T01:25:58","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e5%9e%82%e7%9b%b4%e6%bc%b8%e8%bf%91%e7%b7%9a\/"},"modified":"2023-07-04T01:25:58","modified_gmt":"2023-07-04T01:25:58","slug":"%e5%9e%82%e7%9b%b4%e6%bc%b8%e8%bf%91%e7%b7%9a","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e5%9e%82%e7%9b%b4%e6%bc%b8%e8%bf%91%e7%b7%9a\/","title":{"rendered":"\u5782\u76f4\u6f38\u8fd1\u7dda"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u95a2\u6570\u306e\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u793a\u3057\u307e\u3059 (\u4f8b\u3068\u3068\u3082\u306b)\u3002\u95a2\u6570\u306e\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u3092\u898b\u3064\u3051\u308b\u65b9\u6cd5\u3082\u8aac\u660e\u3057\u3066\u304a\u308a\u3001\u3055\u3089\u306b\u3001\u6bb5\u968e\u7684\u306b\u89e3\u304b\u308c\u305f\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-asintota-vertical\"><\/span>\u5782\u76f4\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u95a2\u6570\u306e\u5782\u76f4\u6f38\u8fd1\u7dda\u306f\u3001\u30b0\u30e9\u30d5\u304c\u6c7a\u3057\u3066\u4ea4\u308f\u308b\u3053\u3068\u306a\u304f\u7121\u9650\u306b\u8fd1\u3065\u304f\u5782\u76f4\u7dda\u3067\u3059\u3002<\/strong>\u3057\u305f\u304c\u3063\u3066\u3001\u5782\u76f4\u6f38\u8fd1\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f<em>x=k<\/em>\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u3001 <em>k<\/em>\u306f\u5782\u76f4\u6f38\u8fd1\u7dda\u306e\u5024\u3067\u3059\u3002<\/p>\n<p>\u3064\u307e\u308a\u3001 <strong><em>x \u304c<\/em><em>k<\/em>\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u95a2\u6570\u306e\u9650\u754c\u304c\u7121\u9650\u5927\u3067\u3042\u308b\u5834\u5408\u3001 <em>k<\/em>\u306f\u5782\u76f4\u6f38\u8fd1\u7dda\u306b\u306a\u308a\u307e\u3059\u3002<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/asymptote-verticale.webp\" alt=\"\u5782\u76f4\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u3067\u3059\u304b\" class=\"wp-image-1281\" width=\"320\" height=\"255\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-asintota-vertical-de-una-funcion\"><\/span>\u95a2\u6570\u306e\u5782\u76f4\u6f38\u8fd1\u7dda\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u95a2\u6570\u306e\u5782\u76f4\u6f38\u8fd1\u7dda\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u624b\u9806\u306b\u5f93\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;border:\">\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u95a2\u6570\u306e\u30c9\u30e1\u30a4\u30f3\u3092\u898b\u3064\u3051\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u70b9\u304c\u30c9\u30e1\u30a4\u30f3\u5185\u306b\u3042\u308b\u5834\u5408\u3001\u95a2\u6570\u306b\u306f\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u304c\u3042\u308a\u307e\u305b\u3093\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u30c9\u30e1\u30a4\u30f3\u5185\u306b\u306a\u3044\u70b9\u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6975\u9650\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/span><\/li>\n<li><span style=\"color:#101010;font-weight: normal;\">\u95a2\u6570\u306e\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u306f\u3001\u5236\u9650\u304c\u7121\u9650\u5927\u3068\u306a\u308b\u3059\u3079\u3066\u306e\u5024\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/li>\n<\/ol>\n<p>\u95a2\u6570\u306b\u306f\u8907\u6570\u306e\u5782\u76f4\u6f38\u8fd1\u7dda\u304c\u5b58\u5728\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u305f\u3068\u3048\u3070\u3001<u style=\"text-decoration-color:#FF9B28;\">\u6b63\u63a5\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306b\u306f\u3001\u7121\u9650\u306b\u591a\u304f\u306e\u5782\u76f4\u6f38\u8fd1\u7dda\u304c\u3042\u308a\u307e\u3059\u3002<\/u><\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u6b63\u63a5\u95a2\u6570\/\">\u6b63\u63a5\u95a2\u6570\u306e\u7279\u6027<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-asintota-vertical\"><\/span>\u5782\u76f4\u6f38\u8fd1\u7dda\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4f8b\u3068\u3057\u3066\u3001\u6b21\u306e\u6709\u7406\u95a2\u6570\u306e\u3059\u3079\u3066\u306e\u6f38\u8fd1\u7dda\u3092\u898b\u3064\u3051\u3066\u3001\u305d\u308c\u304c\u3069\u306e\u3088\u3046\u306b\u884c\u308f\u308c\u308b\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0425f9cc254c22f6e28ad2186732cfdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{1}{x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"101\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4e00\u822c\u306b\u3001\u5782\u76f4\u6f38\u8fd1\u7dda\u304c\u3042\u308b\u70b9\u306f\u95a2\u6570\u306e\u9818\u57df\u306b\u5c5e\u3057\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u521d\u306b\u95a2\u6570\u306e\u5b9a\u7fa9\u57df\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u306f\u6709\u7406\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u5206\u6bcd\u304c\u3044\u3064\u6d88\u3048\u308b\u304b\u306b\u6ce8\u76ee\u3057\u3066\u3001\u30c9\u30e1\u30a4\u30f3\u306b\u5c5e\u3055\u306a\u3044\u70b9\u3092\u7279\u5b9a\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e0aacb848a27943fc0e8fba70f545d78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306e\u5b9a\u7fa9\u57df\u306f x=2 \u3092\u9664\u304f\u3059\u3079\u3066\u5b9f\u6570\u3067\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-298deba50795b5fc3979441d68ef3ed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{2\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001 <strong>x=2 \u306f\u95a2\u6570\u306e\u5782\u76f4\u6f38\u8fd1\u7dda\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/strong>\u3053\u308c\u3092\u691c\u8a3c\u3059\u308b\u306b\u306f\u3001\u3053\u306e\u6642\u70b9\u3067\u306e\u95a2\u6570\u306e\u5236\u9650\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acc5425df8da5bffaa5ee31c29284a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2} \\frac{1}{x-2}=\\frac{1}{2-2}=\\frac{1}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u30bc\u30ed\u9593\u306e\u6570\u5024\u306e\u4e0d\u78ba\u5b9a\u6027\u304c\u5f97\u3089\u308c\u305f\u305f\u3081\u3001\u6975\u9650\u3092\u89e3\u6c7a\u3059\u308b\u306b\u306f\u3001\u6a2a\u65b9\u5411\u306e\u6975\u9650\u3092\u8a08\u7b97\u3057\u3066\u3001\u305d\u308c\u304c\u30d7\u30e9\u30b9\u7121\u9650\u5927\u306a\u306e\u304b\u30de\u30a4\u30ca\u30b9\u7121\u9650\u5927\u306a\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u6975\u9650\u304c\u5b58\u5728\u3057\u306a\u3044\u306e\u304b\u3092\u77e5\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u3092\u8a08\u7b97\u3059\u308b\u5834\u5408\u3001\u6a2a\u65b9\u5411\u306e\u6975\u9650\u3092\u884c\u3046\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u3053\u306e\u4e0d\u78ba\u5b9a\u6027\u304c\u5f97\u3089\u308c\u308c\u3070\u3001\u305d\u308c\u304c\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u3067\u3042\u308b\u3068\u8a00\u3048\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002<\/p>\n<p>\u3064\u307e\u308a\u3001x \u304c 2 \u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u95a2\u6570\u306e\u6975\u9650\u306f\u7121\u9650\u5927\u3068\u306a\u308b\u305f\u3081\u3001 <strong>x=2 \u306f\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u306b\u306a\u308a\u307e\u3059\u3002<\/strong><\/p>\n<p>\u4ee5\u4e0b\u306f\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u3067\u8868\u3057\u305f\u3082\u306e\u3067\u3059\u3002\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u3053\u308c\u306f (\u5de6\u3068\u53f3\u306e\u4e21\u65b9\u304b\u3089) x=2 \u306e\u7dda\u306b\u975e\u5e38\u306b\u8fd1\u3065\u3044\u3066\u3044\u307e\u3059\u304c\u3001\u5782\u76f4\u6f38\u8fd1\u7dda\u3067\u3042\u308b\u305f\u3081\u3001\u6c7a\u3057\u3066\u4ea4\u5dee\u3057\u307e\u305b\u3093\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-dasymptote-verticale.webp\" alt=\"\u5782\u76f4\u6f38\u8fd1\u7dda\u306e\u4f8b\" class=\"wp-image-1294\" width=\"431\" height=\"382\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u3055\u3089\u306b\u3001\u30b0\u30e9\u30d5\u304b\u3089\u70b9 x=2 \u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\u3092\u63a8\u6e2c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bae3e5d8a91ed8bfd4d59e8cf2b2e046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2^-} \\frac{1}{x-2} = -\\infty \\qquad  \\lim_{x \\to 2^+} \\frac{1}{x-2} = +\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"320\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-asintotas-verticales\"><\/span>\u5782\u76f4\u6f38\u8fd1\u7dda\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1<\/h3>\n<p>\u6b21\u306e\u6709\u7406\u95a2\u6570\u306e\u5782\u76f4\u6f38\u8fd1\u7dda\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-911fac1ac9244ceb5c6bff7e4bd14633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{3x-1}{2x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"110\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u95a2\u6570\u306e\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u3092\u8a08\u7b97\u3059\u308b\u516c\u5f0f\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u95a2\u6570\u306e\u5b9a\u7fa9\u57df\u3092\u898b\u3064\u3051\u3066\u3001\u95a2\u6570\u304c\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u306a\u3044\u70b9\u3067\u6975\u9650\u304c\u7121\u9650\u5927\u3068\u306a\u308b\u304b\u3092\u78ba\u8a8d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u30c9\u30e1\u30a4\u30f3\u306b\u5c5e\u3055\u306a\u3044\u70b9\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b\u3001\u6709\u7406\u95a2\u6570\u306e\u5206\u6bcd\u3092 0 \u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eda4c745b07ad63c3060964038aebf0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x -1 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0323089c11e731c307ef7664ecb6710b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x= 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-971df94c9decb86065329338ff4b81ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"45\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306e\u5b9a\u7fa9\u57df\u306f x=1\/2 \u3092\u9664\u304f\u3059\u3079\u3066\u5b9f\u6570\u3067\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d45cfed65d2da3a61311dce298a529a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{ \\cfrac{1}{2} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"149\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001x=1\/2 \u306f\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u78ba\u8a8d\u3059\u308b\u305f\u3081\u306b\u3001\u3053\u306e\u6642\u70b9\u3067\u306e\u95a2\u6570\u306e\u5236\u9650\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-55047465393cc2a65a7214fa64eac93d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to \\frac{1}{2} } \\cfrac{3x-1}{2x-1} = \\cfrac{3\\cdot\\cfrac{1}{2}-1}{2\\cdot\\cfrac{1}{2}-1} = \\cfrac{ \\cfrac{3}{2} -1 }{\\cfrac{2}{2} -1 } = \\cfrac{ \\cfrac{1}{2} }{1-1}=\\cfrac{\\cfrac{1}{2}}{0} =\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"84\" width=\"383\" style=\"vertical-align: -39px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u70b9\u3067\u306e\u95a2\u6570\u306e\u6975\u9650\u306f\u7121\u9650\u5927\u3092\u4e0e\u3048\u308b\u305f\u3081\u3001 <strong>x=1\/2 \u306f\u5782\u76f4\u6f38\u8fd1\u7dda\u306b\u306a\u308a\u307e\u3059<\/strong>\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 2<\/h3>\n<p>\u6b21\u306e\u5206\u6570\u95a2\u6570\u306e\u3059\u3079\u3066\u306e\u5782\u76f4\u6f38\u8fd1\u7dda\u3092\u6c42\u3081\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cc3badbfcece4b7976d30989606ca685_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{2x+1}{x^2-9}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"110\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u307e\u305a\u3001\u5206\u6570\u306e\u5206\u6bcd\u3092\u30bc\u30ed\u306b\u8a2d\u5b9a\u3057\u3066\u3001\u3069\u306e\u5024\u304c\u95a2\u6570\u306e\u9818\u57df\u306b\u542b\u307e\u308c\u306a\u3044\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce55adbc277e9378607d68bce8ef19fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-9=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e0d\u5b8c\u5168\u306a\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304d\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05112cb5a98f653cd1920fb40e5ef9a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0505454de5d542ace3e698cb903893ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\pm 3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u6709\u7406\u95a2\u6570\u306e\u5b9a\u7fa9\u57df\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c91231eb4c883e8c625dba58f070307f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{3, -3\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u308c\u3089 2 \u3064\u306e\u5024\u306e\u3069\u3061\u3089\u304c\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u3067\u3042\u308b\u304b\u3092\u5224\u65ad\u3059\u308b\u306b\u306f\u3001\u5404\u70b9\u3067\u306e\u95a2\u6570\u306e\u6975\u9650\u3092\u89e3\u304d\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1a56d9ceafa2628b7a80603109ceafc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 3}\\frac{2x+1}{x^2-9}=\\frac{2\\cdot3+1}{3^2-9}=\\frac{7}{9-9}=\\frac{7}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"317\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-944d84ad3ab51829df2623a4467cc16a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -3}\\frac{2x+1}{x^2-9}=\\frac{2\\cdot(-3)+1}{(-3)^2-9}=\\frac{-5}{9-9}=\\frac{-5}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"369\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> 2 \u3064\u306e\u6975\u9650\u306f\u7121\u9650\u5927\u3092\u4e0e\u3048\u308b\u305f\u3081\u3001 <strong>x=3 \u3068 x=-3 \u306f\u554f\u984c\u306e\u95a2\u6570 \u306e 2 \u3064\u306e\u5782\u76f4\u6f38\u8fd1\u7dda\u306b\u306a\u308a\u307e\u3059<\/strong>\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 3<\/h3>\n<p>\u6b21\u306e\u6709\u7406\u95a2\u6570\u306e\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u3092\u3059\u3079\u3066\u898b\u3064\u3051\u307e\u3059 (\u3042\u308b\u5834\u5408)\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1dd8356a2f682824a334f15826b31c89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{x+3}{x^2+2x-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"150\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u30bb\u3099\u30ed\u9593\u306e\u30bb\u3099\u30ed-0-0-\u4e0d\u5b9a\/\">\u30bc\u30ed\u9593\u306e\u30bc\u30ed\u4e0d\u78ba\u5b9a\u6027<\/a><\/span><\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u53c2\u7167<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u307e\u305a\u3001\u4e8c\u6b21\u5206\u6bcd\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u3001\u5206\u6570\u306e\u5206\u6bcd\u3092\u6253\u3061\u6d88\u3059\u5024\u3092\u898b\u3064\u3051\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5c5fd813f4a2456efa315766ad90ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+2x-3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b2170358d5d1719077695aba5afa02e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle x&amp;=\\cfrac{-b\\pm\\sqrt{b^2-4ac}}{2a}=\\cfrac{-2\\pm\\sqrt{2^2-4\\cdot1\\cdot(-3)}}{2\\cdot1}=\\\\[3ex]\\displaystyle &amp;=\\cfrac{-2\\pm\\sqrt{16}}{2}=\\cfrac{-2\\pm 4}{2}=\\begin{cases}\\cfrac{-2+4}{2}=1\\\\[3ex]\\cfrac{-2-4}{2}=-3\\end{cases}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"172\" width=\"396\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306e\u30c9\u30e1\u30a4\u30f3\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fd230a1caa7456bca8746870a6d0264a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{1, -3\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u521d\u306b x=1 \u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6975\u9650\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3784526cad2b36766a213c13a5938c6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1}\\frac{x+3}{x^2+2x-3}=\\frac{1+3}{1^2+2\\cdot 1-3}=\\frac{4}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"328\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65b9\u3001x \u304c -3 \u306b\u5411\u304b\u3046\u50be\u5411\u304c\u3042\u308b\u5834\u5408\u306e\u95a2\u6570\u306e\u6975\u9650\u3092\u89e3\u304d\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f0e96a48986cd110e04058e3545290a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x \\to -3}\\frac{x+3}{x^2+2x-3}=\\frac{-3+3}{(-3)^2+2\\cdot(-3)-3}=\\frac{0}{0}=\\\\[3ex]\\displaystyle =\\lim_{x \\to -3}\\frac{\\cancel{x+3}}{(x-1)\\cancel{(x+3)}}=\\lim_{x \\to -3}\\frac{1}{x-1}=\\frac{1}{-3-1}=-\\frac{1}{4}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"94\" width=\"413\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u524d\u306e\u5236\u9650\u3067\u306f\u3001\u30bc\u30ed\u9593\u306e\u4e0d\u5b9a\u5f62\u5f0f\u30bc\u30ed\u304c\u5f97\u3089\u308c\u308b\u305f\u3081\u3001\u3053\u308c\u3092\u89e3\u6c7a\u3059\u308b\u306b\u306f\u3001\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<u style=\"text-decoration-color:#FF9B28;\">\u5236\u9650\u3092\u3069\u306e\u3088\u3046\u306b\u89e3\u6c7a\u3057\u305f\u304b\u306b\u3064\u3044\u3066\u7591\u554f\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u6f14\u7fd2\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u3078\u306e\u30ea\u30f3\u30af\u3067\u3001\u3053\u306e\u7a2e\u306e\u4e0d\u78ba\u5b9a\u6027\u3092\u89e3\u6c7a\u3059\u308b\u65b9\u6cd5\u306e\u5b8c\u5168\u306a\u8aac\u660e\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/u><\/p>\n<p class=\"has-text-align-left\">\u3053\u306e\u5834\u5408\u3001\u70b9 x=1 \u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6975\u9650\u306e\u307f\u304c\u7121\u9650\u5927\u3092\u4e0e\u3048\u308b\u305f\u3081\u3001 <strong>x=1 \u306f\u95a2\u6570 \u306e\u552f\u4e00\u306e\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u306b\u306a\u308a\u307e\u3059<\/strong>\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u95a2\u6570\u306e\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u793a\u3057\u307e\u3059 (\u4f8b\u3068\u3068\u3082\u306b)\u3002\u95a2\u6570\u306e\u5782\u76f4\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u3092\u898b\u3064\u3051\u308b\u65b9\u6cd5\u3082\u8aac\u660e\u3057\u3066\u304a\u308a\u3001\u3055\u3089\u306b\u3001\u6bb5\u968e\u7684\u306b\u89e3\u304b\u308c\u305f\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u5782\u76f4\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u3067\u3059\u304b? \u95a2\u6570\u306e\u5782\u76f4\u6f38\u8fd1 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e5%9e%82%e7%9b%b4%e6%bc%b8%e8%bf%91%e7%b7%9a\/\"> <span class=\"screen-reader-text\">\u5782\u76f4\u6f38\u8fd1\u7dda<\/span> \u3082\u3063\u3068\u8aad\u3080 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