{"id":34314,"date":"2024-11-12T13:00:40","date_gmt":"2024-11-12T13:00:40","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34314"},"modified":"2025-09-07T01:53:49","modified_gmt":"2025-09-07T01:53:49","slug":"%e7%84%a1%e9%99%90%e9%99%90%e7%95%8c%e3%81%a8%e7%99%ba%e6%95%a3","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/%e7%84%a1%e9%99%90%e9%99%90%e7%95%8c%e3%81%a8%e7%99%ba%e6%95%a3\/","title":{"rendered":"\u7121\u9650\u9650\u754c\u3068\u767a\u6563"},"content":{"rendered":"<style>\np {\ntext-align: justify;}\n<\/style>\n<p><center><\/p>\n<h1>\u7121\u9650\u9650\u754c\u3068\u767a\u6563<\/h1>\n<p style=\"text-align:center;\"><em><strong>\u8981\u7d04:<\/strong><br \/>\n\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u7121\u9650\u9650\u754c\u304a\u3088\u3073\u9650\u754c\u306b\u304a\u3051\u308b\u3055\u307e\u3056\u307e\u306a\u767a\u6563\u306e\u5f62\u614b\u306b\u3064\u3044\u3066\u53d6\u308a\u4e0a\u3052\u3001\u7279\u5b9a\u306e\u95a2\u6570\u304c\u5b9a\u7fa9\u3055\u308c\u305f\u5b9f\u6570\u5024\u306b\u53ce\u675f\u3057\u306a\u3044\u7406\u7531\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306e\u57fa\u672c\u6982\u5ff5\u3092\u63a2\u7a76\u3059\u308b\u3002\u5de6\u53f3\u306e\u7570\u306a\u308b\u7247\u5074\u6975\u9650\u3001\u7121\u9650\u306b\u632f\u52d5\u3059\u308b\u95a2\u6570\u3001\u305d\u3057\u3066\u5b9a\u7fa9\u57df\u306e\u554f\u984c\u3084\u7121\u9650\u306e\u5897\u52a0\u306b\u3088\u308a\u9650\u754c\u304c\u5b58\u5728\u3057\u306a\u3044\u72b6\u6cc1\u3092\u78ba\u8a8d\u3059\u308b\u3002<br \/>\n<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u7fd2\u76ee\u6a19:<\/strong><br \/>\n\u672c\u8b1b\u7fa9\u3092\u7d42\u3048\u308b\u6642\u3001\u5b66\u751f\u306f\u4ee5\u4e0b\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3002\n<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u5b9a\u7fa9\u3059\u308b<\/strong> \u767a\u6563\u3059\u308b\u9650\u754c\u3092\u5b9a\u7fa9\u3057\u3001\u3044\u3064\u9650\u754c\u304c\u767a\u6563\u3059\u308b\u304b\u3092\u8a8d\u8b58\u3059\u308b\u3002<\/li>\n<li><strong>\u8b58\u5225\u3059\u308b<\/strong> \u9650\u754c\u306b\u304a\u3051\u308b\u3055\u307e\u3056\u307e\u306a\u767a\u6563\u306e\u7a2e\u985e\u3092\u3001\u4f8b\u3048\u3070\u5de6\u53f3\u306e\u7570\u306a\u308b\u7247\u5074\u6975\u9650\u3084\u7121\u9650\u9650\u754c\u3092\u542b\u3081\u3066\u8b58\u5225\u3059\u308b\u3002<\/li>\n<li><strong>\u5206\u6790\u3059\u308b<\/strong> \u95a2\u6570\u304c\u5b9a\u7fa9\u57df\u306b\u554f\u984c\u3092\u6301\u3064\u72b6\u6cc1\u3092\u5206\u6790\u3057\u3001\u305d\u308c\u304c\u9650\u754c\u306e\u5b58\u5728\u306b\u3069\u306e\u3088\u3046\u306b\u5f71\u97ff\u3059\u308b\u304b\u3092\u7406\u89e3\u3059\u308b\u3002<\/li>\n<li><strong>\u8a55\u4fa1\u3059\u308b<\/strong> \u7247\u5074\u6975\u9650\u3092\u8a55\u4fa1\u3057\u3001\u305d\u308c\u3089\u304c\u7570\u306a\u308b\u304b\u3069\u3046\u304b\u3001\u307e\u305f\u305d\u308c\u304c\u9650\u754c\u306e\u53ce\u675f\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u3092\u5224\u65ad\u3059\u308b\u3002<\/li>\n<li><strong>\u8a08\u7b97\u3059\u308b<\/strong> \u7121\u9650\u9650\u754c\u3092\u8a08\u7b97\u3057\u3001\u9650\u754c\u304c\u6b63\u306e\u7121\u9650\u5927\u3078\u767a\u6563\u3059\u308b\u306e\u304b\u3001\u8ca0\u306e\u7121\u9650\u5927\u3078\u767a\u6563\u3059\u308b\u306e\u304b\u3092\u533a\u5225\u3059\u308b\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\">\n<u><strong>\u76ee\u6b21<\/strong><\/u>:<br \/>\n<a href=\"#1\"><strong>\u3044\u3064\u9650\u754c\u304c\u767a\u6563\u3059\u308b\u3068\u8a00\u3046\u306e\u304b\uff1f<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u9650\u754c\u306b\u304a\u3051\u308b\u767a\u6563\u306e\u7a2e\u985e<\/strong><\/a><br \/>\n<a href=\"#3\">\u5b9a\u7fa9\u57df\u306b\u554f\u984c\u306e\u3042\u308b\u9650\u754c<\/a><br \/>\n<a href=\"#4\">\u5de6\u53f3\u306e\u7570\u306a\u308b\u7247\u5074\u6975\u9650<\/a><br \/>\n<a href=\"#5\">\u7121\u9650\u306b\u632f\u52d5\u3059\u308b\u95a2\u6570\u306e\u9650\u754c<\/a><br \/>\n<a href=\"#6\">\u7121\u9650\u9650\u754c<\/a><br \/>\n<a href=\"#7\">\u7121\u9650\u9060\u306b\u304a\u3051\u308b\u7121\u9650\u9650\u754c<\/a>\n<\/p>\n<p><\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/SFBMSd0Q7Io\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p>\u4eca\u56de\u306f<strong>\u7121\u9650\u9650\u754c<\/strong>\u3060\u3051\u3067\u306a\u304f\u3001\u4e00\u822c\u7684\u306b<strong>\u767a\u6563\u3059\u308b\u9650\u754c<\/strong>\u306b\u3064\u3044\u3066\u3082\u78ba\u8a8d\u3059\u308b\u3002\u767a\u6563\u3059\u308b\u9650\u754c\u306f\u3001\u95a2\u6570\u304c\u53ce\u675f\u3057\u306a\u3044\u3088\u3046\u306b\u898b\u3048\u308b\u72b6\u6cc1\u3092\u793a\u3057\u3001\u305d\u308c\u306f\u591a\u69d8\u306a\u5f62\u3067\u751f\u3058\u5f97\u308b\u3002<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u3044\u3064\u9650\u754c\u304c\u767a\u6563\u3059\u308b\u3068\u8a00\u3046\u306e\u304b\uff1f<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=106s\" target=\"_blank\" rel=\"noopener\"><strong>\u9650\u754c\u304c\u3042\u308b\u5b9f\u6570\u5024\u306b\u53ce\u675f\u3057\u306a\u3044\u3068\u304d\u3001\u305d\u306e\u9650\u754c\u306f\u767a\u6563\u3059\u308b\u3068\u8a00\u3046\u3002<\/strong><\/a> \u3053\u306e\u4e00\u898b\u81ea\u660e\u306b\u805e\u3053\u3048\u308b\u3053\u3068\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u5f62\u3067\u751f\u3058\u5f97\u308b\u3002<\/p>\n<ul>\n<li>\u7247\u5074\u6975\u9650\u304c\u7570\u306a\u308b\u304b\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3001\u4e21\u5074\u6975\u9650\u306f\u5b58\u5728\u3057\u306a\u3044\u3002<\/li>\n<li>\u95a2\u6570\u304c\u6b63\u3057\u304f\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u7121\u9650\u306b\u5897\u5927\u3059\u308b\u5834\u5408\u3001\u307e\u305f\u306f\u8a08\u7b97\u5bfe\u8c61\u306e\u70b9\u306b\u8fd1\u3065\u304f\u969b\u306b\u7121\u9650\u306b\u632f\u52d5\u3059\u308b\u5834\u5408\u3001\u305d\u306e\u7247\u5074\u6975\u9650\u306f\u5b58\u5728\u3057\u5f97\u306a\u3044\u3002<\/li>\n<\/ul>\n<p>\u3053\u308c\u306f\u3001\u6709\u9650\u306e\u9650\u754c\u306b\u3082\u3001\u7121\u9650\u9060\u306b\u304a\u3051\u308b\u9650\u754c\u306b\u3082\u3001\u305d\u308c\u305e\u308c\u306e\u7279\u5fb4\u3092\u6301\u3063\u3066\u9069\u7528\u3055\u308c\u3001\u72b6\u6cc1\u306b\u5fdc\u3058\u3066\u4f55\u3089\u304b\u306e\u767a\u6563\u306e\u5f62\u3092\u6301\u3064\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u9650\u754c\u306b\u304a\u3051\u308b\u767a\u6563\u306e\u7a2e\u985e<\/h2>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u5b9a\u7fa9\u57df\u306b\u554f\u984c\u306e\u3042\u308b\u9650\u754c<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=210s\" target=\"_blank\" rel=\"noopener\"><strong>\u6b21\u306e\u3088\u3046\u306a\u9650\u754c\u3092\u8a08\u7b97\u3057\u3088\u3046\u3068\u3059\u308b\u5834\u5408 <\/strong><\/a><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to x_0}f(x)<\/span> \u307e\u305f\u306f <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to +\\infty}f(x),<\/span> \u5c11\u306a\u304f\u3068\u3082 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u304c <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u4ed8\u8fd1\u306e\u5024\u3001\u3042\u308b\u3044\u306f <span class=\"katex-eq\" data-katex-display=\"false\">[a,+\\infty[ <\/span> \u306e\u5f62\u306e\u533a\u9593\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u671f\u5f85\u3059\u308b\u3002\u3082\u3057\u305d\u3046\u3067\u306a\u3051\u308c\u3070\u3001\u3044\u305a\u308c\u306e\u9650\u754c\u306e\u5b9a\u7fa9\u3082\u610f\u5473\u3092\u6301\u305f\u306a\u3044\u3002\u95a2\u6570\u304c\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u306a\u3044\u9818\u57df\u306b\u8fd1\u3065\u304f\u306e\u3067\u3042\u308c\u3070\u3001\u5024\u306b\u300c\u8fd1\u3065\u304f\u300d\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002\u3053\u306e\u3088\u3046\u306a\u5834\u5408\u3001\u5358\u306b\u9650\u754c\u306f\u5b58\u5728\u3057\u306a\u3044\u3068\u8a18\u3059: <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to x_0}f(x)=\\cancel{\\exists}<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to +\\infty}f(x)=\\cancel{\\exists},<\/span> \u3068\u3059\u308b\u3002\u7247\u5074\u6975\u9650\u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u3067\u3042\u308a\u3001\u3053\u306e\u7a2e\u306e\u72b6\u6cc1\u306b\u3064\u3044\u3066\u3053\u308c\u4ee5\u4e0a\u8ff0\u3079\u308b\u3053\u3068\u306f\u306a\u3044\u3002<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u5de6\u53f3\u306e\u7570\u306a\u308b\u7247\u5074\u6975\u9650<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=180s\" target=\"_blank\" rel=\"noopener\"><strong>\u6b21\u306e\u3088\u3046\u306a\u95a2\u6570\u3092\u8003\u3048\u3066\u307f\u3088\u3046<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = x\/|x|<\/span> \u305d\u3057\u3066 <span class=\"katex-eq\" data-katex-display=\"false\">x\\to 0<\/span> \u306e\u3068\u304d\u306e\u9650\u754c\u3092\u8a08\u7b97\u3059\u308b\u3002\u6700\u521d\u306b\u6c17\u3065\u304f\u306e\u306f\u6b21\u306e\u70b9\u3067\u3042\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0^+} f(x) = 1<\/span>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0^-} f(x) = -1<\/span>\n<p>\u3053\u306e\u5834\u5408\u3001\u7247\u5074\u6975\u9650\u306f\u5b58\u5728\u3059\u308b\u304c\u3001\u305d\u308c\u3089\u306f\u7570\u306a\u308b\u3002\u3053\u308c\u304c\u8d77\u3053\u308b\u3068\u304d\u3001\u4e21\u5074\u306e\u9650\u754c\u306f\u53ce\u675f\u3057\u306a\u3044\u3068\u8a00\u3044\u3001\u3057\u305f\u304c\u3063\u3066\u6b21\u306e\u3088\u3046\u306b\u8a18\u3059\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0} f(x) = \\cancel{\\exists}<\/span>\n<p><a name=\"5\"><\/a><\/p>\n<h3>\u7121\u9650\u306b\u632f\u52d5\u3059\u308b\u95a2\u6570\u306e\u9650\u754c<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=415s\" target=\"_blank\" rel=\"noopener\"><strong>\u307e\u305f\u3001\u7279\u5b9a\u306e\u5024\u306b\u8fd1\u3065\u304f\u306e\u3067\u306f\u306a\u304f<\/strong><\/a>\u3001\u3042\u308b\u7bc4\u56f2\u5185\u3067\u632f\u52d5\u3057\u59cb\u3081\u308b\u95a2\u6570\u306e\u5834\u5408\u3082\u3042\u308b\u3002\u305d\u306e\u4f8b\u3068\u3057\u3066 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)= \\sin(1\/x)<\/span> \u306e\u3088\u3046\u306a\u95a2\u6570\u304c\u3042\u308b\u3002\u3053\u306e\u95a2\u6570\u304c <span class=\"katex-eq\" data-katex-display=\"false\">x\\to 0<\/span> \u306e\u3068\u304d\u306b\u3069\u3046\u306a\u308b\u304b\u3092\u898b\u308b\u3068\u3001\u7121\u9650\u306b\u632f\u52d5\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-vrdcIAmLV50\/YGoC903Q62I\/AAAAAAAAE1M\/6AM7D-RM9lAy9ZrG105MbfCN8ltu6J09ACLcBGAsYHQ\/s0\/sin1sobrex.PNG\" alt=\"f(x) = sin(1\/x)\" class=\"alignnone size-full lazyload\" width=\"856\" height=\"442\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-vrdcIAmLV50\/YGoC903Q62I\/AAAAAAAAE1M\/6AM7D-RM9lAy9ZrG105MbfCN8ltu6J09ACLcBGAsYHQ\/s0\/sin1sobrex.PNG\" alt=\"f(x) = sin(1\/x)\" class=\"alignnone size-full lazyload\" width=\"856\" height=\"442\" \/><\/noscript><\/p>\n<p>\u3053\u306e\u3088\u3046\u306a\u5834\u5408\u3001\u9650\u754c\u306f\u5358\u306b\u5b58\u5728\u3057\u306a\u3044\u3068\u8a00\u3046\u3002<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u7121\u9650\u9650\u754c<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=658s\" target=\"_blank\" rel=\"noopener\"><strong>\u6b21\u306b\u95a2\u6570<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = 1\/x.<\/span> \u3092\u898b\u3066\u307f\u3088\u3046\u3002\u6700\u521d\u306b\u308f\u304b\u308b\u306e\u306f\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x\\to 0<\/span> \u306e\u3068\u304d <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u306e\u5024\u304c\u9650\u308a\u306a\u304f\u5927\u304d\u304f\u306a\u308b\u304c\u3001\u305d\u306e\u69d8\u5b50\u306f\u9650\u754c\u3092\u3069\u3053\u304b\u3089\u8a08\u7b97\u3059\u308b\u304b\u306b\u3088\u3063\u3066\u7570\u306a\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002\u76f4\u611f\u7684\u306b\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0^+} \\dfrac{1}{x} = +\\infty<\/span>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0^-} \\dfrac{1}{x} = -\\infty<\/span>\n<p>\u3053\u306e\u8868\u8a18\u306f\u9650\u754c\u304c\u4f55\u3089\u304b\u306e\u5f62\u3067\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u305d\u306e\u9650\u754c\u304c\u5b58\u5728\u3057\u306a\u3044\u4ed5\u65b9\u3092\u793a\u3057\u3066\u3044\u308b\u3002\u524d\u306e\u4e8b\u4f8b\u3067\u306f\u9650\u754c\u304c\u5b58\u5728\u3057\u306a\u3044\u306e\u306f\u5177\u4f53\u7684\u306a\u5024\u306b\u53ce\u675f\u3057\u306a\u3044\u304b\u3089\u3067\u3042\u3063\u305f\u304c\u3001\u3053\u306e\u5834\u5408\u306f\u5024\u306e\u5927\u304d\u3055\u304c\u3042\u3089\u3086\u308b\u5b9f\u6570\u3092\u8d85\u3048\u3066\u3057\u307e\u3046\u305f\u3081\u306b\u767a\u6563\u3059\u308b\u306e\u3067\u3042\u308b\u3002<\/p>\n<p>\u4eca\u78ba\u8a8d\u3057\u305f\u3053\u3068\u306f\u3001\u6b21\u306e\u5b9a\u7fa9\u3092\u901a\u3058\u3066\u5f62\u5f0f\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0^+}f(x) = +\\infty := \\left(\\forall M \\in \\mathbb{R}\\right)\\left( \\exists \\delta \\gt 0 \\right) ( x_0 \\lt x \\lt x_0 + \\delta \\rightarrow M \\lt f(x) )<\/span>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0^-}f(x) = +\\infty := \\left(\\forall M \\in \\mathbb{R}\\right)\\left( \\exists \\delta \\gt 0 \\right) ( x_0 - \\delta \\lt x \\lt x_0 \\rightarrow M \\lt f(x) )<\/span>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0}f(x) = +\\infty := \\left(\\lim_{x\\to x_0^+}f(x) = +\\infty \\right) \\wedge \\left(\\lim_{x\\to x_0^-}f(x) = +\\infty \\right)<\/span>\n<p>\u540c\u69d8\u306b\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0^+}f(x) = -\\infty := \\left(\\forall m \\in \\mathbb{R}\\right)\\left( \\exists \\delta \\gt 0 \\right) ( x_0 \\lt x \\lt x_0 + \\delta \\rightarrow f(x) \\lt m )<\/span>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0^-}f(x) = -\\infty := \\left(\\forall m \\in \\mathbb{R}\\right)\\left( \\exists \\delta \\gt 0 \\right) ( x_0 - \\delta \\lt x \\lt x_0 \\rightarrow f(x) \\lt m )<\/span>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0}f(x) = -\\infty := \\left(\\lim_{x\\to x_0^+}f(x) = -\\infty \\right) \\wedge \\left(\\lim_{x\\to x_0^-}f(x) = -\\infty \\right)<\/span>\n<p>\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u7b26\u53f7\u3092\u4f34\u308f\u306a\u3044\u7121\u9650\u5927\u306b\u53ce\u675f\u3059\u308b\u9650\u754c\u306b\u3064\u3044\u3066\u3082\u8a00\u53ca\u3055\u308c\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0}f(x) = \\infty := \\lim_{x\\to x_0}|f(x)| = +\\infty <\/span>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u7121\u9650\u9060\u306b\u304a\u3051\u308b\u7121\u9650\u9650\u754c<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=1147s\" target=\"_blank\" rel=\"noopener\"><strong>\u3053\u308c\u307e\u3067\u78ba\u8a8d\u3057\u305f\u9650\u754c\u3068\u540c\u69d8\u306b\u3001<\/strong><\/a> \u7121\u9650\u9060\u306b\u304a\u3051\u308b\u7121\u9650\u9650\u754c\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u308b\u3002\u4f8b\u3048\u3070:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to +\\infty}f(x) = +\\infty := \\left(\\forall M \\in \\mathbb{R}\\right)\\left( \\exists N \\in\\mathbb{R} \\right) ( N\\lt x \\rightarrow M \\lt f(x) )<\/span>\n<p>\u3053\u308c\u3067\u95a2\u6570\u306e\u9650\u754c\u304c\u767a\u6563\u3057\u5f97\u308b\u3059\u3079\u3066\u306e\u5f62\u3092\u78ba\u8a8d\u3057\u305f\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7121\u9650\u9650\u754c\u3068\u767a\u6563 \u8981\u7d04: \u672c\u8b1b\u7fa9\u3067\u306f\u3001\u7121\u9650\u9650\u754c\u304a\u3088\u3073\u9650\u754c\u306b\u304a\u3051\u308b\u3055\u307e\u3056\u307e\u306a\u767a\u6563\u306e\u5f62\u614b\u306b\u3064\u3044\u3066\u53d6\u308a\u4e0a\u3052\u3001\u7279\u5b9a\u306e\u95a2\u6570\u304c\u5b9a\u7fa9\u3055\u308c\u305f\u5b9f\u6570\u5024\u306b\u53ce\u675f\u3057\u306a\u3044\u7406\u7531\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306e\u57fa\u672c\u6982\u5ff5\u3092\u63a2\u7a76\u3059\u308b\u3002\u5de6\u53f3\u306e\u7570\u306a\u308b\u7247\u5074\u6975\u9650\u3001\u7121\u9650\u306b\u632f\u52d5\u3059\u308b\u95a2\u6570\u3001\u305d\u3057\u3066\u5b9a\u7fa9\u57df\u306e\u554f\u984c\u3084\u7121\u9650\u306e\u5897\u52a0\u306b\u3088\u308a\u9650\u754c\u304c\u5b58\u5728\u3057\u306a\u3044\u72b6\u6cc1\u3092\u78ba\u8a8d\u3059\u308b\u3002 \u5b66\u7fd2\u76ee\u6a19: \u672c\u8b1b\u7fa9\u3092\u7d42\u3048\u308b\u6642\u3001\u5b66\u751f\u306f\u4ee5\u4e0b\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3002 \u5b9a\u7fa9\u3059\u308b \u767a\u6563\u3059\u308b\u9650\u754c\u3092\u5b9a\u7fa9\u3057\u3001\u3044\u3064\u9650\u754c\u304c\u767a\u6563\u3059\u308b\u304b\u3092\u8a8d\u8b58\u3059\u308b\u3002 \u8b58\u5225\u3059\u308b \u9650\u754c\u306b\u304a\u3051\u308b\u3055\u307e\u3056\u307e\u306a\u767a\u6563\u306e\u7a2e\u985e\u3092\u3001\u4f8b\u3048\u3070\u5de6\u53f3\u306e\u7570\u306a\u308b\u7247\u5074\u6975\u9650\u3084\u7121\u9650\u9650\u754c\u3092\u542b\u3081\u3066\u8b58\u5225\u3059\u308b\u3002 \u5206\u6790\u3059\u308b \u95a2\u6570\u304c\u5b9a\u7fa9\u57df\u306b\u554f\u984c\u3092\u6301\u3064\u72b6\u6cc1\u3092\u5206\u6790\u3057\u3001\u305d\u308c\u304c\u9650\u754c\u306e\u5b58\u5728\u306b\u3069\u306e\u3088\u3046\u306b\u5f71\u97ff\u3059\u308b\u304b\u3092\u7406\u89e3\u3059\u308b\u3002 \u8a55\u4fa1\u3059\u308b \u7247\u5074\u6975\u9650\u3092\u8a55\u4fa1\u3057\u3001\u305d\u308c\u3089\u304c\u7570\u306a\u308b\u304b\u3069\u3046\u304b\u3001\u307e\u305f\u305d\u308c\u304c\u9650\u754c\u306e\u53ce\u675f\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u3092\u5224\u65ad\u3059\u308b\u3002 \u8a08\u7b97\u3059\u308b \u7121\u9650\u9650\u754c\u3092\u8a08\u7b97\u3057\u3001\u9650\u754c\u304c\u6b63\u306e\u7121\u9650\u5927\u3078\u767a\u6563\u3059\u308b\u306e\u304b\u3001\u8ca0\u306e\u7121\u9650\u5927\u3078\u767a\u6563\u3059\u308b\u306e\u304b\u3092\u533a\u5225\u3059\u308b\u3002 \u76ee\u6b21: \u3044\u3064\u9650\u754c\u304c\u767a\u6563\u3059\u308b\u3068\u8a00\u3046\u306e\u304b\uff1f \u9650\u754c\u306b\u304a\u3051\u308b\u767a\u6563\u306e\u7a2e\u985e \u5b9a\u7fa9\u57df\u306b\u554f\u984c\u306e\u3042\u308b\u9650\u754c \u5de6\u53f3\u306e\u7570\u306a\u308b\u7247\u5074\u6975\u9650 \u7121\u9650\u306b\u632f\u52d5\u3059\u308b\u95a2\u6570\u306e\u9650\u754c \u7121\u9650\u9650\u754c 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