{"id":34302,"date":"2024-10-22T13:00:53","date_gmt":"2024-10-22T13:00:53","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34302"},"modified":"2025-09-07T01:44:18","modified_gmt":"2025-09-07T01:44:18","slug":"%e7%84%a1%e9%99%90%e5%a4%a7%e3%81%ab%e3%81%8a%e3%81%91%e3%82%8b%e6%a5%b5%e9%99%90%ef%bc%9a%e5%ae%9a%e7%be%a9%e3%81%a8%e4%be%8b","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/%e7%84%a1%e9%99%90%e5%a4%a7%e3%81%ab%e3%81%8a%e3%81%91%e3%82%8b%e6%a5%b5%e9%99%90%ef%bc%9a%e5%ae%9a%e7%be%a9%e3%81%a8%e4%be%8b\/","title":{"rendered":"\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\uff1a\u5b9a\u7fa9\u3068\u4f8b"},"content":{"rendered":"<p><center><\/p>\n<h1>\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\uff1a\u5b9a\u7fa9\u3068\u4f8b<\/h1>\n<p><em><\/p>\n<p><strong>\u8981\u7d04:<\/strong><br \/>\n\u3053\u306e\u6388\u696d\u3067\u306f\u3001<span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u304c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u6319\u52d5\u306b\u3064\u3044\u3066\u6271\u3046\u3002\u57fa\u672c\u7684\u306a\u6975\u9650\u3001\u4f8b\u3048\u3070 <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to \\infty} \\frac{1}{x} = 0<\/span> \u3084 <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to \\infty} k = k<\/span> \u3092\u8aac\u660e\u3057\u3001\u6709\u9650\u306e\u6975\u9650\u3068\u985e\u4f3c\u3057\u305f\u4ee3\u6570\u7684\u6027\u8cea\u306b\u3064\u3044\u3066\u3082\u8ff0\u3079\u308b\u3002\n<\/p>\n<p><\/em><\/p>\n<p><strong>\u5b66\u7fd2\u76ee\u6a19:<\/strong><br \/>\n\u672c\u6388\u696d\u306e\u7d42\u4e86\u6642\u306b\u3001\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u8aac\u660e\u3059\u308b<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u304c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u6319\u52d5\u3002<\/li>\n<li><strong>\u5b9a\u7fa9\u3059\u308b<\/strong> \u6570\u5b66\u7684\u5f62\u5f0f\u7684\u8a18\u6cd5\u3092\u7528\u3044\u305f\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u3002<\/li>\n<li><strong>\u9069\u7528\u3059\u308b<\/strong> \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u8a08\u7b97\u306b\u304a\u3051\u308b\u4ee3\u6570\u7684\u6027\u8cea\u3002<\/li>\n<li><strong>\u533a\u5225\u3059\u308b<\/strong> \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6709\u7406\u95a2\u6570\u306e\u7570\u306a\u308b\u5834\u5408\u306e\u6975\u9650\u3002<\/li>\n<li><strong>\u8a3c\u660e\u3059\u308b<\/strong> \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306b\u95a2\u3059\u308b\u548c\u3001\u5dee\u3001\u7a4d\u3001\u5546\u304a\u3088\u3073\u3079\u304d\u306e\u6027\u8cea\u306e\u59a5\u5f53\u6027\u3002<\/li>\n<li><strong>\u89e3\u304f<\/strong> \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u5b9f\u8df5\u7684\u306a\u6f14\u7fd2\u554f\u984c\u3002<\/li>\n<\/ol>\n<p><u>\u76ee\u6b21<\/u>:<br \/>\n<a href=\"#1\">\u5e8f\u8ad6<\/a><br \/>\n<a href=\"#2\">\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u5b9a\u7fa9<\/a><br \/>\n<a href=\"#3\">\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u57fa\u672c\u7684\u306a\u6975\u9650<\/a><br \/>\n<a href=\"#4\">\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u4ee3\u6570<\/a><br \/>\n<a href=\"#5\">\u6709\u7406\u95a2\u6570\u306b\u304a\u3051\u308b\u7121\u9650\u5927\u306e\u6975\u9650<\/a><br \/>\n<a href=\"#6\">\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u4f8b<\/a><br \/>\n<\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/MjjSAQLeNBE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>\u5e8f\u8ad6<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=41s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5fae\u7a4d\u5206\u306b\u304a\u3051\u308b\u6700\u3082\u7279\u5fb4\u7684\u306a\u8981\u7d20\u306e\u4e00\u3064\u306f\u3001\u7121\u9650\u5927\u304a\u3088\u3073\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u3067\u3042\u308b\u3002<\/span><\/strong><\/a> \u7121\u9650\u5927\u306e\u6982\u5ff5\u306f\u5b9f\u6570\u3092\u6307\u3059\u3082\u306e\u3067\u306f\u306a\u304f\u3001\u3080\u3057\u308d\u3042\u3089\u3086\u308b\u5b9f\u6570\u306e\u4e0a\u754c\u3092\u8d85\u3048\u308b\u5927\u304d\u3055\u3092\u8a18\u8ff0\u3057\u3088\u3046\u3068\u3059\u308b\u3082\u306e\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = 1\/x<\/span> \u304c\u3042\u308a\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u304c\u3044\u304f\u3089\u3067\u3082\u5927\u304d\u304f\u306a\u308b\u3068\u304d\u3001\u3059\u306a\u308f\u3061 <span class=\"katex-eq\" data-katex-display=\"false\">x\\to \\infty<\/span> \u306e\u3068\u304d\u3001\u305d\u306e\u6319\u52d5\u3092\u8003\u3048\u308b\u3068\u3001<span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u306f\u3044\u304f\u3089\u3067\u3082\u30bc\u30ed\u306b\u8fd1\u3065\u304f\u3053\u3068\u304c\u89b3\u5bdf\u3055\u308c\u308b\u3002\u3053\u306e\u3068\u304d\u6b21\u306e\u3088\u3046\u306b\u66f8\u304f\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to + \\infty}\\dfrac{1}{x} = 0<\/span>\n<p style=\"text-align: justify;\">\u56f3\u7684\u306b\u306f\u3001\u3053\u306e\u4e8b\u8c61\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\uff1a<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-fX0lg2ICTTU\/YGD0hNJWI6I\/AAAAAAAAEwQ\/0v8hW6ARkQYDIzT_eG5WVgZ0-pPwwPBwgCLcBGAsYHQ\/s0\/limiteAlinfinito.PNG\" alt=\"limite al infinito\" class=\"alignnone size-full lazyload\" width=\"400\" height=\"300\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-fX0lg2ICTTU\/YGD0hNJWI6I\/AAAAAAAAEwQ\/0v8hW6ARkQYDIzT_eG5WVgZ0-pPwwPBwgCLcBGAsYHQ\/s0\/limiteAlinfinito.PNG\" alt=\"limite al infinito\" class=\"alignnone size-full lazyload\" width=\"400\" height=\"300\" \/><\/noscript><\/center><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u5b9a\u7fa9<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=144s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5148\u307b\u3069\u5c0e\u5165\u3057\u305f\u3053\u306e\u8003\u3048\u304b\u3089<\/span><\/strong><\/a> \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u3092\u5b9a\u5f0f\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff1a<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}f(x) = L := (\\forall\\epsilon\\gt 0) (\\exists M\\in\\mathbb{R})(M\\lt x \\rightarrow |f(x) - L|\\lt \\epsilon )<\/span>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -\\infty}f(x) = L := (\\forall\\epsilon\\gt 0) (\\exists N\\in\\mathbb{R})(x\\lt N \\rightarrow |f(x) - L|\\lt \\epsilon )<\/span>\n<p style=\"text-align: justify;\">\u3053\u306e\u6975\u9650\u306e\u76f4\u611f\u7684\u306a\u6982\u5ff5\u306f\u3001<span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u304c\u539f\u70b9\u304b\u3089\u3044\u304f\u3089\u3067\u3082\u9060\u3056\u304b\u308b\u3068\u304d\u3001\u53f3\u306b\u884c\u304f\u5834\u5408\u3082\u5de6\u306b\u884c\u304f\u5834\u5408\u3082\u3001\u3069\u306e\u3088\u3046\u306a\u6319\u52d5\u3092\u793a\u3059\u304b\u3092\u793a\u3057\u3066\u3044\u308b\u3002\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u8a08\u7b97\u65b9\u6cd5\u306f\u3001\u6709\u9650\u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u969b\u306e\u65b9\u6cd5\u3068\u5927\u304d\u304f\u306f\u7570\u306a\u3089\u306a\u3044\u3002\u306a\u305c\u306a\u3089\u3001\u305d\u306e\u4ee3\u6570\u306f\u307b\u307c\u540c\u3058\u3067\u3042\u308a\u3001\u6b21\u306e\u7d50\u679c\u3092\u8003\u616e\u3059\u308c\u3070\u3088\u3044\u304b\u3089\u3067\u3042\u308b\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u57fa\u672c\u7684\u306a\u6975\u9650<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=450s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3053\u308c\u3089\u306e\u5b9a\u7fa9\u304b\u3089\u3001\u6b21\u306e\u57fa\u672c\u7684\u306a\u6975\u9650\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/span><\/strong><\/a><\/p>\n<ol style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}k = k <\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}\\dfrac{1}{x} = 0 <\/span><\/li>\n<\/ol>\n<p style=\"text-align: justify;\"><span style=\"color: #000080;\">\u8a3c\u660e:<\/span><\/p>\n<ol style=\"text-align: justify;\">\n<li>\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u5b9a\u7fa9\u306b\u3088\u308c\u3070\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}k = k <\/span> \u306f\u6b21\u306e\u3088\u3046\u306b\u8a00\u3044\u63db\u3048\u3089\u308c\u308b\uff1a<span class=\"katex-eq\" data-katex-display=\"false\">(\\forall\\epsilon\\gt 0) (\\exists M\\in\\mathbb{R})\\left(M\\lt x \\rightarrow \\left|k-k\\right|\\lt \\epsilon \\right)<\/span>\u3002\u3057\u304b\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">\\left|k-k\\right|=0\\lt \\epsilon <\/span> \u306f\u5e38\u306b\u3001\u4efb\u610f\u306e <span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon \\gt 0<\/span> \u306b\u3064\u3044\u3066\u6210\u308a\u7acb\u3061\u3001<span class=\"katex-eq\" data-katex-display=\"false\">M<\/span> \u306e\u5024\u306b\u4f9d\u5b58\u3057\u306a\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u6975\u9650\u306f\u4fdd\u8a3c\u3055\u308c\u308b\u3002\n<p>&nbsp;<\/li>\n<li>\u5b9a\u7fa9\u306b\u3088\u308a\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{1}{x} = 0 <\/span> \u306f\u6b21\u306e\u3088\u3046\u306b\u8a00\u3044\u63db\u3048\u3089\u308c\u308b\uff1a<span class=\"katex-eq\" data-katex-display=\"false\">(\\forall\\epsilon\\gt 0) (\\exists M\\in\\mathbb{R})\\left(M\\lt x \\rightarrow \\left|\\dfrac{1}{x}\\right|\\lt \\epsilon \\right)<\/span>\u3002\u3053\u306e\u542b\u610f\u306f <span class=\"katex-eq\" data-katex-display=\"false\">M=1\/\\epsilon<\/span> \u3092\u8003\u3048\u308c\u3070\u76f4\u3061\u306b\u6e80\u305f\u3055\u308c\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u6975\u9650\u306f\u4fdd\u8a3c\u3055\u308c\u308b\u3002\n<p>&nbsp;<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">\u3053\u308c\u3089\u306e\u8a3c\u660e\u306f\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x\\to -\\infty<\/span> \u306e\u5834\u5408\u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u306b\u884c\u308f\u308c\u308b\u3002<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u4ee3\u6570<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=620s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u4ee3\u6570\u306f\u6709\u9650\u306e\u6975\u9650\u306e\u4ee3\u6570\u3068\u985e\u4f3c\u3057\u3066\u3044\u308b\u3002<\/span> <\/strong><\/a>\u3082\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm \\infty}f(x) = L<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm \\infty}g(x) = M<\/span> \u3067\u3042\u308b\u306a\u3089\u3001\u6b21\u306e\u898f\u5247\u304c\u6210\u308a\u7acb\u3064\uff1a<\/p>\n<ol style=\"text-align: justify;\">\n<li><strong>\u6975\u9650\u306e\u548c\u3068\u5dee:<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}(f(x)\\pm g(x)) = L \\pm M<\/span><\/li>\n<li><strong>\u5b9a\u6570\u500d:<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}cf(x) = cL<\/span><\/li>\n<li><strong>\u6975\u9650\u306e\u7a4d:<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}f(x)g(x) = LM<\/span><\/li>\n<li><strong>\u6975\u9650\u306e\u5546:<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">M\\neq 0<\/span> \u306e\u3068\u304d\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}f(x)\/g(x)=L\/M<\/span><\/li>\n<li><strong>\u6975\u9650\u306e\u3079\u304d\u4e57:<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">p,q \\in\\mathbb{Z}<\/span> \u304b\u3064 <span class=\"katex-eq\" data-katex-display=\"false\">q\\neq 0<\/span> \u306e\u3068\u304d\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}[f(x)]^{p\/q} = L^{p\/q}<\/span>\u3002<br \/>\n<span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u304c\u5076\u6570\u306e\u5834\u5408\u3001<span class=\"katex-eq\" data-katex-display=\"false\">L\\geq 0<\/span> \u3067\u3042\u308b\u3053\u3068\u304c\u524d\u63d0\u3068\u306a\u308b\u3002<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">\u5b9f\u969b\u306b\u306f\u3001\u3053\u308c\u3089\u3059\u3079\u3066\u306e\u6027\u8cea\u306e\u8a3c\u660e\u306f <a href=\"https:\/\/toposuranos.com\/la-definicion-de-limite-demostraciones-y-teoremas\/\" target=\"_blank\" rel=\"noopener\">\u6709\u9650\u306e\u6975\u9650<\/a> \u306e\u5834\u5408\u3068\u985e\u4f3c\u3057\u3066\u3044\u308b\u3002<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u6709\u7406\u95a2\u6570\u306b\u304a\u3051\u308b\u7121\u9650\u5927\u306e\u6975\u9650<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=792s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6709\u7406\u95a2\u6570\u3068\u306f\u3001\u4e8c\u3064\u306e\u591a\u9805\u5f0f\u306e\u5546\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u95a2\u6570\u3067\u3042\u308b\u3002<\/span><\/strong><\/a> \u3053\u306e\u7a2e\u306e\u95a2\u6570\u306b\u5bfe\u3057\u3066\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001\u975e\u5e38\u306b\u6709\u7528\u306a\u6027\u8cea\u304c\u89b3\u5bdf\u3055\u308c\u308b\u3002<\/p>\n<p style=\"text-align: justify;\">\u6b21\u3092\u8a08\u7b97\u3057\u305f\u3044\u3068\u4eee\u5b9a\u3059\u308b\uff1a<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\infty}P(x)\/Q(x)<\/span>\n<ul style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u306e\u6b21\u6570\u304c <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u306e\u6b21\u6570\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x\\to\\infty<\/span> \u306e\u3068\u304d\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u306e\u5927\u304d\u3055\u306f\u7121\u9650\u306b\u5897\u5927\u3057\u3001\u6975\u9650\u306f\u5b58\u5728\u3057\u306a\u3044\u3002<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u306e\u6b21\u6570\u304c <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u306e\u6b21\u6570\u3088\u308a\u5c0f\u3055\u3044\u5834\u5408\u3001\u6975\u9650\u306f\u30bc\u30ed\u3068\u306a\u308b\u3002<\/li>\n<li>\u6700\u5f8c\u306b\u3001<span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u306e\u6b21\u6570\u304c <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u306e\u6b21\u6570\u3068\u7b49\u3057\u3044\u5834\u5408\u3001\u6975\u9650\u306f\u6700\u9ad8\u6b21\u306e\u9805\u306b\u4ed8\u968f\u3059\u308b\u4fc2\u6570\u306e\u6bd4\u306b\u7b49\u3057\u304f\u306a\u308b\u3002<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u3053\u306e\u7d50\u679c\u306e\u6700\u3082\u512a\u308c\u305f\u70b9\u306f\u3001\u6b21\u306b\u793a\u3059\u4f8b\u3067\u898b\u308b\u3088\u3046\u306b\u3001\u95a2\u4e0e\u3059\u308b\u3079\u304d\u4e57\u304c\u6574\u6570\u3067\u306a\u3044\u5834\u5408\u3067\u3082\u540c\u69d8\u306b\u6a5f\u80fd\u3059\u308b\u3053\u3068\u3067\u3042\u308b\u3002<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u4f8b<\/h2>\n<ol style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{x+1}{x^2+3}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=907s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -\\infty}\\dfrac{2x^3 + 7}{x^3 - x^2 + x + 7}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=986s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{9x^4 + x}{2x^4 + 5x^2 - x + 6}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1049s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{10x^5 + x4 + 31}{x^4 - 7x^3 + 7x^2 + 9}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1111s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{2\\sqrt{x}+x^{-1}}{3x - 7}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1220s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -\\infty}\\dfrac{2x^{5\/3} - x^{1\/3} + 7}{x^{8\/5}+3x + \\sqrt{x}}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1284s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{\\sqrt[3]{x}-5x+3}{2x + x^{2\/3} - 4}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1406s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{x^{8\/3}+2x + \\sqrt{x}}{x^2+x-3}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1521s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\uff1a\u5b9a\u7fa9\u3068\u4f8b \u8981\u7d04: \u3053\u306e\u6388\u696d\u3067\u306f\u3001 \u304c \u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u6319\u52d5\u306b\u3064\u3044\u3066\u6271\u3046\u3002\u57fa\u672c\u7684\u306a\u6975\u9650\u3001\u4f8b\u3048\u3070 \u3084 \u3092\u8aac\u660e\u3057\u3001\u6709\u9650\u306e\u6975\u9650\u3068\u985e\u4f3c\u3057\u305f\u4ee3\u6570\u7684\u6027\u8cea\u306b\u3064\u3044\u3066\u3082\u8ff0\u3079\u308b\u3002 \u5b66\u7fd2\u76ee\u6a19: \u672c\u6388\u696d\u306e\u7d42\u4e86\u6642\u306b\u3001\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3002 \u8aac\u660e\u3059\u308b \u304c \u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u6319\u52d5\u3002 \u5b9a\u7fa9\u3059\u308b \u6570\u5b66\u7684\u5f62\u5f0f\u7684\u8a18\u6cd5\u3092\u7528\u3044\u305f\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u3002 \u9069\u7528\u3059\u308b \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u8a08\u7b97\u306b\u304a\u3051\u308b\u4ee3\u6570\u7684\u6027\u8cea\u3002 \u533a\u5225\u3059\u308b \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6709\u7406\u95a2\u6570\u306e\u7570\u306a\u308b\u5834\u5408\u306e\u6975\u9650\u3002 \u8a3c\u660e\u3059\u308b \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306b\u95a2\u3059\u308b\u548c\u3001\u5dee\u3001\u7a4d\u3001\u5546\u304a\u3088\u3073\u3079\u304d\u306e\u6027\u8cea\u306e\u59a5\u5f53\u6027\u3002 \u89e3\u304f \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u5b9f\u8df5\u7684\u306a\u6f14\u7fd2\u554f\u984c\u3002 \u76ee\u6b21: \u5e8f\u8ad6 \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u5b9a\u7fa9 \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u57fa\u672c\u7684\u306a\u6975\u9650 \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u4ee3\u6570 \u6709\u7406\u95a2\u6570\u306b\u304a\u3051\u308b\u7121\u9650\u5927\u306e\u6975\u9650 \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u4f8b \u5e8f\u8ad6 \u5fae\u7a4d\u5206\u306b\u304a\u3051\u308b\u6700\u3082\u7279\u5fb4\u7684\u306a\u8981\u7d20\u306e\u4e00\u3064\u306f\u3001\u7121\u9650\u5927\u304a\u3088\u3073\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u3067\u3042\u308b\u3002 \u7121\u9650\u5927\u306e\u6982\u5ff5\u306f\u5b9f\u6570\u3092\u6307\u3059\u3082\u306e\u3067\u306f\u306a\u304f\u3001\u3080\u3057\u308d\u3042\u3089\u3086\u308b\u5b9f\u6570\u306e\u4e0a\u754c\u3092\u8d85\u3048\u308b\u5927\u304d\u3055\u3092\u8a18\u8ff0\u3057\u3088\u3046\u3068\u3059\u308b\u3082\u306e\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001\u95a2\u6570 \u304c\u3042\u308a\u3001 \u304c\u3044\u304f\u3089\u3067\u3082\u5927\u304d\u304f\u306a\u308b\u3068\u304d\u3001\u3059\u306a\u308f\u3061 \u306e\u3068\u304d\u3001\u305d\u306e\u6319\u52d5\u3092\u8003\u3048\u308b\u3068\u3001 \u306f\u3044\u304f\u3089\u3067\u3082\u30bc\u30ed\u306b\u8fd1\u3065\u304f\u3053\u3068\u304c\u89b3\u5bdf\u3055\u308c\u308b\u3002\u3053\u306e\u3068\u304d\u6b21\u306e\u3088\u3046\u306b\u66f8\u304f\uff1a \u56f3\u7684\u306b\u306f\u3001\u3053\u306e\u4e8b\u8c61\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\uff1a \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u5b9a\u7fa9 \u5148\u307b\u3069\u5c0e\u5165\u3057\u305f\u3053\u306e\u8003\u3048\u304b\u3089 \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u3092\u5b9a\u5f0f\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff1a \u3053\u306e\u6975\u9650\u306e\u76f4\u611f\u7684\u306a\u6982\u5ff5\u306f\u3001 \u304c\u539f\u70b9\u304b\u3089\u3044\u304f\u3089\u3067\u3082\u9060\u3056\u304b\u308b\u3068\u304d\u3001\u53f3\u306b\u884c\u304f\u5834\u5408\u3082\u5de6\u306b\u884c\u304f\u5834\u5408\u3082\u3001\u3069\u306e\u3088\u3046\u306a\u6319\u52d5\u3092\u793a\u3059\u304b\u3092\u793a\u3057\u3066\u3044\u308b\u3002\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u8a08\u7b97\u65b9\u6cd5\u306f\u3001\u6709\u9650\u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u969b\u306e\u65b9\u6cd5\u3068\u5927\u304d\u304f\u306f\u7570\u306a\u3089\u306a\u3044\u3002\u306a\u305c\u306a\u3089\u3001\u305d\u306e\u4ee3\u6570\u306f\u307b\u307c\u540c\u3058\u3067\u3042\u308a\u3001\u6b21\u306e\u7d50\u679c\u3092\u8003\u616e\u3059\u308c\u3070\u3088\u3044\u304b\u3089\u3067\u3042\u308b\u3002 \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u57fa\u672c\u7684\u306a\u6975\u9650 \u3053\u308c\u3089\u306e\u5b9a\u7fa9\u304b\u3089\u3001\u6b21\u306e\u57fa\u672c\u7684\u306a\u6975\u9650\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002 \u8a3c\u660e: \u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u5b9a\u7fa9\u306b\u3088\u308c\u3070\u3001 \u306f\u6b21\u306e\u3088\u3046\u306b\u8a00\u3044\u63db\u3048\u3089\u308c\u308b\uff1a\u3002\u3057\u304b\u3057 \u306f\u5e38\u306b\u3001\u4efb\u610f\u306e \u306b\u3064\u3044\u3066\u6210\u308a\u7acb\u3061\u3001 \u306e\u5024\u306b\u4f9d\u5b58\u3057\u306a\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u6975\u9650\u306f\u4fdd\u8a3c\u3055\u308c\u308b\u3002 &nbsp; \u5b9a\u7fa9\u306b\u3088\u308a\u3001 \u306f\u6b21\u306e\u3088\u3046\u306b\u8a00\u3044\u63db\u3048\u3089\u308c\u308b\uff1a\u3002\u3053\u306e\u542b\u610f\u306f 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