{"id":34326,"date":"2024-11-18T13:00:43","date_gmt":"2024-11-18T13:00:43","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34326"},"modified":"2025-09-07T03:27:51","modified_gmt":"2025-09-07T03:27:51","slug":"%e6%bc%b8%e8%bf%91%e7%b7%9a%e3%80%81%e6%a5%b5%e9%99%90%e3%81%8a%e3%82%88%e3%81%b3%e3%82%b0%e3%83%a9%e3%83%95%e8%a1%a8%e7%8f%be%e6%8a%80%e6%b3%95","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/%e6%bc%b8%e8%bf%91%e7%b7%9a%e3%80%81%e6%a5%b5%e9%99%90%e3%81%8a%e3%82%88%e3%81%b3%e3%82%b0%e3%83%a9%e3%83%95%e8%a1%a8%e7%8f%be%e6%8a%80%e6%b3%95\/","title":{"rendered":"\u6f38\u8fd1\u7dda\u3001\u6975\u9650\u304a\u3088\u3073\u30b0\u30e9\u30d5\u8868\u73fe\u6280\u6cd5"},"content":{"rendered":"<style>\np {\ntext-align:justify;\n}\n<\/style>\n<h1 style=\"text-align:center;\">\u6f38\u8fd1\u7dda\u3001\u6975\u9650\u304a\u3088\u3073\u30b0\u30e9\u30d5\u8868\u73fe\u6280\u6cd5<\/h1>\n<p style=\"text-align:center;\"><em><strong>\u6982\u8981:<\/strong><br \/>\n\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u95a2\u6570\u89e3\u6790\u306b\u304a\u3051\u308b\u6f38\u8fd1\u7dda\u3068\u4e3b\u8981\u9805\u306e\u6982\u5ff5\u3092\u6271\u3046\u3002\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6319\u52d5\u3092\u8a18\u8ff0\u3059\u308b\u6c34\u5e73\u6f38\u8fd1\u7dda\u3001\u3042\u308b\u5024\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u7121\u9650\u5927\u6975\u9650\u3092\u793a\u3059\u5782\u76f4\u6f38\u8fd1\u7dda\u3001\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u3092\u8d85\u3048\u308b\u6709\u7406\u95a2\u6570\u306b\u73fe\u308c\u308b\u659c\u6f38\u8fd1\u7dda\u306b\u3064\u3044\u3066\u8003\u5bdf\u3059\u308b\u3002\u307e\u305f\u3001\u95a2\u6570\u306e\u4e3b\u8981\u9805\u3092\u5206\u6790\u3057\u3001\u305d\u308c\u304c\u5927\u304d\u306a\u5024\u3084\u7279\u5b9a\u306e\u70b9\u4ed8\u8fd1\u306b\u304a\u3051\u308b\u8fd1\u4f3c\u3092\u4e0e\u3048\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u7fd2\u76ee\u6a19<\/strong><br \/>\n\u672c\u8b1b\u7fa9\u7d42\u4e86\u6642\u3001\u5b66\u751f\u306f\u4ee5\u4e0b\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\uff1a\n<\/p>\n<ol>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong> \u6c34\u5e73\u6f38\u8fd1\u7dda\u306e\u6982\u5ff5\u3068\u3001\u305d\u308c\u3092\u95a2\u6570\u306e\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6319\u52d5\u306e\u89e3\u6790\u306b\u5fdc\u7528\u3059\u308b\u65b9\u6cd5\u3002<\/li>\n<li><strong>\u8b58\u5225\u3059\u308b<\/strong> \u5782\u76f4\u6f38\u8fd1\u7dda\u306e\u5b58\u5728\u6761\u4ef6\u3092\u660e\u3089\u304b\u306b\u3057\u3001\u3042\u308b\u5024\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u7121\u9650\u5927\u6975\u9650\u3092\u6301\u3064\u95a2\u6570\u306e\u89e3\u6790\u306b\u9069\u7528\u3059\u308b\u65b9\u6cd5\u3002<\/li>\n<li><strong>\u5206\u6790\u3059\u308b<\/strong> \u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u3092\u8d85\u3048\u308b\u3068\u304d\u306b\u6709\u7406\u95a2\u6570\u306b\u73fe\u308c\u308b\u659c\u6f38\u8fd1\u7dda\u306e\u51fa\u73fe\u3002<\/li>\n<li><strong>\u5fdc\u7528\u3059\u308b<\/strong> \u95a2\u6570\u306e\u4e3b\u8981\u9805\u306e\u6982\u5ff5\u3092\u7528\u3044\u3066\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u306e\u5927\u304d\u306a\u5024\u3084\u7279\u5b9a\u306e\u70b9\u4ed8\u8fd1\u3067\u306e\u95a2\u6570\u306e\u6319\u52d5\u3092\u8fd1\u4f3c\u3059\u308b\u3002<\/li>\n<li><strong>\u8aac\u660e\u3059\u308b<\/strong> \u6f38\u8fd1\u7dda\u304a\u3088\u3073\u4e3b\u8981\u9805\u306e\u89e3\u6790\u304c\u95a2\u6570\u306e\u5168\u4f53\u7684\u306a\u6319\u52d5\u306e\u7406\u89e3\u306b\u3069\u306e\u3088\u3046\u306b\u5bc4\u4e0e\u3059\u308b\u304b\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u76ee\u6b21<\/u>:<\/strong><br \/>\n<a href=\"#1\">\u5e8f\u8ad6<\/a><br \/>\n<a href=\"#2\">\u6c34\u5e73\u6f38\u8fd1\u7dda\u3068\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650<\/a><br \/>\n<a href=\"#3\">\u5782\u76f4\u6f38\u8fd1\u7dda\u3068\u7121\u9650\u5927\u6975\u9650<\/a><br \/>\n<a href=\"#4\">\u659c\u6f38\u8fd1\u7dda\u3001\u66f2\u7dda\u304a\u3088\u3073\u4e3b\u8981\u9805<\/a><br \/>\n<a href=\"#5\">\u89e3\u7b54\u4ed8\u304d\u6f14\u7fd2<\/a><br \/>\n<a href=\"#6\">\u63d0\u6848\u6f14\u7fd2<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/Ekd0oSvMbfE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u5e8f\u8ad6<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=98s\" target=\"_blank\" rel=\"noopener\"><strong>\u3053\u308c\u307e\u3067\u306b\u78ba\u8a8d\u3057\u305f\u6975\u9650<\/strong><\/a> \u306b\u3088\u3063\u3066\u3001\u95a2\u6570\u306e\u5168\u4f53\u7684\u306a\u6319\u52d5\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u6709\u7528\u306a\u6982\u5ff5\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u305d\u308c\u306f\u4e3b\u8981\u9805\u3068\u6c34\u5e73\u304a\u3088\u3073\u5782\u76f4\u6f38\u8fd1\u7dda\u3067\u3042\u308b\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u3053\u308c\u3089\u306f <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u304c\u3042\u308b\u5024\u306b\u8fd1\u3065\u304f\u306b\u3064\u308c\u3066\u3001\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u304c\u4efb\u610f\u306b\u8fd1\u3065\u304f\u66f2\u7dda\u3067\u3042\u308b\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u6c34\u5e73\u6f38\u8fd1\u7dda\u3068\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u6975\u9650<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=137s\" target=\"_blank\" rel=\"noopener\"><strong><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u304c<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">]a,+\\infty[<\/span> \u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570\u3067\u3042\u308a\u3001\u3042\u308b <span class=\"katex-eq\" data-katex-display=\"false\">a\\in\\mathbb{R}<\/span> \u306b\u5bfe\u3057\u3066\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u304c\u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002\u3082\u3057\u305d\u306e\u6975\u9650\u304c\u5b58\u5728\u3059\u308b\u306a\u3089\u3070\u3001<strong>\u53f3\u5074\u6c34\u5e73\u6f38\u8fd1\u7dda<\/strong> \u306f\u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u6301\u3064\u76f4\u7dda\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">A_+(x) = L^+<\/span>\n<p>\u3053\u3053\u3067<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to+\\infty}f(x) = L^+<\/span>\n<p>\u540c\u69d8\u306b\u3001<strong>\u5de6\u5074\u6c34\u5e73\u6f38\u8fd1\u7dda<\/strong> \u306f\u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u6301\u3064\u76f4\u7dda\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">A_-(x) = L^-<\/span>\n<p>\u305f\u3060\u3057<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to-\\infty}f(x) = L^-<\/span>\n<p>\u6c34\u5e73\u6f38\u8fd1\u7dda\u306f\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u306e\u5024\u304c\u5236\u9650\u306a\u304f\u5897\u5927\u3059\u308b\u3068\u304d\u306e\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u306e\u6319\u52d5\u3092\u8a18\u8ff0\u3059\u308b\u306e\u306b\u5f79\u7acb\u3064\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-ckBGkFWse2w\/YH1GWClIciI\/AAAAAAAAE6s\/zZ_se7yShqMLiEHKNT_jkgAWuK9cme5wwCLcBGAsYHQ\/s0\/as%25C3%25ADntotahorizontal.PNG\" alt=\"\u6c34\u5e73\u6f38\u8fd1\u7dda\" class=\"aligncenter lazyload\" width=\"478\" height=\"290\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-ckBGkFWse2w\/YH1GWClIciI\/AAAAAAAAE6s\/zZ_se7yShqMLiEHKNT_jkgAWuK9cme5wwCLcBGAsYHQ\/s0\/as%25C3%25ADntotahorizontal.PNG\" alt=\"\u6c34\u5e73\u6f38\u8fd1\u7dda\" class=\"aligncenter lazyload\" width=\"478\" height=\"290\" \/><\/noscript><br \/>\n<a name=\"3\"><\/a><\/p>\n<h2>\u5782\u76f4\u6f38\u8fd1\u7dda\u3068\u7121\u9650\u5927\u6975\u9650<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=277s\" target=\"_blank\" rel=\"noopener\"><strong>\u6c34\u5e73\u6f38\u8fd1\u7dda\u3068\u540c\u69d8\u306b\u3001<\/strong><\/a> \u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u306e <strong>\u4e0a\u65b9\u5411\u306e\u5782\u76f4\u6f38\u8fd1\u7dda<\/strong> \u306f\u3001\u6b21\u306e\u6761\u4ef6\u304c\u6210\u308a\u7acb\u3064\u3068\u304d\u306e\u76f4\u7dda <span class=\"katex-eq\" data-katex-display=\"false\">x=a<\/span> \u3068\u3057\u3066\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 a}f(x) = +\\infty<\/span>\n<p>\u307e\u305f\u3001\u6b21\u306e\u6761\u4ef6\u304c\u6210\u308a\u7acb\u3064\u5834\u5408\u3001\u305d\u306e\u6f38\u8fd1\u7dda\u306f\u4e0b\u65b9\u5411\u306e\u5782\u76f4\u6f38\u8fd1\u7dda\u3068\u306a\u308b\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to a}f(x) = -\\infty<\/span>\n<p>\u3055\u3089\u306b\u3001\u7247\u5074\u6975\u9650\u306e\u8ad6\u7406\u306b\u5f93\u3063\u3066\u3001\u6f38\u8fd1\u7dda\u306f\u53f3\u5074\u307e\u305f\u306f\u5de6\u5074\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-ptEipMpyIhc\/YH1VDclyMxI\/AAAAAAAAE60\/LmzpK2HAU7oLpswJQy5_TLIv9jSf9whDwCLcBGAsYHQ\/s0\/asintotavertical.PNG\" alt=\"\u5782\u76f4\u6f38\u8fd1\u7dda\" class=\" aligncenter lazyload\" width=\"428\" height=\"283\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-ptEipMpyIhc\/YH1VDclyMxI\/AAAAAAAAE60\/LmzpK2HAU7oLpswJQy5_TLIv9jSf9whDwCLcBGAsYHQ\/s0\/asintotavertical.PNG\" alt=\"\u5782\u76f4\u6f38\u8fd1\u7dda\" class=\" aligncenter lazyload\" width=\"428\" height=\"283\" \/><\/noscript><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u659c\u6f38\u8fd1\u7dda\u3001\u66f2\u7dda\u304a\u3088\u3073\u4e3b\u8981\u9805<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=400s\" target=\"_blank\" rel=\"noopener\"><strong>\u6700\u3082\u5358\u7d14\u306a\u51fa\u73fe\u4f8b\u306f\u3001<\/strong><\/a> <strong>\u659c\u6f38\u8fd1\u7dda<\/strong> \u304c\u6709\u7406\u95a2\u6570\u306b\u304a\u3044\u3066\u73fe\u308c\u308b\u5834\u5408\u3067\u3042\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{P(x)}{Q(x)}<\/span>\n<p>\u3053\u3053\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u306f\u591a\u9805\u5f0f\u3067\u3042\u308b\u3002<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\u591a\u9805\u5f0f\u306e\u5272\u308a\u7b97\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u3001\u305d\u306e\u7d50\u679c\u306f\u6b21\u306e\u5f62\u3092\u3068\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{P(x)}{Q(x)} = C(x) + \\dfrac{r(x)}{Q(x)}<\/span>\n<p>\u3053\u3053\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u306f\u5546\u3067\u3042\u308a\u3001<span class=\"katex-eq\" data-katex-display=\"false\">r(x)<\/span> \u306f\u4f59\u308a\u3067\u3042\u308b\u3002\u3082\u3057 <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\u30921\u3060\u3051\u8d85\u3048\u308b\u306a\u3089\u3070\u3001<span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u306f1\u6b21\u5f0f\u3001\u3059\u306a\u308f\u3061\u76f4\u7dda\u306e\u5f62\u3092\u6301\u3061\u3001\u3053\u308c\u306f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u306e\u659c\u6f38\u8fd1\u7dda\u3068\u547c\u3070\u308c\u308b\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-wRTmSl2Z3HE\/YH1dSl-noDI\/AAAAAAAAE68\/og2lPX_ydUUGlxYnn5hgj2mNCSeAPoQKACLcBGAsYHQ\/s0\/asintotaoblicua.PNG\" alt=\"\u659c\u6f38\u8fd1\u7dda\" class=\" aligncenter lazyload\" width=\"404\" height=\"239\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-wRTmSl2Z3HE\/YH1dSl-noDI\/AAAAAAAAE68\/og2lPX_ydUUGlxYnn5hgj2mNCSeAPoQKACLcBGAsYHQ\/s0\/asintotaoblicua.PNG\" alt=\"\u659c\u6f38\u8fd1\u7dda\" class=\" aligncenter lazyload\" width=\"404\" height=\"239\" \/><\/noscript><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=633s\" target=\"_blank\" rel=\"noopener\"><strong>\u4e00\u822c\u306b\u3001<span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u304c<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u306e\u6b21\u6570\u3092\u4efb\u610f\u306e\u5927\u304d\u3055\u3060\u3051\u4e0a\u56de\u308b\u5834\u5408\u3001<span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u306e\u6b21\u6570\u306f <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u306e\u6b21\u6570\u306e\u5dee\u306b\u7b49\u3057\u304f\u306a\u308a\u3001\u7d50\u679c\u3068\u3057\u3066\u4e00\u822c\u306b\u591a\u9805\u5f0f\u66f2\u7dda\u3068\u306a\u308b\u3002\u3053\u306e\u5834\u5408\u3001\u901a\u5e38\u306f <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u3092\u6f38\u8fd1\u7dda\u3068\u306f\u547c\u3070\u306a\u3044\u304c\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x\\to\\pm\\infty<\/span> \u306b\u304a\u3044\u3066 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u306e\u4e00\u822c\u7684\u306a\u6319\u52d5\u306f <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u306b\u300c\u6f38\u8fd1\u7684\u306b\u8fd1\u3065\u304f\u300d\u3082\u306e\u3067\u3042\u308b\u3002\u3053\u306e\u5834\u5408\u3001<span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u306f <strong><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u306e\u5927\u304d\u306a\u5024\u306b\u5bfe\u3059\u308b <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u306e\u4e3b\u8981\u9805\u3067\u3042\u308b<\/strong> \u3068\u8a00\u3046\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-IEYO071tTuY\/YH1fjR-WWnI\/AAAAAAAAE7E\/ga2rZ02i8QU5R1IMvQB9rpgFuDknAGfbACLcBGAsYHQ\/s0\/terminoDominante.PNG\" alt=\"\u4e3b\u8981\u9805\u3068\u5782\u76f4\u6f38\u8fd1\u7dda\" class=\" aligncenter lazyload\" width=\"479\" height=\"437\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-IEYO071tTuY\/YH1fjR-WWnI\/AAAAAAAAE7E\/ga2rZ02i8QU5R1IMvQB9rpgFuDknAGfbACLcBGAsYHQ\/s0\/terminoDominante.PNG\" alt=\"\u4e3b\u8981\u9805\u3068\u5782\u76f4\u6f38\u8fd1\u7dda\" class=\" aligncenter lazyload\" width=\"479\" height=\"437\" \/><\/noscript><\/p>\n<p>\u307e\u305f\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u304c <span class=\"katex-eq\" data-katex-display=\"false\">a\\in\\mathbb{R}<\/span> \u306e\u8fd1\u304f\u306b\u3042\u308b\u3068\u304d\u306b\u3082\u4e3b\u8981\u9805\u306b\u3064\u3044\u3066\u8b70\u8ad6\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p>\u3082\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = P(x)\/Q(x) = C(x) + r(x)\/Q(x),<\/span> \u3053\u3053\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">P(x),<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x),<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">r(x)<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u306f\u591a\u9805\u5f0f\u3067\u3042\u308b\u3002\u3055\u3089\u306b <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to a}f(x) = \\infty<\/span> \u3067\u3042\u308b\u306a\u3089\u3070\u3001\u5546 <span class=\"katex-eq\" data-katex-display=\"false\">r(x)\/Q(x)<\/span> \u306f <strong><span class=\"katex-eq\" data-katex-display=\"false\">x=a<\/span> \u4ed8\u8fd1\u306b\u304a\u3051\u308b <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u306e\u4e3b\u8981\u9805\u3067\u3042\u308b<\/strong> \u3068\u8a00\u3046\u3002<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u89e3\u7b54\u4ed8\u304d\u6f14\u7fd2<\/h2>\n<h3><strong>\u6f14\u7fd2 1:<\/strong><\/h3>\n<p>\u6b21\u306e\u95a2\u6570\u306e\u6c34\u5e73\u6f38\u8fd1\u7dda\u3068\u5782\u76f4\u6f38\u8fd1\u7dda\u3092\u6c42\u3081\u3088\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{3x + 1}{x - 2}<\/span>\n<p><strong>\u89e3\u7b54:<\/strong><\/p>\n<p><strong>\u6c34\u5e73\u6f38\u8fd1\u7dda<\/strong> \u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x \\to \\pm\\infty<\/span> \u306e\u3068\u304d\u306e <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to \\pm\\infty} \\dfrac{3x + 1}{x - 2} = 3<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u6c34\u5e73\u6f38\u8fd1\u7dda\u306f <span class=\"katex-eq\" data-katex-display=\"false\">y = 3<\/span> \u3067\u3042\u308b\u3002<\/p>\n<p><strong>\u5782\u76f4\u6f38\u8fd1\u7dda<\/strong> \u306b\u3064\u3044\u3066\u306f\u3001\u5206\u6bcd\u304c\u30bc\u30ed\u3068\u306a\u308b\u5024\u3001\u3059\u306a\u308f\u3061 <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span> \u3092\u7279\u5b9a\u3059\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to 2^\\pm} \\dfrac{3x + 1}{x - 2} = \\pm\\infty<\/span>\n<p>\u3053\u308c\u306f <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span> \u306b\u5782\u76f4\u6f38\u8fd1\u7dda\u304c\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u308b\u3002<\/p>\n<p><strong>\u6700\u7d42\u7d50\u679c:<\/strong> \u95a2\u6570\u306f <span class=\"katex-eq\" data-katex-display=\"false\">y = 3<\/span> \u306b\u6c34\u5e73\u6f38\u8fd1\u7dda\u3092\u6301\u3061\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span> \u306b\u5782\u76f4\u6f38\u8fd1\u7dda\u3092\u6301\u3064\u3002<\/p>\n<h3><strong>\u6f14\u7fd2 2:<\/strong><\/h3>\n<p>\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">g(x) = \\frac{2x^2 + 3x + 4}{x + 1}<\/span> \u306e\u6c34\u5e73\u6f38\u8fd1\u7dda\u3068\u659c\u6f38\u8fd1\u7dda\uff08\u5b58\u5728\u3059\u308b\u5834\u5408\uff09\u3092\u6c42\u3081\u3088\u3002<\/p>\n<p><strong>\u89e3\u7b54:<\/strong><\/p>\n<p>\u307e\u305a\u3001<strong>\u6c34\u5e73\u6f38\u8fd1\u7dda<\/strong> \u3092\u6c42\u3081\u308b\u305f\u3081\u306b <span class=\"katex-eq\" data-katex-display=\"false\">x \\to \\pm\\infty<\/span> \u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u3002\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u3088\u308a\u5927\u304d\u3044\u305f\u3081\u3001\u6c34\u5e73\u6f38\u8fd1\u7dda\u306f\u5b58\u5728\u3057\u306a\u3044\u3002<\/p>\n<p><strong>\u659c\u6f38\u8fd1\u7dda<\/strong> \u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u3001\u591a\u9805\u5f0f\u306e\u5272\u308a\u7b97\u3092\u884c\u3046\u3068\u6b21\u306e\u7d50\u679c\u3092\u5f97\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{2x^2 + 3x + 4}{x + 1} = 2x + 1 + \\dfrac{3}{x + 1}<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u659c\u6f38\u8fd1\u7dda\u306f\u76f4\u7dda <span class=\"katex-eq\" data-katex-display=\"false\">y = 2x + 1<\/span> \u3067\u3042\u308a\u3001\u3053\u308c\u306f\u95a2\u6570\u306e\u4e3b\u8981\u9805\u3067\u3042\u308b\u3002<\/p>\n<p><strong>\u6700\u7d42\u7d50\u679c:<\/strong> \u95a2\u6570\u306f\u6c34\u5e73\u6f38\u8fd1\u7dda\u3092\u6301\u305f\u306a\u3044\u304c\u3001\u659c\u6f38\u8fd1\u7dda\u306f\u76f4\u7dda <span class=\"katex-eq\" data-katex-display=\"false\">y = 2x + 1<\/span> \u3067\u3042\u308b\u3002<\/p>\n<h3><strong>\u6f14\u7fd2 3:<\/strong><\/h3>\n<span class=\"katex-eq\" data-katex-display=\"false\">h(x) = \\frac{5}{x^2 - 4}<\/span> \u306e\u5782\u76f4\u6f38\u8fd1\u7dda\u3092\u6c42\u3081\u3088\u3002<\/p>\n<p><strong>\u89e3\u7b54:<\/strong><\/p>\n<p><strong>\u5782\u76f4\u6f38\u8fd1\u7dda<\/strong> \u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u3001\u5206\u6bcd\u304c\u30bc\u30ed\u3068\u306a\u308b\u5024\u3092\u7279\u5b9a\u3059\u308b\u3002\u3059\u306a\u308f\u3061 <span class=\"katex-eq\" data-katex-display=\"false\">x^2 - 4 = 0<\/span> \u306e\u3068\u304d\u3067\u3042\u308b\u3002\u3053\u308c\u306f <span class=\"katex-eq\" data-katex-display=\"false\">x = \\pm 2<\/span> \u3067\u8d77\u3053\u308b\u3002<\/p>\n<p>\u305d\u308c\u305e\u308c\u306e\u5024\u306b\u5bfe\u3057\u3066\u7247\u5074\u6975\u9650\u3092\u8a55\u4fa1\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to 2^\\pm} \\dfrac{5}{x^2 - 4} = \\pm\\infty<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to -2^\\pm} \\dfrac{5}{x^2 - 4} = \\pm\\infty<\/span>\n<p><strong>\u6700\u7d42\u7d50\u679c:<\/strong> \u95a2\u6570\u306f <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">x = -2<\/span> \u306b\u5782\u76f4\u6f38\u8fd1\u7dda\u3092\u6301\u3064\u3002<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u63d0\u6848\u6f14\u7fd2<\/h2>\n<ol>\n<li>\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\frac{2x^2 - 3x + 1}{x^2 + x - 2}<\/span> \u3092\u89e3\u6790\u305b\u3088\u3002\u6c34\u5e73\u6f38\u8fd1\u7dda\u3001\u5782\u76f4\u6f38\u8fd1\u7dda\u304a\u3088\u3073\u659c\u6f38\u8fd1\u7dda\u304c\u5b58\u5728\u3059\u308b\u304b\u3092\u6c7a\u5b9a\u305b\u3088\u3002\u5404\u30b9\u30c6\u30c3\u30d7\u3092\u8aac\u660e\u3057\u3001\u6f38\u8fd1\u7dda\u306e\u6982\u5ff5\u3068\u6975\u9650\u306e\u8a08\u7b97\u3092\u5f37\u5316\u305b\u3088\u3002<\/li>\n<li>\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">g(x) = \\frac{3x^3 + 2x}{x^2 + 1}<\/span> \u3092\u8a55\u4fa1\u305b\u3088\u3002<span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u304c\u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u4e3b\u8981\u9805\u3092\u7279\u5b9a\u305b\u3088\u3002\u305d\u306e\u5f8c\u3001\u659c\u6f38\u8fd1\u7dda\u304c\u5b58\u5728\u3059\u308b\u304b\u3092\u78ba\u8a8d\u3057\u3001\u305d\u306e\u7406\u7531\u3092\u6b63\u5f53\u5316\u305b\u3088\u3002<\/li>\n<li>\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">h(x) = \\frac{5x - 4}{x + 1}<\/span> \u306e\u304a\u304a\u3088\u305d\u306e\u30b0\u30e9\u30d5\u3092\u8a2d\u8a08\u305b\u3088\u3002\u6c34\u5e73\u6f38\u8fd1\u7dda\u3001\u5782\u76f4\u6f38\u8fd1\u7dda\u304a\u3088\u3073\u659c\u6f38\u8fd1\u7dda\uff08\u5b58\u5728\u3059\u308b\u5834\u5408\uff09\u3092\u542b\u3081\u3001<span class=\"katex-eq\" data-katex-display=\"false\">h(x)<\/span> \u306e <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u306e\u6975\u7aef\u306a\u5024\u306b\u304a\u3051\u308b\u6319\u52d5\u3092\u5206\u6790\u305b\u3088\u3002<\/li>\n<li>\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">k(x) = \\frac{x^2 - 4x + 3}{x^2 - 1}<\/span> \u306b\u5782\u76f4\u6f38\u8fd1\u7dda\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u305b\u3088\u3002\u95a2\u6570\u304c\u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u5024\u306b\u304a\u3051\u308b\u6975\u9650\u306e\u89e3\u6790\u306b\u304a\u3044\u3066\u3001\u4e3b\u8981\u9805\u306e\u5f79\u5272\u3092\u8ad6\u3058\u3088\u3002<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">m(x) = \\frac{2x^4 + 3x^2 - x + 5}{x^3 - x^2 + 2}<\/span> \u306e\u4e3b\u8981\u9805\u3092\u8abf\u3079\u3088\u3002<span class=\"katex-eq\" data-katex-display=\"false\">x \\to \\pm\\infty<\/span> \u306e\u3068\u304d\u306e <span class=\"katex-eq\" data-katex-display=\"false\">m(x)<\/span> \u306e\u6319\u52d5\u3092\u6c7a\u5b9a\u3057\u3001\u76f4\u7dda\u3067\u306f\u306a\u304f\u591a\u9805\u5f0f\u66f2\u7dda\u306b\u8fd1\u3065\u304f\u304b\u3069\u3046\u304b\u3092\u7d50\u8ad6\u3065\u3051\u3088\u3002<\/li>\n<li>\u4efb\u610f\u306b\u6709\u7406\u95a2\u6570\u3092\u69cb\u6210\u3057\u3001\u305d\u306e\u6c34\u5e73\u6f38\u8fd1\u7dda\u3001\u5782\u76f4\u6f38\u8fd1\u7dda\u304a\u3088\u3073\u659c\u6f38\u8fd1\u7dda\u306b\u52a0\u3048\u3001\u4e3b\u8981\u9805\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u8a73\u7d30\u306b\u8a18\u8ff0\u305b\u3088\u3002\u5404\u7a2e\u306e\u6f38\u8fd1\u7dda\u3092\u53ef\u8996\u5316\u3059\u308b\u305f\u3081\u306b\u30b0\u30e9\u30d5\u3092\u7528\u3044\u3066\u7d50\u679c\u3092\u63d0\u793a\u305b\u3088\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u6f38\u8fd1\u7dda\u3001\u6975\u9650\u304a\u3088\u3073\u30b0\u30e9\u30d5\u8868\u73fe\u6280\u6cd5 \u6982\u8981: \u672c\u8b1b\u7fa9\u3067\u306f\u3001\u95a2\u6570\u89e3\u6790\u306b\u304a\u3051\u308b\u6f38\u8fd1\u7dda\u3068\u4e3b\u8981\u9805\u306e\u6982\u5ff5\u3092\u6271\u3046\u3002\u7121\u9650\u5927\u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6319\u52d5\u3092\u8a18\u8ff0\u3059\u308b\u6c34\u5e73\u6f38\u8fd1\u7dda\u3001\u3042\u308b\u5024\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u7121\u9650\u5927\u6975\u9650\u3092\u793a\u3059\u5782\u76f4\u6f38\u8fd1\u7dda\u3001\u5206\u5b50\u306e\u6b21\u6570\u304c\u5206\u6bcd\u306e\u6b21\u6570\u3092\u8d85\u3048\u308b\u6709\u7406\u95a2\u6570\u306b\u73fe\u308c\u308b\u659c\u6f38\u8fd1\u7dda\u306b\u3064\u3044\u3066\u8003\u5bdf\u3059\u308b\u3002\u307e\u305f\u3001\u95a2\u6570\u306e\u4e3b\u8981\u9805\u3092\u5206\u6790\u3057\u3001\u305d\u308c\u304c\u5927\u304d\u306a\u5024\u3084\u7279\u5b9a\u306e\u70b9\u4ed8\u8fd1\u306b\u304a\u3051\u308b\u8fd1\u4f3c\u3092\u4e0e\u3048\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u3002 \u5b66\u7fd2\u76ee\u6a19 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[&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29511,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":7,"footnotes":""},"categories":[1332,1300],"tags":[],"class_list":["post-34326","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-1332","category--ja"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u6f38\u8fd1\u7dda\u3001\u6975\u9650\u304a\u3088\u3073\u30b0\u30e9\u30d5\u8868\u73fe\u6280\u6cd5 - toposuranos.com\/material<\/title>\n<meta name=\"description\" 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