{"id":22,"date":"2023-09-17T11:07:37","date_gmt":"2023-09-17T11:07:37","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/"},"modified":"2023-09-17T11:07:37","modified_gmt":"2023-09-17T11:07:37","slug":"%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/","title":{"rendered":"\u659c\u7dda\u6f38\u8fd1\u7dda"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u95a2\u6570\u306e\u659c\u3081\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u304b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u95a2\u6570\u306b\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u304c\u3042\u308b\u5834\u5408\u3068\u3001\u305d\u308c\u304c\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u304b\u3092\u5b66\u3073\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u306e\u4f8b\u3092\u78ba\u8a8d\u3057\u3001\u6bb5\u968e\u7684\u306b\u89e3\u304f\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-asintota-oblicua\"><\/span>\u659c\u7dda\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda\u306f\u3001\u30b0\u30e9\u30d5\u304c\u6c7a\u3057\u3066\u4ea4\u5dee\u3059\u308b\u3053\u3068\u306a\u304f\u7121\u9650\u306b\u8fd1\u3065\u304f\u50be\u659c\u7dda\u3067\u3059\u3002<\/strong>\u3057\u305f\u304c\u3063\u3066\u3001\u3059\u3079\u3066\u306e\u659c\u7dda\u306e\u6f38\u8fd1\u7dda\u306f\u3001\u65b9\u7a0b\u5f0f<em>y=mx+n<\/em>\u306e\u76f4\u7dda\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u306e\u50be\u304d\u3068\u539f\u70b9\u306f\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\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\/asymptote-oblique-dune-fonction.webp\" alt=\"\u95a2\u6570\u306e\u659c\u3081\u6f38\u8fd1\u7dda\" class=\"wp-image-1362\" width=\"290\" height=\"328\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-asintota-oblicua-de-una-funcion\"><\/span>\u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u624b\u9806\u3092\u5b9f\u884c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;border:\">\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u95a2\u6570\u306e\u7121\u9650\u5927\u306e\u6975\u9650\u3092 x \u3067\u5272\u3063\u305f\u5024\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u4e0a\u8a18\u306e\u5236\u9650\u306e\u7d50\u679c\u304c\u30bc\u30ed\u4ee5\u5916\u306e\u5b9f\u6570\u306b\u306a\u308b\u5834\u5408\u306f\u3001\u95a2\u6570\u306b\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u304c\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u524d\u8a18\u659c\u3081\u6f38\u8fd1\u7dda\u306e\u50be\u304d\u306f\u6975\u9650\u3067\u5f97\u3089\u308c\u308b\u5024\u3068\u306a\u308b\u3002<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-004f6e72e10d1ba23da76d2fd8ea13f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m = \\lim_{x \\to \\pm\\infty}\\frac{f(x)}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"125\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u3053\u306e\u5834\u5408\u3001\u6b8b\u3063\u3066\u3044\u308b\u306e\u306f\u3001\u6b21\u306e\u5236\u9650\u3092\u89e3\u3044\u3066\u659c\u7dda\u306e\u6f38\u8fd1\u7dda\u306e\u5207\u7247\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3060\u3051\u3067\u3059\u3002<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9cc74ce0447b0a9148cae947674ad085_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} [f(x)-mx]\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"170\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/ol>\n<p><strong>\u6ce8:<\/strong>\u5236\u9650\u306f\u30d7\u30e9\u30b9\u7121\u9650\u5927\u3068\u30de\u30a4\u30ca\u30b9\u7121\u9650\u5927\u3067\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u901a\u5e38\u306f\u540c\u3058\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b\u305f\u3081\u3001\u00b1\u221e \u3092\u7f6e\u304f\u3053\u3068\u3067\u7c21\u7565\u5316\u3057\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u30d7\u30e9\u30b9\u7121\u9650\u5927\u3068\u30de\u30a4\u30ca\u30b9\u7121\u9650\u5927\u3067\u306e\u9650\u754c\u304c\u7570\u306a\u308b\u5834\u5408\u306f\u3001\u5de6\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u3068\u53f3\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u3092\u5225\u3005\u306b\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-asintota-oblicua\"><\/span>\u659c\u7dda\u6f38\u8fd1\u7dda\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306b\u3001\u6b21\u306e\u6709\u7406\u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda\u3092\u53d6\u5f97\u3057\u3066\u3001\u3053\u308c\u304c\u3069\u306e\u3088\u3046\u306b\u884c\u308f\u308c\u308b\u304b\u306e\u4f8b\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-b02f6283fd481e890a943badfa2c876f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^2+1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"109\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u306f\u6b21\u306e\u30bf\u30a4\u30d7\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-ad313410fc976bc53709807aa8aed8e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=mx+n.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u305d\u3053\u3067\u3001\u307e\u305a\u76f4\u7dda\u306e\u50be\u304d\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5bfe\u5fdc\u3059\u308b\u5f0f\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-9b50ee5cbc3cf33f7fd42c3fe03a3d71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m = \\lim_{x \\to \\pm\\infty} \\frac{f(x)}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"125\" 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-870fc158a1aabb54cb5f3b4296381512_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m= \\lim_{x \\to \\pm\\infty} \\cfrac{\\cfrac{x^2+1}{x}}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"141\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5236\u9650\u3092\u89e3\u6c7a\u3059\u308b\u306b\u306f\u3001\u5206\u6570\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3092\u9069\u7528\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-7f313d826cd1a2dd1ef66b1d0a40efb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\cfrac{a}{b}}{\\cfrac{c}{d}}=\\cfrac{a\\cdot d}{b\\cdot c}\" title=\"Rendered by QuickLaTeX.com\" height=\"80\" width=\"69\" style=\"vertical-align: -39px;\"><\/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-dfc6b6aa917846535c6c4b6158961988_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m= \\lim_{x \\to \\pm\\infty} \\cfrac{\\cfrac{x^2+1}{x}}{x}=\\lim_{x \\to \\pm\\infty} \\cfrac{x^2+1}{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"264\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u4eca\u3001\u9650\u754c\u3092\u8a08\u7b97\u3057\u307e\u3059:<\/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-542fc353481ddc465b7a40f665d3661d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m = \\lim_{x \\to \\pm\\infty} \\cfrac{x^2+1}{x^2} = \\cfrac{+\\infty}{+\\infty} = \\cfrac{1}{1} = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"269\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u5206\u5b50\u3068\u5206\u6bcd\u304c\u540c\u3058\u6b21\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u7121\u9650\u5927\u9593\u306e\u7121\u9650\u5927\u306e\u4e0d\u78ba\u5b9a\u6027\u306e\u7d50\u679c\u306f\u3001\u6700\u9ad8\u6b21\u6570\u306e x \u306e\u4fc2\u6570\u306e\u9664\u7b97\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u4e0a\u8a18\u306e\u5236\u9650\u306f\u30bc\u30ed\u4ee5\u5916\u306e\u5b9f\u6570\u3092\u4e0e\u3048\u308b\u305f\u3081\u3001\u95a2\u6570\u306f\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u3092\u6301\u3061\u307e\u3059\u3002\u3053\u3053\u3067 y \u5207\u7247\u3092\u8a08\u7b97\u3057\u307e\u3059<\/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-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5bfe\u5fdc\u3059\u308b\u5f0f\u3092\u4f7f\u7528\u3057\u3066\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-45119c7a74d77a92d7a6cfd5b5c3544f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[f(x)-mx\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"173\" 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-9197669cc0e41aa22224b552b21b31ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[\\cfrac{x^2+1}{x}-1x\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"191\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p>\u5236\u9650\u3092\u8a08\u7b97\u3057\u3066\u307f\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-4d7fa012eace37e82c243012c91f1a5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[\\cfrac{x^2+1}{x}-x\\right] = \\cfrac{+\\infty}{+\\infty} - (+\\infty) = \\bm{+\\infty - \\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"412\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p>\u3057\u304b\u3057\u3001\u7121\u9650\u304b\u3089\u7121\u9650\u3092\u5f15\u3044\u305f\u4e0d\u78ba\u5b9a\u6027\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u9805\u3092\u5171\u901a\u306e\u5206\u6bcd\u306b\u6e1b\u3089\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001x \u3092\u5206\u6570\u306e\u5206\u6bcd\u3067\u4e57\u7b97\u304a\u3088\u3073\u9664\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-a2355ed9411470b9fd20a50ebbd48726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n=\\lim_{x \\to \\pm\\infty} \\left[\\cfrac{x^2+1}{x}-\\cfrac{x\\cdot x}{x} \\right] = \\lim_{x \\to \\pm\\infty} \\left[\\cfrac{x^2+1}{x}-\\cfrac{x^2}{x}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"391\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p> 2 \u3064\u306e\u9805\u306e\u5206\u6bcd\u304c\u540c\u3058\u306b\u306a\u3063\u305f\u306e\u3067\u3001\u305d\u308c\u3089\u3092\u30b0\u30eb\u30fc\u30d7\u5316\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-f932ebc8728669c7c6b57e115c444fc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[\\cfrac{x^2+1}{x}-\\cfrac{x^2}{x} \\right] =  \\lim_{x \\to \\pm\\infty} \\cfrac{x^2+1-x^2}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"358\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p>\u5206\u5b50\u3092\u64cd\u4f5c\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-c39259f829c9e99fc88819c6ae266e82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty}  \\cfrac{\\phantom{2}1\\phantom{2}}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"112\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u5236\u9650\u3092\u89e3\u6c7a\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-16a0044416d02e77b05f65f1bb93d4cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty}  \\cfrac{\\phantom{2}1\\phantom{2}}{x}= \\cfrac{1}{\\pm\\infty} = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"201\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001 <em>n<\/em> = 0 \u3068\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u306f\u4e00\u6b21\u95a2\u6570\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-6fbe1cc5f3362ddbd80ed0b29c0bb4ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/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-a68ac5c51acd0f68bd022aee64cd9cd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 1x+0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\"><\/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-4909df7491ef54f0df1e922bc29417f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=x}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u7814\u7a76\u3057\u305f\u95a2\u6570\u306f\u4ee5\u4e0b\u306e\u30b0\u30e9\u30d5\u306b\u8868\u3055\u308c\u307e\u3059\u3002\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u3053\u306e\u95a2\u6570\u306f\u7dda y=x \u306b\u975e\u5e38\u306b\u8fd1\u3065\u304d\u307e\u3059\u304c\u3001\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u3067\u3042\u308b\u305f\u3081\u3001\u7dda\u306b\u89e6\u308c\u308b\u3053\u3068\u306f\u3042\u308a\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\/image-1.png\" alt=\"\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u306e\u4f8b\" class=\"wp-image-1374\" width=\"424\" height=\"478\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-asintotas-oblicuas\"><\/span>\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u306b\u95a2\u3059\u308b\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2<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\u659c\u3081\u306e\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-8ecc70adc78bf259cf6e36c0dcf1bee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\frac{x^2+2x+3}{x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"150\" style=\"vertical-align: -14px;\"><\/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\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u306f\u6b21\u306e\u5f62\u5f0f\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-8e4adcc4368f6296906b6231bf17a6a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc<em>m<\/em>\u3068<em>n<\/em>\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u307e\u305a\u3001\u6b21\u306e\u5f0f\u3092\u9069\u7528\u3057\u3066<em>m<\/em>\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-dc38f695cee95c4c60c6e2591345119e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m = \\lim_{x \\to \\pm\\infty} \\frac{f(x)}{x} = \\lim_{x \\to \\pm\\infty} \\cfrac{\\cfrac{x^2+2x+3}{x+1}}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"293\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5206\u6570\u306e\u6027\u8cea\u3092\u9069\u7528\u3057\u3066\u5206\u6570\u3092\u5358\u7d14\u5316\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-ef59ac0cd51c39c615896543993c12b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty} \\frac{x^2+2x+3}{(x+1)\\cdot x}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"180\" style=\"vertical-align: -17px;\"><\/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-c51e373fd07a821f8e75d63e38f252dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty} \\frac{x^2+2x+3}{x^2+x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"180\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u3001\u305d\u306e\u9650\u754c\u3092\u89e3\u6c7a\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-653fa714bca94b5cc4f3ed715d7c1520_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty} \\frac{x^2+2x+3}{x^2+x}= \\frac{+\\infty}{+\\infty} = \\frac{1}{1} = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"308\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001 <em>m<\/em> = 1 \u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u516c\u5f0f\u3092\u9069\u7528\u3057\u3066\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u306e\u5207\u7247\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\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-e779b5ac239ae56c53427510dbd54dcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[f(x)-mx\\right] = \\lim_{x \\to \\pm\\infty} \\left[ \\frac{x^2+2x+3}{x+1}-1x\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"395\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5236\u9650\u3092\u8a08\u7b97\u3057\u3066\u307f\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-f95f290fbf258d45aa5765008d7aad13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[ \\frac{x^2+2x+3}{x+1}-x\\right]= \\bm{+\\infty - \\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"320\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u304b\u3057\u3001\u7121\u9650\u5f62\u5f0f\u304b\u3089\u7121\u9650\u5927\u3092\u5f15\u3044\u305f\u4e0d\u5b9a\u5f62\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u9805\u3092\u5171\u901a\u306e\u5206\u6bcd\u306b\u6e1b\u3089\u3057\u3066\u304b\u3089\u30b0\u30eb\u30fc\u30d7\u5316\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-0712d34ed442d9e12ef2490f04df078a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[ \\frac{x^2+2x+3}{x+1}-x\\right] =\\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty} \\left[ \\frac{x^2+2x+3}{x+1}-\\frac{x \\cdot (x+1)}{x+1} \\right] = \\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty} \\left[ \\frac{x^2+2x+3}{x+1}-\\frac{x^2+x}{x+1} \\right]=\\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty} \\frac{x^2+2x+3-(x^2+x)}{x+1}\\\\[6ex]\\displaystyle =\\lim_{x \\to \\pm\\infty} \\frac{x^2+2x+3-x^2-x}{x+1}=\\\\[6ex]=\\displaystyle \\lim_{x \\to \\pm\\infty} \\frac{x+3}{x+1}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"434\" width=\"300\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u5236\u9650\u3092\u89e3\u6c7a\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-ee7e1fdd8e781abed322fed1182ddb15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n =\\lim_{x \\to \\pm\\infty} \\frac{x+3}{x+1} = \\frac{\\infty}{\\infty} = \\frac{1}{1} = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"241\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3064\u307e\u308a\u3001\u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda\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-6fbe1cc5f3362ddbd80ed0b29c0bb4ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/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-69c0f50795c1f6034c0cd04201f614d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 1x + 1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\"><\/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-5ffe94db5ae8fa1abc72e6007c2c0586_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y = x + 1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\"><\/p>\n<\/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\u6709\u7406\u95a2\u6570\u306e\u3059\u3079\u3066\u306e\u659c\u7dda\u6f38\u8fd1\u7dda\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-144807b8c72afbd43bb3f97d69cedb35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{2x^2-5}{x+3}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"118\" style=\"vertical-align: -14px;\"><\/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\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u307e\u305a\u3001\u659c\u3081\u6f38\u8fd1\u7dda\u306e\u50be\u304d\u306e\u516c\u5f0f\u3092\u4f7f\u7528\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-bc900ded359235b2293ec151e715daea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m = \\lim_{x \\to \\pm\\infty} \\frac{f(x)}{x} = \\lim_{x \\to \\pm\\infty} \\cfrac{\\cfrac{2x^2-5}{x+3}}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"261\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5206\u6570\u306e\u6027\u8cea\u3092\u9069\u7528\u3057\u3066\u5206\u6570\u3092\u5358\u7d14\u5316\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-1c5afa9b1ca5f1c73e6b8e64c8fb9420_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty}\\frac{2x^2-5}{(x+3)\\cdot x}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"168\" style=\"vertical-align: -17px;\"><\/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-03a4b53a445bded103e8de4404620693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty}\\frac{2x^2-5}{x^2+3x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"149\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u9650\u754c\u3092\u6c7a\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-461c274fc210474eddaf061463e92aaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m =\\lim_{x \\to \\pm\\infty}\\frac{2x^2-5}{x^2+3x}= \\frac{+\\infty}{+\\infty} = \\frac{2}{1} = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"278\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3053\u306e\u6975\u9650\u306f\u30bc\u30ed\u4ee5\u5916\u306e\u5b9f\u6570\u3092\u4e0e\u3048\u308b\u305f\u3081\u3001\u50be\u304d\u304c 2 \u3067\u3042\u308b\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u3092\u6301\u3064\u6709\u7406\u95a2\u6570\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-left\">\u6b21\u306b\u3001\u5bfe\u5fdc\u3059\u308b\u5f0f\u3092\u9069\u7528\u3057\u3066\u5207\u7247\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\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-4a04a1abaebfc5e1781dd7d98399888e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[f(x)-mx\\right] = \\lim_{x \\to \\pm\\infty} \\left[\\frac{2x^2-5}{x+3}-2x\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"364\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5236\u9650\u3092\u8a08\u7b97\u3057\u3066\u307f\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-00f35703d153fe6911328d143588e1cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[\\frac{2x^2-5}{x+3}-2x\\right]= \\bm{+\\infty - \\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"298\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u304b\u3057\u3001\u7121\u9650\u5927\u306e\u5dee\u5206\u4e0d\u78ba\u5b9a\u6027\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u9805\u3092\u5171\u901a\u306e\u5206\u6bcd\u306b\u6e1b\u3089\u3057\u3066\u3001\u6b21\u306e\u64cd\u4f5c\u3092\u884c\u3044\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-4920e8b21b180c4f2740ce712d9f30d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle n = \\lim_{x \\to \\pm\\infty} \\left[\\frac{2x^2-5}{x+3}-2x\\right]=\\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty} \\left[\\frac{2x^2-5}{x+3}-\\frac{2x\\cdot (x+3)}{x+3} \\right] = \\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty} \\left[ \\frac{2x^2-5}{x+3}-\\frac{2x^2+6x}{x+3}\\right]=\\\\[6ex]=\\displaystyle\\lim_{x \\to \\pm\\infty}\\frac{2x^2-5-(2x^2+6x)}{x+3}\\\\[6ex]\\displaystyle =\\lim_{x \\to \\pm\\infty}\\frac{2x^2-5-2x^2-6x}{x+3}=\\\\[6ex]=\\displaystyle \\lim_{x \\to \\pm\\infty} \\frac{-6x-5}{x+3}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"434\" width=\"277\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u5236\u9650\u3092\u89e3\u6c7a\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-00b75da44399a44a4e215fd4baccf214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n =\\lim_{x \\to \\pm\\infty} \\frac{-6x-5}{x+3}= \\frac{\\infty}{\\infty}=\\frac{-6}{1} = \\bm{-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"292\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8981\u7d04\u3059\u308b\u3068\u3001\u5206\u6570\u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda\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-6fbe1cc5f3362ddbd80ed0b29c0bb4ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/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-ac6ac25ec7b85209d4d7d855e3d0b501_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=2x-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u95a2\u6570\u306e\u659c\u3081\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u304b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u95a2\u6570\u306b\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u304c\u3042\u308b\u5834\u5408\u3068\u3001\u305d\u308c\u304c\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u304b\u3092\u5b66\u3073\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u659c\u3081\u306e\u6f38\u8fd1\u7dda\u306e\u4f8b\u3092\u78ba\u8a8d\u3057\u3001\u6bb5\u968e\u7684\u306b\u89e3\u304f\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 \u659c\u7dda\u6f38\u8fd1\u7dda\u3068 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/\"> <span class=\"screen-reader-text\">\u659c\u7dda\u6f38\u8fd1\u7dda<\/span> \u3082\u3063\u3068\u8aad\u3080 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[11],"tags":[],"class_list":["post-22","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda (\u89e3\u6c7a\u6e08\u307f\u6f14\u7fd2)<\/title>\n<meta name=\"description\" content=\"\u95a2\u6570\u306e\u659c\u3081\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002 \u2705 \u659c\u3081\u6f38\u8fd1\u7dda\u306e\u6f14\u7fd2\u3092\u89e3\u3044\u305f\u3082\u306e\u3002 \u2705\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/ja\/\u659c\u3081\u306e\u6f38\u8fd1\u7dda\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 \u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda (\u89e3\u6c7a\u6e08\u307f\u6f14\u7fd2)\" \/>\n<meta property=\"og:description\" content=\"\u95a2\u6570\u306e\u659c\u3081\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002 \u2705 \u659c\u3081\u6f38\u8fd1\u7dda\u306e\u6f14\u7fd2\u3092\u89e3\u3044\u305f\u3082\u306e\u3002 \u2705\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/ja\/\u659c\u3081\u306e\u6f38\u8fd1\u7dda\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T11:07:37+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/asymptote-oblique-dune-fonction.webp\" \/>\n<meta name=\"author\" content=\"B1oN0W1@L5\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u57f7\u7b46\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"B1oN0W1@L5\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/\",\"url\":\"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/\",\"name\":\"\u25b7 \u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda (\u89e3\u6c7a\u6e08\u307f\u6f14\u7fd2)\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/ja\/#website\"},\"datePublished\":\"2023-09-17T11:07:37+00:00\",\"dateModified\":\"2023-09-17T11:07:37+00:00\",\"author\":{\"@id\":\"https:\/\/mathority.org\/ja\/#\/schema\/person\/c5d030d51df9fedd3b375fd3c5be378e\"},\"description\":\"\u95a2\u6570\u306e\u659c\u3081\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002 \u2705 \u659c\u3081\u6f38\u8fd1\u7dda\u306e\u6f14\u7fd2\u3092\u89e3\u3044\u305f\u3082\u306e\u3002 \u2705\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/#breadcrumb\"},\"inLanguage\":\"ja\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/ja\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u659c\u7dda\u6f38\u8fd1\u7dda\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/ja\/#website\",\"url\":\"https:\/\/mathority.org\/ja\/\",\"name\":\"\",\"description\":\"\u597d\u5947\u5fc3\u3068\u8a08\u7b97\u304c\u51fa\u4f1a\u3046\u5834\u6240 !\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/ja\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"ja\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/ja\/#\/schema\/person\/c5d030d51df9fedd3b375fd3c5be378e\",\"name\":\"B1oN0W1@L5\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ja\",\"@id\":\"https:\/\/mathority.org\/ja\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"B1oN0W1@L5\"},\"sameAs\":[\"http:\/\/mathority.org\/ja\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u25b7 \u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda (\u89e3\u6c7a\u6e08\u307f\u6f14\u7fd2)","description":"\u95a2\u6570\u306e\u659c\u3081\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002 \u2705 \u659c\u3081\u6f38\u8fd1\u7dda\u306e\u6f14\u7fd2\u3092\u89e3\u3044\u305f\u3082\u306e\u3002 \u2705","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/ja\/\u659c\u3081\u306e\u6f38\u8fd1\u7dda\/","og_locale":"ja_JP","og_type":"article","og_title":"\u25b7 \u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda (\u89e3\u6c7a\u6e08\u307f\u6f14\u7fd2)","og_description":"\u95a2\u6570\u306e\u659c\u3081\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002 \u2705 \u659c\u3081\u6f38\u8fd1\u7dda\u306e\u6f14\u7fd2\u3092\u89e3\u3044\u305f\u3082\u306e\u3002 \u2705","og_url":"https:\/\/mathority.org\/ja\/\u659c\u3081\u306e\u6f38\u8fd1\u7dda\/","article_published_time":"2023-09-17T11:07:37+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/asymptote-oblique-dune-fonction.webp"}],"author":"B1oN0W1@L5","twitter_card":"summary_large_image","twitter_misc":{"\u57f7\u7b46\u8005":"B1oN0W1@L5"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/","url":"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/","name":"\u25b7 \u95a2\u6570\u306e\u659c\u7dda\u6f38\u8fd1\u7dda (\u89e3\u6c7a\u6e08\u307f\u6f14\u7fd2)","isPartOf":{"@id":"https:\/\/mathority.org\/ja\/#website"},"datePublished":"2023-09-17T11:07:37+00:00","dateModified":"2023-09-17T11:07:37+00:00","author":{"@id":"https:\/\/mathority.org\/ja\/#\/schema\/person\/c5d030d51df9fedd3b375fd3c5be378e"},"description":"\u95a2\u6570\u306e\u659c\u3081\u6f38\u8fd1\u7dda\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002 \u2705 \u659c\u3081\u6f38\u8fd1\u7dda\u306e\u6f14\u7fd2\u3092\u89e3\u3044\u305f\u3082\u306e\u3002 \u2705","breadcrumb":{"@id":"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/#breadcrumb"},"inLanguage":"ja","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/ja\/%e6%96%9c%e3%82%81%e3%81%ae%e6%bc%b8%e8%bf%91%e7%b7%9a\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/ja\/"},{"@type":"ListItem","position":2,"name":"\u659c\u7dda\u6f38\u8fd1\u7dda"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/ja\/#website","url":"https:\/\/mathority.org\/ja\/","name":"","description":"\u597d\u5947\u5fc3\u3068\u8a08\u7b97\u304c\u51fa\u4f1a\u3046\u5834\u6240 !","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/ja\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"ja"},{"@type":"Person","@id":"https:\/\/mathority.org\/ja\/#\/schema\/person\/c5d030d51df9fedd3b375fd3c5be378e","name":"B1oN0W1@L5","image":{"@type":"ImageObject","inLanguage":"ja","@id":"https:\/\/mathority.org\/ja\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"B1oN0W1@L5"},"sameAs":["http:\/\/mathority.org\/ja"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/ja\/wp-json\/wp\/v2\/posts\/22","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/ja\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/ja\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/ja\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/ja\/wp-json\/wp\/v2\/comments?post=22"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/ja\/wp-json\/wp\/v2\/posts\/22\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/ja\/wp-json\/wp\/v2\/media?parent=22"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/ja\/wp-json\/wp\/v2\/categories?post=22"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/ja\/wp-json\/wp\/v2\/tags?post=22"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}