{"id":18,"date":"2023-09-17T11:09:13","date_gmt":"2023-09-17T11:09:13","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e3%82%bc%e3%83%ad%e9%96%93%e3%81%ae%e3%82%bc%e3%83%ad-0-0-%e4%b8%8d%e5%ae%9a\/"},"modified":"2023-09-17T11:09:13","modified_gmt":"2023-09-17T11:09:13","slug":"%e3%82%bc%e3%83%ad%e9%96%93%e3%81%ae%e3%82%bc%e3%83%ad-0-0-%e4%b8%8d%e5%ae%9a","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e3%82%bc%e3%83%ad%e9%96%93%e3%81%ae%e3%82%bc%e3%83%ad-0-0-%e4%b8%8d%e5%ae%9a\/","title":{"rendered":"\u30bc\u30ed\u9593\u306e\u30bc\u30ed\u4e0d\u78ba\u5b9a\u6027 (0\/0)"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u4e0d\u78ba\u5b9f\u6027\u304c 0\/0 \u306b\u306a\u308b\u95a2\u6570\u306e\u5236\u9650\u3092\u4fdd\u5b58\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30bc\u30ed\u9593\u306e\u30bc\u30ed\u306e\u4e0d\u78ba\u5b9a\u6027\u306b\u95a2\u3059\u308b\u89e3\u7b54\u6e08\u307f\u306e\u6f14\u7fd2\u3092\u4f7f\u7528\u3057\u3066\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\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\/indetermination-zero-entre-zero-00.webp\" alt=\"\" class=\"wp-image-888\" width=\"213\" height=\"214\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-resolver-la-indeterminacion-cero-entre-cero-00\"><\/span>\u30bc\u30ed (0\/0) \u9593\u306e\u30bc\u30ed\u4e0d\u78ba\u5b9a\u6027\u3092\u89e3\u304f\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306b\u3001\u30bc\u30ed (0\/0) \u9593\u306e\u4e0d\u78ba\u5b9a\u6027\u304c\u30bc\u30ed\u306b\u306a\u308b\u95a2\u6570\u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u305f\u3081\u306b\u3001\u4f8b\u3092\u6bb5\u968e\u7684\u306b\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-8756377c47addb7fc7c1a9101d6fe29c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 2} \\frac{x^2-x-2}{x^2-3x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"123\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u307e\u305a\u3001\u95a2\u6570\u306b x \u306e\u5024\u3092\u4ee3\u5165\u3057\u3066\u5236\u9650\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-57f54a6e222522bf26a65b6dee7e2334_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 2} \\frac{x^2 - x -2}{x^2-3x+2}=\\frac{2^2 -2-2}{2^2-3\\cdot 2+2}=\\frac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"286\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u3057\u304b\u3057\u3001\u4e0d\u78ba\u5b9a\u6027 0 \u3092 0 \u3067\u5272\u3063\u305f\u5024\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px; margin-bottom:30px\">\n<p style=\"text-align:left\">\u70b9\u95a2\u6570\u306e\u6975\u9650\u306b\u3088\u3063\u3066<strong>\u4e0d\u78ba\u5b9f\u6027 0\/0 \u304c<\/strong>\u4e0e\u3048\u3089\u308c\u308b\u5834\u5408\u3001\u5206\u5b50\u3068\u5206\u6bcd\u306e\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\u3057\u3001\u5171\u901a\u56e0\u6570\u3092\u5358\u7d14\u5316\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5206\u6570\u306e\u5206\u5b50\u3068\u5206\u6bcd\u306e\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u30eb\u30d5\u30a3\u30cb\u306e\u6cd5\u5247\u3092\u4f7f\u7528\u3057\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\/factorisation-indetermination-00.webp\" alt=\"\u4e0d\u78ba\u5b9a\u56e0\u6570\u5206\u89e3 0\/0\" class=\"wp-image-894\" width=\"429\" height=\"312\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> <span style=\"color:#FF9B28;\">\u27a4<\/span><u style=\"text-decoration-color:#FF9B28;\">\u591a\u9805\u5f0f\u306e\u56e0\u6570\u5206\u89e3\u306e\u65b9\u6cd5<\/u>\u304c\u308f\u304b\u3089\u306a\u3044\u5834\u5408\u306f\u3001\u591a\u9805\u5f0f\u306b\u7279\u5316\u3057\u305f\u30b5\u30a4\u30c8 ( <u style=\"text-decoration-color:#FF9B28;\">www.polinomios.org)<\/u>\u3067\u8aac\u660e\u3092\u53c2\u7167\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u591a\u9805\u5f0f\u304c\u56e0\u6570\u5206\u89e3\u3055\u308c\u308b\u3068\u3001\u6975\u9650\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-225121e089bcdcdb7ea055e9fd01c61d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 2} \\cfrac{x^2-x-2}{x^2-3x+2}=\\lim_{x \\to 2}\\frac{(x+1)(x-2)}{(x-1)(x-2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"288\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5206\u6570\u306e\u5206\u5b50\u3068\u5206\u6bcd\u3067\u7e70\u308a\u8fd4\u3055\u308c\u308b\u56e0\u6570\u3092\u524a\u9664\u3059\u308b\u3053\u3068\u3067\u3001\u6975\u9650\u3092\u5358\u7d14\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-461b8157cb8cdf50595cc35c590dc720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 2} \\cfrac{(x+1)\\cancel{(x-2)}}{(x-1)\\cancel{(x-2)}}=\\lim_{x \\to 2} \\cfrac{(x+1)}{(x-1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"254\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u5236\u9650\u3092\u518d\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-c1d6173c0ee113815a638c71e1c36e7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 2} \\cfrac{x+1}{x-1}=\\cfrac{2+1}{2-1}=\\cfrac{3}{1}=\\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"206\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\u3057\u3066\u5358\u7d14\u5316\u3059\u308b\u3068\u3001\u6975\u9650\u3067\u306e\u89e3\u3092\u898b\u3064\u3051\u308b\u306e\u306f\u975e\u5e38\u306b\u7c21\u5358\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-00-con-raices\"><\/span>\u6839\u3092\u6301\u3064\u4e0d\u78ba\u5b9a\u6027 0\/0<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6709\u7406\u95a2\u6570\u306e 0\/0 \u306e\u4e0d\u78ba\u5b9a\u6027\u304c\u3069\u306e\u3088\u3046\u306b\u89e3\u6c7a\u3055\u308c\u308b\u304b\u3092\u898b\u3066\u304d\u307e\u3057\u305f\u3002\u305f\u3060\u3057\u3001\u6975\u9650\u304c\u7121\u7406\u6570 (\u307e\u305f\u306f\u30e9\u30b8\u30ab\u30eb) \u95a2\u6570\u306e\u5834\u5408\u30010\/0 \u306e\u4e0d\u78ba\u5b9a\u6027\u306f\u5225\u306e\u65b9\u6cd5\u3067\u89e3\u6c7a\u3055\u308c\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-077724689257ed57dfb621061adba77e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1} \\frac{x-1}{\\sqrt{x}-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"89\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u307e\u305a\u3001\u6b21\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u5236\u9650\u3092\u89e3\u6c7a\u3057\u3088\u3046\u3068\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-27ddc1a2cc56460b9f511d4c7d6b48c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1} \\frac{x-1}{\\sqrt{x}-1}=\\frac{1-1}{\\sqrt{1}-1}=\\frac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"207\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u3057\u304b\u3057\u3001\u30bc\u30ed\u30aa\u30fc\u30d0\u30fc\u30bc\u30ed\u306e\u4e0d\u78ba\u5b9a\u6027\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px; margin-bottom:30px\">\n<p style=\"text-align:left\"><strong>\u6839\u3092\u6301\u3064\u95a2\u6570\u306e\u6975\u9650\u306b\u3088\u308a\u4e0d\u78ba\u5b9a\u6027 0\/0 \u304c\u5f97\u3089\u308c\u308b<\/strong>\u5834\u5408\u3001\u5206\u6570\u306e\u5206\u5b50\u3068\u5206\u6bcd\u306b\u6839\u53f7\u5f0f\u306e\u5171\u5f79\u3092\u4e57\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<p> \u27a4 \u5171\u5f79\u306f\u540c\u3058\u7121\u7406\u6570\u5f0f\u3067\u3059\u304c\u3001\u4e2d\u592e\u306e\u7b26\u53f7\u304c\u5909\u66f4\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p>\u6b21\u306b\u3001\u5206\u6570\u306e\u5206\u5b50\u3068\u5206\u6bcd\u306e\u4e21\u65b9\u306b\u6839\u53f7\u5f0f\u306e\u5171\u5f79\u3092\u639b\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-28c2950e1fe30fbda237ea5d154fdbd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1} \\frac{\\left(x-1\\right)\\cdot\\left(\\sqrt{x}+1\\right)}{\\left(\\sqrt{x}-1\\right)\\cdot\\left(\\sqrt{x}+1\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"185\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u30bf\u30a4\u30d7\u306e\u5236\u9650\u5185\u3067\u306f\u3001\u3053\u306e\u30b9\u30c6\u30c3\u30d7\u3092\u5b9f\u884c\u3059\u308b\u3053\u3068\u3067\u3001\u7c21\u7d20\u5316\u3067\u304d\u308b\u6ce8\u76ee\u3059\u3079\u304d\u30a2\u30a4\u30c7\u30f3\u30c6\u30a3\u30c6\u30a3\u3092\u5e38\u306b\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u5206\u6bcd\u306b\u306f\u548c\u3068\u5dee\u306e\u7a4d\u304c\u542b\u307e\u308c\u308b\u305f\u3081\u3001\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-c2ec8901a2ec84af3d8b70143894ca38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1} \\frac{\\left(x-1\\right)\\cdot\\left(\\sqrt{x}+1\\right)}{\\left(\\sqrt{x}\\right)^2-1^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"170\" style=\"vertical-align: -20px;\"><\/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-785777714acb47d4f3772980575c4dac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1} \\frac{\\left(x-1\\right)\\cdot\\left(\\sqrt{x}+1\\right)}{x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"170\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5206\u5b50\u3068\u5206\u6bcd\u3067\u7e70\u308a\u8fd4\u3055\u308c\u308b\u56e0\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-27813ee911be89725aa9e79230e1e76a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1} \\frac{\\cancel{\\left(x-1\\right)}\\cdot\\left(\\sqrt{x}+1\\right)}{\\cancel{x-1}}=\\lim_{x \\to 1}\\left(\\sqrt{x}+1\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"296\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001\u5236\u9650\u306e\u7d50\u679c\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\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-a7746fb54d762beeeb44041650a78004_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1}\\left(\\sqrt{x}+1\\right)=\\sqrt{1}+1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"212\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-indeterminacion-00\"><\/span>\u4e0d\u78ba\u5b9a\u6027\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f 0\/0<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4ee5\u4e0b\u306b\u30010\/0 \u306e\u4e0d\u78ba\u5b9a\u6027\u3092\u4e0e\u3048\u308b\u95a2\u6570\u306e\u6975\u9650\u306b\u3064\u3044\u3066\u3001\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3059\u308b\u6f14\u7fd2\u3092\u3044\u304f\u3064\u304b\u7528\u610f\u3057\u307e\u3057\u305f\u3002\u305d\u308c\u3089\u3092\u5b9f\u884c\u3057\u3066\u3001\u89e3\u6c7a\u7b56\u3092\u78ba\u8a8d\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p>\u5236\u9650\u306e\u89e3\u6c7a\u306b\u3064\u3044\u3066\u8cea\u554f\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u30b3\u30e1\u30f3\u30c8\u6b04\u3067\u8cea\u554f\u3067\u304d\u308b\u3053\u3068\u3092\u5fd8\u308c\u306a\u3044\u3067\u304f\u3060\u3055\u3044\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1<\/h3>\n<p>\u6b21\u306e\u6709\u7406\u95a2\u6570\u306e\u70b9 x=-2 \u306b\u304a\u3051\u308b\u6975\u9650\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-75edf8ebdda678fce2752f4ee280e8de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -2}\\frac{x^2 +2x}{x^2-x-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"125\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8ad6\u7406\u7684\u306b\u306f\u3001\u307e\u305a\u5236\u9650\u3092\u89e3\u6c7a\u3057\u3088\u3046\u3068\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-9698cb3f234f704a80727c0a46642932_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -2} \\frac{x^2 +2x}{x^2-x-6}=\\frac{(-2)^2+2\\cdot (-2)}{(-2)^2-(-2)-6}=\\frac{4-4}{4+2-6}=\\frac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"418\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u304b\u3057\u3001\u6700\u7d42\u7684\u306b\u306f 0\/0 \u306e\u4e0d\u78ba\u5b9a\u6027\u304c\u751f\u3058\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5206\u5b50\u3068\u5206\u6bcd\u306e\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\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-1dce911a3cd5359ea3b28e3e42159de9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -2}\\frac{x^2 +2x}{x^2-x-6}=\\lim_{x \\to -2}\\frac{x(x+2)}{(x+2)(x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"303\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3053\u3053\u3067\u3001\u5206\u5b50\u3068\u5206\u6bcd\u3067\u7e70\u308a\u8fd4\u3055\u308c\u3066\u3044\u308b\u62ec\u5f27\u3092\u524a\u9664\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-c38f52ab7f40e158b0a100bd9768a5d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -2}\\frac{x\\cancel{(x+2)}}{\\cancel{(x+2)}(x-3)}=\\lim_{x \\to -2}\\frac{x}{x-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"263\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u5f8c\u306b\u3001\u7c21\u7565\u5316\u3055\u308c\u305f\u5206\u6570\u3092\u4f7f\u7528\u3057\u3066\u5236\u9650\u3092\u518d\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-30649d52cdf83b256558d41b7b4ccaf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -2}\\frac{x}{x-3}=\\cfrac{-2}{-2-3}=\\cfrac{-2}{-5}=\\mathbf{\\cfrac{2}{5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"258\" style=\"vertical-align: -12px;\"><\/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> x \u304c -1 \u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u6b21\u306e\u95a2\u6570\u306e\u6975\u9650\u3092\u89e3\u304d\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-72320d2638e9bc82cfc3f5f27b57857d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1}\\frac{x^3+2x^2-x-2}{x^3-5x^2+2x+8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"182\" 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\u3044\u3064\u3082\u306e\u3088\u3046\u306b\u5236\u9650\u3092\u89e3\u6c7a\u3057\u3088\u3046\u3068\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-a8e730787abc8d8843e4a818b84ee19e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1}\\frac{x^3+2x^2-x-2}{x^3-5x^2+2x+8}=\\frac{(-1)^3+2(-1)^2-(-1)-2}{(-1)^3-5(-1)^2+2(-1)+8} =\\frac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"462\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u304b\u3057\u30010 \u3068 0 \u306e\u9593\u306e\u4e0d\u78ba\u5b9a\u6027 0 \u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5206\u6570\u306e 2 \u3064\u306e\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\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-bab10366d036af48209c29fa26582f3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1}\\frac{x^3+2x^2-x-2}{x^3-5x^2+2x+8}=\\lim_{x \\to -1}\\frac{(x-1)(x+1)(x+2)}{(x+1)(x-2)(x-4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"415\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3053\u308c\u3067\u591a\u9805\u5f0f\u3092\u5358\u7d14\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-3e66552225f948ec300edb84385118a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1}\\frac{(x-1)\\cancel{(x+1)}(x+2)}{\\cancel{(x+1)}(x-2)(x-4)}=\\lim_{x \\to -1}\\frac{(x-1)(x+2)}{(x-2)(x-4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"386\" style=\"vertical-align: -17px;\"><\/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-91295719745ca73b6874a7ebbf382bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1} \\frac{(x-1)(x+2)}{(x-2)(x-4)}=\\frac{ (-1-1)(-1+2)}{(-1-2)(-1-4)}=\\frac{(-2)\\cdot (1)}{(-3)\\cdot (-5)}=\\frac{\\bm{-2}}{\\bm{15}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"478\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 3<\/h3>\n<p>\u6b21\u306e\u6839\u95a2\u6570\u306e\u6975\u9650\u306e\u89e3\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-d836a32312bb9851913a731ed3ee00e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2}\\frac{x^2-3x+2}{2-\\sqrt{2x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"123\" style=\"vertical-align: -16px;\"><\/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\u5236\u9650\u306b\u3088\u3063\u3066\u4f55\u3089\u304b\u306e\u4e0d\u78ba\u5b9a\u6027\u304c\u751f\u3058\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c9b81e0139d2863ee0c5a47c0de67ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2}\\frac{x^2-3x+2}{2-\\sqrt{2x}}=\\frac{2^2-3\\cdot2+2}{2-\\sqrt{2\\cdot 2}}=\\frac{4-6+2}{2-2}=\\frac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"383\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3053\u306e\u6975\u9650\u306b\u3088\u308a\u3001\u4e0d\u78ba\u5b9a\u6027\u30bc\u30ed\u304c\u30bc\u30ed\u3067\u9664\u7b97\u3055\u308c\u3001\u95a2\u6570\u5185\u306b\u6839\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5206\u6570\u306e\u5206\u5b50\u3068\u5206\u6bcd\u306b\u6839\u53f7\u5f0f\u306e\u5171\u5f79\u3092\u4e57\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-063e060aed092d9be29b22ed951b160e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2}\\frac{\\left(x^2-3x+2\\right)\\cdot \\left(2+\\sqrt{2x}\\right)}{\\left(2-\\sqrt{2x}\\right)\\cdot \\left(2+\\sqrt{2x}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"232\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5206\u6bcd\u306f\u3001\u548c\u3068\u5dee\u306e\u7a4d\u306e\u6ce8\u76ee\u3059\u3079\u304d\u6052\u7b49\u5f0f\u306e\u5c55\u958b\u306b\u5bfe\u5fdc\u3059\u308b\u305f\u3081\u3001\u6b21\u306e\u3088\u3046\u306b\u5358\u7d14\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-eee18c8d1ddc9d4b6ccffd46123d23b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2}\\frac{\\left(x^2-3x+2\\right)\\cdot \\left(2+\\sqrt{2x}\\right)}{2^2-\\left(\\sqrt{2x}\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"53\" width=\"232\" style=\"vertical-align: -24px;\"><\/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-a2bf66723dd14d247966d1e5a39455fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2}\\frac{\\left(x^2-3x+2\\right)\\cdot \\left(2+\\sqrt{2x}\\right)}{4-2x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"232\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305f\u3060\u3057\u3001\u5206\u6570\u306e\u9805\u3092\u5358\u7d14\u5316\u3059\u308b\u3053\u3068\u306f\u307e\u3060\u3067\u304d\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\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-3fd2ce5086ce32fbee964b19d6e89b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2}\\frac{\\left(x^2-3x+2\\right)\\cdot \\left(2+\\sqrt{2x}\\right)}{4-2x}=\\lim_{x\\to 2}\\frac{(x-1)(x-2)\\cdot\\left(2+\\sqrt{2x}\\right)}{-2(x-2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"494\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u5206\u6570\u3092\u5358\u7d14\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-714622fdaaae18830b983aafc10d59a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2}\\frac{(x-1)\\cancel{(x-2)}\\left(2+\\sqrt{2x}\\right)}{-2\\cancel{(x-2)}}=\\lim_{x\\to 2}\\frac{(x-1)\\left(2+\\sqrt{2x}\\right)}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"423\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3053\u308c\u3067\u3001\u5236\u9650\u306e\u7d50\u679c\u3092\u5224\u65ad\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u305f\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-0cdb8a8503f2cca27da58166341770e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2}\\frac{(x-1)\\left(2+\\sqrt{2x}\\right)}{-2}=\\frac{(2-1)\\left(2+\\sqrt{2\\cdot 2}\\right)}{-2}=\\frac{1\\cdot (2+2)}{-2}=\\bm{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"497\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 4<\/h3>\n<p>\u6b21\u306e\u6839\u95a2\u6570\u306e x \u304c 0 \u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u6975\u9650\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d51d72812833040f2ae7849fde8a200_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{x^2+6x}{3-\\sqrt{4x+9}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"129\" style=\"vertical-align: -16px;\"><\/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\u3044\u3064\u3082\u306e\u3088\u3046\u306b\u95a2\u6570\u306e\u6975\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-cc916be15d7628e8d06e6e7e1599497d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{x^2+6x}{3-\\sqrt{4x+9}}=\\frac{0+0}{3-\\sqrt{4\\cdot 0+9}}=\\frac{0}{3-3}=\\frac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"365\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u304b\u3057\u30010\/0 \u3068\u3044\u3046\u4e0d\u5b9a\u5f62\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306e\u5206\u5b50\u3068\u5206\u6bcd\u306b\u7121\u7406\u6570\u5f0f\u306e\u5171\u5f79\u3092\u639b\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-78fa62a7006cedf8722392497434d9e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{\\left(x^2+6x\\right)\\cdot\\left(3+\\sqrt{4x+9}\\right)}{\\left(3-\\sqrt{4x+9}\\right)\\cdot\\left(3+\\sqrt{4x+9}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"268\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5bfe\u5fdc\u3059\u308b\u6ce8\u76ee\u3059\u3079\u304d\u6052\u7b49\u5f0f\u3092\u9069\u7528\u3057\u3066\u5206\u6bcd\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-0836db36961bb85ab26e94b3a2dc9f8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{\\left(x^2+6x\\right)\\cdot\\left(3+\\sqrt{4x+9}\\right)}{3^2-\\left(\\sqrt{4x+9}\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"232\" style=\"vertical-align: -23px;\"><\/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-ae003c861a15eaf19b8b7b2babd9aca1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{\\left(x^2+6x\\right)\\cdot\\left(3+\\sqrt{4x+9}\\right)}{9-(4x+9)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"232\" 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-7fbf174fd70460599e41408dba1cf1da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{\\left(x^2+6x\\right)\\cdot\\left(3+\\sqrt{4x+9}\\right)}{-4x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"232\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b21\u306b\u3001\u5171\u901a\u56e0\u6570\u3092\u53d6\u5f97\u3057\u3066\u5206\u5b50\u306e\u4e8c\u9805\u3092\u56e0\u6570\u5206\u89e3\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-f1a55c3d856552106a7f81eb9bcc6eff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{\\left(x^2+6x\\right)\\cdot\\left(3+\\sqrt{4x+9}\\right)}{-4x}=\\lim_{x\\to 0}\\frac{\\bigl[x(x+6)\\bigr]\\cdot\\left(3+\\sqrt{4x+9}\\right)}{-4x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"495\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u95a2\u6570\u306e\u5206\u5b50\u3068\u5206\u6bcd\u3067\u7e70\u308a\u8fd4\u3055\u308c\u308b\u56e0\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-9d3996ef26d5889e65bf941fc268ed93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{\\cancel{x}\\left(x+6\\right)\\left(3+\\sqrt{4x+9}\\right)}{-4\\cancel{x}}=\\lim_{x\\to 0}\\frac{(x+6)\\left(3+\\sqrt{4x+9}\\right)}{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"443\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u95a2\u6570\u306e\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-1b4874df2f48ad131d48c4e5923a5b02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x\\to 0}\\frac{(x+6)\\left(3+\\sqrt{4x+9}\\right)}{-4}=\\\\[3ex]\\displaystyle=\\frac{(0+6)\\left(3+\\sqrt{4\\cdot 0+9}\\right)}{-4}=\\\\[3ex]\\displaystyle=\\frac{6\\cdot (3+3)}{-4}=\\frac{36}{-4}=\\bm{-9}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"153\" width=\"222\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 5<\/h3>\n<p> 0\/0 \u4e0d\u78ba\u5b9a\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u6b21\u306e\u6975\u9650\u3092\u89e3\u304d\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-351bbe422f066b4d599d9c71145555ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1}\\frac{x^3+2x^2-x-2}{x^3+5x^2+7x+3}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"182\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u6a2a\u65b9\u5411\u306e\u9650\u754c\/\">\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/a><\/span><\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u307e\u305a\u3001\u5236\u9650\u3092\u89e3\u6c7a\u3057\u3088\u3046\u3068\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-3ac5769f9f54b659b8472de66387df17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1}\\frac{x^3+2x^2-x-2}{x^3+5x^2+7x+3}=\\frac{(-1)^3+2(-1)^2-(-1)-2}{(-1)^3+5(-1)^2+7(-1)+3}=\\frac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"462\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u304b\u3057\u3001\u6975\u9650\u3067\u306f\u30bc\u30ed\u5bfe\u30bc\u30ed\u306e\u4e0d\u78ba\u5b9a\u6027\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5206\u5b50\u3068\u5206\u6bcd\u306e\u591a\u9805\u5f0f\u3092\u56e0\u6570\u5206\u89e3\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-db8f9479bc9c37f7aab1b1547eb85040_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1}\\frac{x^3+2x^2-x-2}{x^3+5x^2+7x+3}=\\lim_{x \\to -1}\\frac{(x-1)(x+1)(x+2)}{(x+1)^2(x+3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"415\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3053\u3053\u3067\u3001\u5206\u5b50\u3068\u5206\u6bcd\u3067\u7e70\u308a\u8fd4\u3055\u308c\u308b\u56e0\u5b50\u3092\u524a\u9664\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-d338fd493df4716cc935542aa9caa99b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1} \\cfrac{(x-1)\\cancel{(x+1)}(x+2)}{(x+1)^{\\cancel{2}}(x+3)}=\\lim_{x \\to -1}\\cfrac{(x-1)(x+2)}{(x+1)(x+3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"384\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u3001\u5236\u9650\u3092\u518d\u5ea6\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-7e67777781db8e107e153fd445404f40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1}\\frac{(x-1)(x+2)}{(x+1)(x+3)}=\\frac{(-1-1)(-1+2)}{(-1+1)(-1+3)}=\\frac{-2\\cdot 1}{0 \\cdot 2}=\\frac{-2}{0} =\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"479\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u304b\u3057\u3001\u3053\u3053\u3067\u3001\u6570\u5024\u3092 0 \u3067\u5272\u3063\u305f\u5024\u304c\u4e0d\u78ba\u5b9a\u3067\u3042\u308b\u3053\u3068\u306b\u6c17\u3065\u304d\u307e\u3057\u305f\u3002\u3057\u305f\u304c\u3063\u3066\u3001x \u304c -1 \u306b\u306a\u308b\u50be\u5411\u304c\u3042\u308b\u5834\u5408\u306e\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-left\">\u307e\u305a\u3001\u5de6\u5074\u306e\u70b9 x=-1 \u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u6975\u9650\u3092\u89e3\u304d\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9d9a116a8f65f341ea8a4e497d8687d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1^{-}}\\frac{(x-1)(x+2)}{(x+1)(x+3)}=\\frac{(-1-1)\\cdot (-1+2)}{(-1+1)\\cdot (-1+3)}=\\frac{-2}{-0}=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"444\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b21\u306b\u3001\u53f3\u5074\u306e\u70b9 x=-1 \u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6a2a\u65b9\u5411\u306e\u9650\u754c\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-3ebfe6934dca4dae43c3c305708e1965_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -1^{+}}\\frac{(x-1)(x+2)}{(x+1)(x+3)}=\\frac{(-1-1)\\cdot (-1+2)}{(-1+1)\\cdot (-1+3)}=\\frac{-2}{+0}=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"444\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u6a2a\u65b9\u5411\u306e\u6975\u9650\u304c\u4e00\u81f4\u3057\u306a\u3044\u305f\u3081\u3001x=-1 \u306b\u304a\u3051\u308b\u95a2\u6570\u306e\u6975\u9650\u306f\u5b58\u5728\u3057\u307e\u305b\u3093\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-0d26d76501f64d72e6b980c160f7858b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\displaystyle \\lim_{x \\to -1^-}f(x)= +\\infty\\neq\\lim_{x \\to -1^+}f(x)=-\\infty\\ \\bm{\\longrightarrow} \\ \\cancel{\\exists} \\lim_{x \\to -1} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"436\" style=\"vertical-align: -14px;\"><\/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\u4e0d\u78ba\u5b9f\u6027\u304c 0\/0 \u306b\u306a\u308b\u95a2\u6570\u306e\u5236\u9650\u3092\u4fdd\u5b58\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30bc\u30ed\u9593\u306e\u30bc\u30ed\u306e\u4e0d\u78ba\u5b9a\u6027\u306b\u95a2\u3059\u308b\u89e3\u7b54\u6e08\u307f\u306e\u6f14\u7fd2\u3092\u4f7f\u7528\u3057\u3066\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u30bc\u30ed (0\/0) \u9593\u306e\u30bc\u30ed\u4e0d\u78ba\u5b9a\u6027\u3092\u89e3\u304f\u65b9\u6cd5 \u6b21\u306b\u3001\u30bc &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e3%82%bc%e3%83%ad%e9%96%93%e3%81%ae%e3%82%bc%e3%83%ad-0-0-%e4%b8%8d%e5%ae%9a\/\"> <span class=\"screen-reader-text\">\u30bc\u30ed\u9593\u306e\u30bc\u30ed\u4e0d\u78ba\u5b9a\u6027 (0\/0)<\/span> \u3082\u3063\u3068\u8aad\u3080 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