{"id":18,"date":"2023-09-17T11:09:13","date_gmt":"2023-09-17T11:09:13","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e9%9b%b6%e4%b9%8b%e9%97%b4-%e9%9b%b6-0-0-%e4%b8%8d%e7%a1%ae%e5%ae%9a\/"},"modified":"2023-09-17T11:09:13","modified_gmt":"2023-09-17T11:09:13","slug":"%e9%9b%b6%e4%b9%8b%e9%97%b4-%e9%9b%b6-0-0-%e4%b8%8d%e7%a1%ae%e5%ae%9a","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e9%9b%b6%e4%b9%8b%e9%97%b4-%e9%9b%b6-0-0-%e4%b8%8d%e7%a1%ae%e5%ae%9a\/","title":{"rendered":"\u96f6\u4e4b\u95f4\u7684\u96f6\u4e0d\u786e\u5b9a\u6027 (0\/0)"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u5f53\u4e0d\u786e\u5b9a\u6027\u4e3a 0\/0 \u65f6\u5982\u4f55\u4fdd\u5b58\u51fd\u6570\u7684\u6781\u9650\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u6765\u7ec3\u4e60\u96f6\u4e0e\u96f6\u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u6027\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>\u5982\u4f55\u89e3\u51b3\u96f6\uff080\/0\uff09\u4e4b\u95f4\u7684\u96f6\u4e0d\u786e\u5b9a\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7136\u540e\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u5f53\u51fd\u6570\u7ed9\u51fa\u96f6 (0\/0) \u4e4b\u95f4\u7684\u96f6\u4e0d\u786e\u5b9a\u6027\u65f6\uff0c\u5982\u4f55\u8ba1\u7b97\u51fd\u6570\u7684\u6781\u9650\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u9010\u6b65\u8ba1\u7b97\u4e00\u4e2a\u793a\u4f8b\uff1a<\/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>\u6211\u4eec\u9996\u5148\u5c1d\u8bd5\u901a\u8fc7\u5c06 x \u7684\u503c\u4ee3\u5165\u51fd\u6570\u6765\u8ba1\u7b97\u6781\u9650\uff1a<\/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>\u4f46\u6211\u4eec\u5f97\u5230\u4e0d\u786e\u5b9a\u6027 0 \u9664\u4ee5 0\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\">\u5f53\u70b9\u51fd\u6570\u7684\u6781\u9650\u7ed9\u51fa<strong>\u4e0d\u786e\u5b9a\u6027 0\/0<\/strong>\u65f6\uff0c\u9700\u8981\u5bf9\u5206\u5b50\u548c\u5206\u6bcd\u7684\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u7136\u540e\u7b80\u5316\u516c\u56e0\u5f0f\u3002<\/p>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u5bf9\u5206\u6570\u7684\u5206\u5b50\u548c\u5206\u6bcd\u7684\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u4f7f\u7528\u9c81\u83f2\u5c3c\u89c4\u5219\uff1a <\/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\u786e\u5b9a\u6027\u56e0\u5f0f\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>\u5982\u679c\u60a8\u4e0d\u77e5\u9053<u style=\"text-decoration-color:#FF9B28;\">\u5982\u4f55\u5206\u89e3\u591a\u9879\u5f0f<\/u>\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u67e5\u770b\u6211\u4eec\u4e13\u95e8\u7814\u7a76\u591a\u9879\u5f0f\u7684\u7f51\u7ad9\u4e0a\u7684\u8bf4\u660e\uff1a <u style=\"text-decoration-color:#FF9B28;\">www.polinomios.org<\/u><\/p>\n<p>\u56e0\u6b64\uff0c\u4e00\u65e6\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u6781\u9650\u5982\u4e0b\uff1a<\/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>\u73b0\u5728\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6d88\u9664\u5206\u6570\u5206\u5b50\u548c\u5206\u6bcd\u4e2d\u91cd\u590d\u7684\u56e0\u5b50\u6765\u7b80\u5316\u6781\u9650\uff1a<\/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\">\u6700\u540e\uff0c\u6211\u4eec\u91cd\u65b0\u8ba1\u7b97\u6781\u9650\uff1a<\/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>\u6b63\u5982\u4f60\u6240\u770b\u5230\u7684\uff0c\u4e00\u65e6\u6211\u4eec\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u548c\u5316\u7b80\uff0c\u5c31\u5f88\u5bb9\u6613\u627e\u5230\u6781\u9650\u89e3\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"indeterminacion-00-con-raices\"><\/span>\u4e0d\u786e\u5b9a\u6027 0\/0 \u6709\u6839<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6211\u4eec\u521a\u521a\u770b\u5230\u4e86\u6709\u7406\u51fd\u6570\u7684 0\/0 \u4e0d\u786e\u5b9a\u6027\u662f\u5982\u4f55\u89e3\u51b3\u7684\u3002\u7136\u800c\uff0c\u5982\u679c\u6781\u9650\u662f\u65e0\u7406\uff08\u6216\u6839\u5f0f\uff09\u51fd\u6570\uff0c\u5219 0\/0 \u4e0d\u786e\u5b9a\u6027\u7684\u89e3\u6790\u65b9\u5f0f\u4e0d\u540c\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>\u9996\u5148\uff0c\u6211\u4eec\u5c1d\u8bd5\u901a\u8fc7\u6267\u884c\u4ee5\u4e0b\u64cd\u4f5c\u6765\u89e3\u51b3\u8be5\u9650\u5236\uff1a<\/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>\u4f46\u6211\u4eec\u7684\u4e0d\u786e\u5b9a\u6027\u4e3a\u96f6\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\">\u5982\u679c<strong>\u6709\u6839\u51fd\u6570\u7684\u6781\u9650\u7ed9\u51fa\u4e0d\u786e\u5b9a\u6027 0\/0<\/strong> \uff0c\u5219\u5fc5\u987b\u5c06\u5206\u6570\u7684\u5206\u5b50\u548c\u5206\u6bcd\u4e58\u4ee5\u6839\u5f0f\u8868\u8fbe\u5f0f\u7684\u5171\u8f6d\u3002<\/p>\n<\/div>\n<p> \u27a4 \u8bf7\u8bb0\u4f4f\uff0c\u5171\u8f6d\u662f\u76f8\u540c\u7684\u65e0\u7406\u8868\u8fbe\u5f0f\uff0c\u4f46\u4fee\u6539\u4e86\u4e2d\u95f4\u7b26\u53f7\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u5206\u6570\u7684\u5206\u5b50\u548c\u5206\u6bcd\u90fd\u4e58\u4ee5\u6839\u5f0f\u8868\u8fbe\u5f0f\u7684\u5171\u8f6d\uff1a<\/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>\u5728\u8fd9\u79cd\u7c7b\u578b\u7684\u9650\u5236\u5185\uff0c\u901a\u8fc7\u6267\u884c\u6b64\u6b65\u9aa4\uff0c\u6211\u4eec\u5c06\u59cb\u7ec8\u83b7\u5f97\u53ef\u4ee5\u7b80\u5316\u7684\u663e\u7740\u8eab\u4efd\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5206\u6bcd\u4e2d\u6211\u4eec\u6709\u548c\u4e0e\u5dee\u7684\u4e58\u79ef\uff0c\u56e0\u6b64\uff1a<\/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>\u6211\u4eec\u7b80\u5316\u5206\u5b50\u548c\u5206\u6bcd\u4e2d\u91cd\u590d\u7684\u56e0\u5b50\uff1a<\/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>\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u6c42\u51fa\u6781\u9650\u7684\u7ed3\u679c\uff1a <\/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>\u5df2\u89e3\u51b3\u4e0d\u786e\u5b9a\u6027\u7ec3\u4e60 0\/0<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e0b\u9762\u6211\u4eec\u51c6\u5907\u4e86\u51e0\u4e2a\u5173\u4e8e\u7ed9\u51fa 0\/0 \u4e0d\u786e\u5b9a\u6027\u7684\u51fd\u6570\u6781\u9650\u7684\u9010\u6b65\u89e3\u51b3\u7ec3\u4e60\u3002\u60a8\u53ef\u4ee5\u5c1d\u8bd5\u6267\u884c\u8fd9\u4e9b\u64cd\u4f5c\uff0c\u7136\u540e\u68c0\u67e5\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n<p>\u4e0d\u8981\u5fd8\u8bb0\uff0c\u60a8\u53ef\u4ee5\u5728\u8bc4\u8bba\u4e2d\u5411\u6211\u4eec\u8be2\u95ee\u6709\u5173\u89e3\u51b3\u9650\u5236\u7684\u4efb\u4f55\u95ee\u9898\uff01<\/p>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u5728\u70b9 x=-2 \u5904\u7684\u6781\u9650\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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u6211\u4eec\u9996\u5148\u5c1d\u8bd5\u89e3\u51b3\u6781\u9650\uff1a<\/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\">\u4f46\u6211\u4eec\u6700\u7ec8\u5f97\u5230 0\/0 \u4e0d\u786e\u5b9a\u6027\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u5bf9\u5206\u5b50\u548c\u5206\u6bcd\u7684\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1a<\/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\">\u73b0\u5728\u6211\u4eec\u901a\u8fc7\u5220\u9664\u5206\u5b50\u548c\u5206\u6bcd\u4e2d\u91cd\u590d\u7684\u62ec\u53f7\u6765\u7b80\u5316\u5206\u6570\uff1a<\/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\u540e\uff0c\u6211\u4eec\u7528\u7b80\u5316\u5206\u6570\u91cd\u65b0\u8ba1\u7b97\u6781\u9650\uff1a <\/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\">\u7ec3\u4e602<\/h3>\n<p>\u5f53 x \u63a5\u8fd1 -1 \u65f6\uff0c\u6c42\u89e3\u4ee5\u4e0b\u51fd\u6570\u7684\u6781\u9650\uff1a <\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6211\u4eec\u9996\u5148\u50cf\u5f80\u5e38\u4e00\u6837\u5c1d\u8bd5\u89e3\u51b3\u9650\u5236\uff1a<\/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\">\u4f46\u6211\u4eec\u5f97\u5230 0 \u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u6027 0\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u5bf9\u5206\u6570\u7684 2 \u4e2a\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1a<\/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\">\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u7b80\u5316\u591a\u9879\u5f0f\uff1a<\/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\">\u6211\u4eec\u89e3\u51b3\u6781\u9650\uff1a <\/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\">\u7ec3\u4e603<\/h3>\n<p>\u786e\u5b9a\u4e0b\u5217\u6839\u5f0f\u51fd\u6570\u6781\u9650\u7684\u89e3\uff1a <\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9996\u5148\uff0c\u6211\u4eec\u68c0\u67e5\u6781\u9650\u662f\u5426\u7ed9\u51fa\u67d0\u79cd\u4e0d\u786e\u5b9a\u6027\uff1a<\/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\">\u6781\u9650\u7ed9\u51fa\u4e86\u4e0d\u786e\u5b9a\u6027\u96f6\u9664\u4ee5\u96f6\uff0c\u6211\u4eec\u5728\u51fd\u6570\u4e2d\u6709\u4e00\u4e2a\u6839\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u5c06\u5206\u6570\u7684\u5206\u5b50\u548c\u5206\u6bcd\u4e58\u4ee5\u6839\u5f0f\u8868\u8fbe\u5f0f\u7684\u5171\u8f6d\uff1a<\/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\u5bf9\u5e94\u4e8e\u548c\u4e0e\u5dee\u7684\u4e58\u79ef\u7684\u663e\u7740\u6052\u7b49\u5f0f\u7684\u53d1\u5c55\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u7b80\u5316\u5b83\uff1a <\/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\">\u7136\u800c\uff0c\u6211\u4eec\u8fd8\u4e0d\u80fd\u7b80\u5316\u5206\u6570\u9879\u3002\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1a<\/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\">\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u7b80\u5316\u5206\u6570\uff1a<\/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\">\u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a\u6781\u9650\u7684\u7ed3\u679c\uff1a <\/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\">\u7ec3\u4e604<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u6839\u5f0f\u51fd\u6570\u7684 x \u63a5\u8fd1 0 \u65f6\u7684\u6781\u9650\uff1a <\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9996\u5148\uff0c\u6211\u4eec\u50cf\u5f80\u5e38\u4e00\u6837\u5c1d\u8bd5\u8ba1\u7b97\u51fd\u6570\u7684\u6781\u9650\uff1a<\/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\">\u4f46\u6211\u4eec\u5f97\u5230\u4e86 0\/0 \u7684\u4e0d\u786e\u5b9a\u5f62\u5f0f\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u51fd\u6570\u7684\u5206\u5b50\u548c\u5206\u6bcd\u4e58\u4ee5\u65e0\u7406\u8868\u8fbe\u5f0f\u7684\u5171\u8f6d\uff1a<\/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\">\u6211\u4eec\u5e94\u7528\u76f8\u5e94\u7684\u8457\u540d\u6052\u7b49\u516c\u5f0f\u6765\u7b80\u5316\u5206\u6bcd\uff1a <\/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\">\u73b0\u5728\u6211\u4eec\u901a\u8fc7\u53d6\u516c\u56e0\u5b50\u6765\u5bf9\u5206\u5b50\u7684\u4e8c\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1a<\/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\">\u6211\u4eec\u7b80\u5316\u51fd\u6570\u5206\u5b50\u548c\u5206\u6bcd\u4e2d\u91cd\u590d\u7684\u56e0\u5b50\uff1a<\/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\">\u6700\u540e\uff0c\u6211\u4eec\u89e3\u51b3\u4e86\u51fd\u6570\u7684\u6781\u9650\uff1a <\/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\">\u7ec3\u4e605<\/h3>\n<p>\u4f7f\u7528 0\/0 \u4e0d\u786e\u5b9a\u6027\u65b9\u6cd5\u6c42\u89e3\u4ee5\u4e0b\u6781\u9650\uff1a<\/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>\u8bf7\u53c2\u9605\uff1a<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6a2a\u5411\u9650\u5236\/\">\u5982\u4f55\u8ba1\u7b97\u51fd\u6570\u7684\u6a2a\u5411\u6781\u9650<\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6211\u4eec\u9996\u5148\u5c1d\u8bd5\u89e3\u51b3\u9650\u5236\uff1a<\/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\">\u4f46\u5728\u6781\u9650\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u83b7\u5f97\u4e86\u96f6\u5bf9\u96f6\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5bf9\u5206\u5b50\u548c\u5206\u6bcd\u7684\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1a<\/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\">\u73b0\u5728\u6211\u4eec\u901a\u8fc7\u6d88\u9664\u5206\u5b50\u548c\u5206\u6bcd\u4e2d\u91cd\u590d\u7684\u56e0\u5b50\u6765\u7b80\u5316\u5206\u6570\uff1a<\/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\">\u6211\u4eec\u518d\u6b21\u8ba1\u7b97\u6781\u9650\uff1a<\/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\">\u4f46\u73b0\u5728\u6211\u4eec\u53d1\u73b0\u6570\u5b57\u9664\u4ee5 0 \u662f\u4e0d\u786e\u5b9a\u7684\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u5f53 x \u8d8b\u4e8e -1 \u65f6\u51fd\u6570\u7684\u6a2a\u5411\u6781\u9650\u3002<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u9996\u5148\u6c42\u89e3\u51fd\u6570\u5728\u5de6\u4fa7\u70b9 x=-1 \u5904\u7684\u6a2a\u5411\u6781\u9650\uff1a<\/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\">\u7136\u540e\u6211\u4eec\u8ba1\u7b97\u51fd\u6570\u5728\u53f3\u4fa7 x=-1 \u5904\u7684\u6a2a\u5411\u6781\u9650\uff1a<\/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\">\u56e0\u6b64\uff0c\u7531\u4e8e\u4e24\u4e2a\u6a2a\u5411\u6781\u9650\u4e0d\u91cd\u5408\uff0c\u56e0\u6b64\u51fd\u6570\u5728 x=-1 \u5904\u7684\u6781\u9650\u4e0d\u5b58\u5728\uff1a <\/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>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u5f53\u4e0d\u786e\u5b9a\u6027\u4e3a 0\/0 \u65f6\u5982\u4f55\u4fdd\u5b58\u51fd\u6570\u7684\u6781\u9650\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u6765\u7ec3\u4e60\u96f6\u4e0e\u96f6\u4e4b\u95f4 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e9%9b%b6%e4%b9%8b%e9%97%b4-%e9%9b%b6-0-0-%e4%b8%8d%e7%a1%ae%e5%ae%9a\/\"> <span class=\"screen-reader-text\">\u96f6\u4e4b\u95f4\u7684\u96f6\u4e0d\u786e\u5b9a\u6027 (0\/0)<\/span> \u67e5\u770b\u5168\u6587 &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-18","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized 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