{"id":367,"date":"2023-07-04T01:25:58","date_gmt":"2023-07-04T01:25:58","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%9e%82%e7%9b%b4%e6%b8%90%e8%bf%91%e7%ba%bf\/"},"modified":"2023-07-04T01:25:58","modified_gmt":"2023-07-04T01:25:58","slug":"%e5%9e%82%e7%9b%b4%e6%b8%90%e8%bf%91%e7%ba%bf","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%9e%82%e7%9b%b4%e6%b8%90%e8%bf%91%e7%ba%bf\/","title":{"rendered":"\u5782\u76f4\u6e10\u8fd1\u7ebf"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u627e\u5230\u51fd\u6570\u7684\u5782\u76f4\u6e10\u8fd1\u7ebf\u662f\u4ec0\u4e48\uff08\u5e26\u6709\u793a\u4f8b\uff09\u3002\u6211\u4eec\u8fd8\u89e3\u91ca\u4e86\u5982\u4f55\u627e\u5230\u51fd\u6570\u7684\u5782\u76f4\u6e10\u8fd1\u7ebf\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-asintota-vertical\"><\/span>\u4ec0\u4e48\u662f\u5782\u76f4\u6e10\u8fd1\u7ebf\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u51fd\u6570\u7684\u5782\u76f4\u6e10\u8fd1\u7ebf\u662f\u4e00\u6761\u5782\u76f4\u7ebf\uff0c\u5176\u56fe\u5f62\u65e0\u9650\u903c\u8fd1\u800c\u4e0d\u4e0e\u5176\u76f8\u4ea4\u3002<\/strong>\u56e0\u6b64\uff0c\u5782\u76f4\u6e10\u8fd1\u7ebf\u7684\u65b9\u7a0b\u4e3a<em>x=k<\/em> \uff0c\u5176\u4e2d<em>k<\/em>\u662f\u5782\u76f4\u6e10\u8fd1\u7ebf\u7684\u503c\u3002<\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c<strong>\u5982\u679c<em>x<\/em>\u63a5\u8fd1<em>k<\/em>\u65f6\u51fd\u6570\u7684\u6781\u9650\u662f\u65e0\u7a77\u5927\uff0c\u5219<em>k<\/em>\u662f\u5782\u76f4\u6e10\u8fd1\u7ebf\u3002<\/strong> <\/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-verticale.webp\" alt=\"\u4ec0\u4e48\u662f\u5782\u76f4\u6e10\u8fd1\u7ebf\" class=\"wp-image-1281\" width=\"320\" height=\"255\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-asintota-vertical-de-una-funcion\"><\/span>\u5982\u4f55\u8ba1\u7b97\u51fd\u6570\u7684\u5782\u76f4\u6e10\u8fd1\u7ebf<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981\u8ba1\u7b97\u51fd\u6570\u7684\u5782\u76f4\u6e10\u8fd1\u7ebf\uff0c\u5fc5\u987b\u9075\u5faa\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;border:\">\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u6c42\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3002\u5982\u679c\u6240\u6709\u70b9\u90fd\u5728\u5b9a\u4e49\u57df\u5185\uff0c\u5219\u8be5\u51fd\u6570\u6ca1\u6709\u5782\u76f4\u6e10\u8fd1\u7ebf\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u8ba1\u7b97\u51fd\u6570\u5728\u57df\u5916\u7684\u70b9\u5904\u7684\u6781\u9650\u3002<\/span><\/li>\n<li><span style=\"color:#101010;font-weight: normal;\">\u51fd\u6570\u7684\u5782\u76f4\u6e10\u8fd1\u7ebf\u5c06\u662f\u6781\u9650\u4e3a\u65e0\u7a77\u5927\u7684\u6240\u6709\u503c\u3002<\/span><\/li>\n<\/ol>\n<p>\u8bf7\u6ce8\u610f\uff0c\u4e00\u4e2a\u51fd\u6570\u53ef\u4ee5\u6709\u591a\u4e2a\u5782\u76f4\u6e10\u8fd1\u7ebf\u3002\u4f8b\u5982\uff0c<u style=\"text-decoration-color:#FF9B28;\">\u6b63\u5207\u51fd\u6570\u7684\u56fe\u50cf\u6709\u65e0\u7a77\u591a\u4e2a\u5782\u76f4\u6e10\u8fd1\u7ebf\u3002<\/u><\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u89c1\uff1a<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6b63\u5207\u51fd\u6570\/\">\u6b63\u5207\u51fd\u6570\u7684\u7279\u5f81<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-asintota-vertical\"><\/span>\u5782\u76f4\u6e10\u8fd1\u7ebf\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4f5c\u4e3a\u793a\u4f8b\uff0c\u6211\u4eec\u5c06\u627e\u5230\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u7684\u6240\u6709\u6e10\u8fd1\u7ebf\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u4e86\u89e3\u5b83\u662f\u5982\u4f55\u5b8c\u6210\u7684\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-0425f9cc254c22f6e28ad2186732cfdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{1}{x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"101\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4e00\u822c\u6765\u8bf4\uff0c\u5b58\u5728\u5782\u76f4\u6e10\u8fd1\u7ebf\u7684\u70b9\u4e0d\u5c5e\u4e8e\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u8981\u8ba1\u7b97\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3002<\/p>\n<p>\u8fd9\u662f\u4e00\u4e2a\u6709\u7406\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u901a\u8fc7\u89c2\u5bdf\u5206\u6bcd\u4f55\u65f6\u6d88\u5931\u6765\u786e\u5b9a\u4e0d\u5c5e\u4e8e\u8be5\u57df\u7684\u70b9\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-e0aacb848a27943fc0e8fba70f545d78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" style=\"vertical-align: 0px;\"><\/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-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u9664 x=2 \u5916\u5747\u4e3a\u5b9e\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-298deba50795b5fc3979441d68ef3ed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{2\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5<strong>x=2 \u53ef\u80fd\u662f\u51fd\u6570\u7684\u5782\u76f4\u6e10\u8fd1\u7ebf\u3002<\/strong>\u4e3a\u4e86\u9a8c\u8bc1\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u6b64\u65f6\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-acc5425df8da5bffaa5ee31c29284a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2} \\frac{1}{x-2}=\\frac{1}{2-2}=\\frac{1}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5df2\u7ecf\u83b7\u5f97\u4e86\u96f6\u4e4b\u95f4\u7684\u6570\u5b57\u7684\u4e0d\u786e\u5b9a\u6027\uff0c\u56e0\u6b64\uff0c\u4e3a\u4e86\u6c42\u89e3\u6781\u9650\uff0c\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u6a2a\u5411\u6781\u9650\uff0c\u4ee5\u786e\u5b9a\u5b83\u662f\u6b63\u65e0\u7a77\u5927\u3001\u8d1f\u65e0\u7a77\u5927\u8fd8\u662f\u6781\u9650\u4e0d\u5b58\u5728\u3002\u7136\u800c\uff0c\u5f53\u6211\u4eec\u8ba1\u7b97\u5782\u76f4\u6e10\u8fd1\u7ebf\u65f6\uff0c\u6211\u4eec\u4e0d\u9700\u8981\u505a\u6a2a\u5411\u6781\u9650\uff0c\u4f46\u83b7\u5f97\u8fd9\u4e2a\u4e0d\u786e\u5b9a\u6027\u5c31\u8db3\u4ee5\u8bf4\u660e\u5b83\u662f\u5782\u76f4\u6e10\u8fd1\u7ebf\u3002<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u7531\u4e8e\u5f53 x \u63a5\u8fd1 2 \u65f6\u51fd\u6570\u7684\u6781\u9650\u7ed9\u51fa\u65e0\u7a77\u5927\uff0c<strong>\u56e0\u6b64 x=2 \u662f\u5782\u76f4\u6e10\u8fd1\u7ebf\u3002<\/strong><\/p>\n<p>\u4e0b\u9762\u662f\u4ee5\u56fe\u5f62\u65b9\u5f0f\u8868\u793a\u7684\u51fd\u6570\u3002\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u5b83\u975e\u5e38\u63a5\u8fd1 x=2 \u7ebf\uff08\u4ece\u5de6\u4fa7\u548c\u53f3\u4fa7\uff09\uff0c\u4f46\u5b83\u6c38\u8fdc\u4e0d\u4f1a\u4e0e\u5b83\u76f8\u4ea4\uff0c\u56e0\u4e3a\u5b83\u662f\u4e00\u6761\u5782\u76f4\u6e10\u8fd1\u7ebf\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\/exemple-dasymptote-verticale.webp\" alt=\"\u5782\u76f4\u6e10\u8fd1\u7ebf\u793a\u4f8b\" class=\"wp-image-1294\" width=\"431\" height=\"382\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u4ece\u56fe\u4e2d\u63a8\u5bfc\u51fa\u51fd\u6570\u5728 x=2 \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-bae3e5d8a91ed8bfd4d59e8cf2b2e046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2^-} \\frac{1}{x-2} = -\\infty \\qquad  \\lim_{x \\to 2^+} \\frac{1}{x-2} = +\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"320\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-asintotas-verticales\"><\/span>\u89e3\u51b3\u4e86\u5782\u76f4\u6e10\u8fd1\u7ebf\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u7684\u5782\u76f4\u6e10\u8fd1\u7ebf\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-911fac1ac9244ceb5c6bff7e4bd14633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{3x-1}{2x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"110\" 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\">\u6ca1\u6709\u8ba1\u7b97\u51fd\u6570\u5782\u76f4\u6e10\u8fd1\u7ebf\u7684\u516c\u5f0f\uff0c\u4f46\u60a8\u5fc5\u987b\u627e\u5230\u51fd\u6570\u7684\u57df\uff0c\u5e76\u67e5\u770b\u5728\u51fd\u6570\u672a\u5b9a\u4e49\u7684\u54ea\u4e9b\u70b9\u5904\u6781\u9650\u7ed9\u51fa\u65e0\u7a77\u5927\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u6709\u7406\u51fd\u6570\u7684\u5206\u6bcd\u8bbe\u7f6e\u4e3a0\u6765\u67e5\u627e\u4e0d\u5c5e\u4e8e\u57df\u7684\u70b9\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-eda4c745b07ad63c3060964038aebf0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x -1 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" style=\"vertical-align: 0px;\"><\/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-0323089c11e731c307ef7664ecb6710b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x= 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\"><\/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-971df94c9decb86065329338ff4b81ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"45\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u9664 x=1\/2 \u5916\u5747\u4e3a\u5b9e\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-d45cfed65d2da3a61311dce298a529a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{ \\cfrac{1}{2} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"149\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5 x=1\/2 \u53ef\u80fd\u662f\u5782\u76f4\u6e10\u8fd1\u7ebf\u3002\u4e3a\u4e86\u68c0\u67e5\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u8ba1\u7b97\u6b64\u65f6\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-55047465393cc2a65a7214fa64eac93d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to \\frac{1}{2} } \\cfrac{3x-1}{2x-1} = \\cfrac{3\\cdot\\cfrac{1}{2}-1}{2\\cdot\\cfrac{1}{2}-1} = \\cfrac{ \\cfrac{3}{2} -1 }{\\cfrac{2}{2} -1 } = \\cfrac{ \\cfrac{1}{2} }{1-1}=\\cfrac{\\cfrac{1}{2}}{0} =\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"84\" width=\"383\" style=\"vertical-align: -39px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5<strong>x=1\/2 \u662f\u4e00\u4e2a\u5782\u76f4\u6e10\u8fd1\u7ebf<\/strong>\uff0c\u56e0\u4e3a\u6b64\u65f6\u51fd\u6570\u7684\u6781\u9650\u7ed9\u51fa\u65e0\u7a77\u5927\u3002<\/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>\u6c42\u4ee5\u4e0b\u5206\u6570\u51fd\u6570\u7684\u6240\u6709\u5782\u76f4\u6e10\u8fd1\u7ebf\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-cc3badbfcece4b7976d30989606ca685_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{2x+1}{x^2-9}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"110\" 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\">\u9996\u5148\uff0c\u6211\u4eec\u5c06\u5206\u6570\u7684\u5206\u6bcd\u8bbe\u7f6e\u4e3a\u96f6\uff0c\u770b\u770b\u54ea\u4e9b\u503c\u4e0d\u5728\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u5185\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-ce55adbc277e9378607d68bce8ef19fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-9=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u6c42\u89e3\u4e0d\u5b8c\u5168\u4e8c\u6b21\u65b9\u7a0b\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-05112cb5a98f653cd1920fb40e5ef9a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: 0px;\"><\/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-0505454de5d542ace3e698cb903893ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\pm 3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6709\u7406\u51fd\u6570\u7684\u57df\u662f\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-c91231eb4c883e8c625dba58f070307f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{3, -3\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e3a\u4e86\u786e\u5b9a\u8fd9\u4e24\u4e2a\u503c\u4e2d\u54ea\u4e00\u4e2a\u662f\u5782\u76f4\u6e10\u8fd1\u7ebf\uff0c\u6211\u4eec\u6c42\u89e3\u51fd\u6570\u5728\u6bcf\u4e2a\u70b9\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-1a56d9ceafa2628b7a80603109ceafc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 3}\\frac{2x+1}{x^2-9}=\\frac{2\\cdot3+1}{3^2-9}=\\frac{7}{9-9}=\\frac{7}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"317\" 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-944d84ad3ab51829df2623a4467cc16a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -3}\\frac{2x+1}{x^2-9}=\\frac{2\\cdot(-3)+1}{(-3)^2-9}=\\frac{-5}{9-9}=\\frac{-5}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"369\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8fd9\u4e24\u4e2a\u6781\u9650\u7ed9\u51fa\u65e0\u7a77\u5927\uff0c\u56e0\u6b64<strong>x=3 \u548c x=-3 \u662f\u95ee\u9898\u51fd\u6570 \u7684\u4e24\u4e2a\u5782\u76f4\u6e10\u8fd1\u7ebf<\/strong>\u3002<\/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>\u5982\u679c\u6709\u7684\u8bdd\uff0c\u627e\u5230\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u7684\u6240\u6709\u5782\u76f4\u6e10\u8fd1\u7ebf\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-1dd8356a2f682824a334f15826b31c89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{x+3}{x^2+2x-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"150\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u89c1\uff1a<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u96f6\u4e4b\u95f4-\u96f6-0-0-\u4e0d\u786e\u5b9a\/\">\u96f6\u4e4b\u95f4\u7684\u4e0d\u786e\u5b9a\u6027<\/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\">\u9996\u5148\uff0c\u6211\u4eec\u6c42\u89e3\u4e8c\u6b21\u5206\u6bcd\u65b9\u7a0b\uff0c\u627e\u5230\u62b5\u6d88\u5206\u6570\u5206\u6bcd\u7684\u503c\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-d5c5fd813f4a2456efa315766ad90ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+2x-3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -2px;\"><\/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-9b2170358d5d1719077695aba5afa02e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle x&amp;=\\cfrac{-b\\pm\\sqrt{b^2-4ac}}{2a}=\\cfrac{-2\\pm\\sqrt{2^2-4\\cdot1\\cdot(-3)}}{2\\cdot1}=\\\\[3ex]\\displaystyle &amp;=\\cfrac{-2\\pm\\sqrt{16}}{2}=\\cfrac{-2\\pm 4}{2}=\\begin{cases}\\cfrac{-2+4}{2}=1\\\\[3ex]\\cfrac{-2-4}{2}=-3\\end{cases}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"172\" width=\"396\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u662f\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-fd230a1caa7456bca8746870a6d0264a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{1, -3\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u51fd\u6570\u5728 x=1 \u5904\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-3784526cad2b36766a213c13a5938c6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1}\\frac{x+3}{x^2+2x-3}=\\frac{1+3}{1^2+2\\cdot 1-3}=\\frac{4}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"328\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u5f53 x \u8d8b\u4e8e -3 \u65f6\uff0c\u6211\u4eec\u6c42\u89e3\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-f0e96a48986cd110e04058e3545290a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x \\to -3}\\frac{x+3}{x^2+2x-3}=\\frac{-3+3}{(-3)^2+2\\cdot(-3)-3}=\\frac{0}{0}=\\\\[3ex]\\displaystyle =\\lim_{x \\to -3}\\frac{\\cancel{x+3}}{(x-1)\\cancel{(x+3)}}=\\lim_{x \\to -3}\\frac{1}{x-1}=\\frac{1}{-3-1}=-\\frac{1}{4}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"94\" width=\"413\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u524d\u9762\u7684\u6781\u9650\u7ed9\u51fa\u4e86\u96f6\u4e4b\u95f4\u7684\u4e0d\u5b9a\u5f62\u5f0f\u96f6\uff0c\u56e0\u6b64\u4e3a\u4e86\u89e3\u51b3\u5b83\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002<u style=\"text-decoration-color:#FF9B28;\">\u5982\u679c\u60a8\u5bf9\u6211\u4eec\u5982\u4f55\u89e3\u51b3\u6781\u9650\u6709\u4efb\u4f55\u7591\u95ee\uff0c\u60a8\u53ef\u4ee5\u5728\u7ec3\u4e60\u8bed\u53e5\u7684\u94fe\u63a5\u4e2d\u67e5\u770b\u5982\u4f55\u89e3\u51b3\u6b64\u7c7b\u4e0d\u786e\u5b9a\u6027\u7684\u5b8c\u6574\u8bf4\u660e\u3002<\/u><\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u53ea\u6709\u51fd\u6570\u5728\u70b9 x=1 \u5904\u7684\u6781\u9650\u7ed9\u51fa\u65e0\u7a77\u5927\uff0c\u56e0\u6b64<strong>x=1 \u662f\u51fd\u6570 \u7684\u552f\u4e00\u5782\u76f4\u6e10\u8fd1\u7ebf<\/strong>\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u627e\u5230\u51fd\u6570\u7684\u5782\u76f4\u6e10\u8fd1\u7ebf\u662f\u4ec0\u4e48\uff08\u5e26\u6709\u793a\u4f8b\uff09\u3002\u6211\u4eec\u8fd8\u89e3\u91ca\u4e86\u5982\u4f55\u627e\u5230\u51fd\u6570\u7684\u5782\u76f4\u6e10\u8fd1\u7ebf\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u9010\u6b65 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%9e%82%e7%9b%b4%e6%b8%90%e8%bf%91%e7%ba%bf\/\"> <span class=\"screen-reader-text\">\u5782\u76f4\u6e10\u8fd1\u7ebf<\/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-367","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized 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