{"id":23,"date":"2023-09-17T11:07:18","date_gmt":"2023-09-17T11:07:18","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e4%b8%8d%e8%bf%9e%e7%bb%ad%e6%80%a7%e7%9a%84%e7%b1%bb%e5%9e%8b\/"},"modified":"2023-09-17T11:07:18","modified_gmt":"2023-09-17T11:07:18","slug":"%e4%b8%8d%e8%bf%9e%e7%bb%ad%e6%80%a7%e7%9a%84%e7%b1%bb%e5%9e%8b","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e4%b8%8d%e8%bf%9e%e7%bb%ad%e6%80%a7%e7%9a%84%e7%b1%bb%e5%9e%8b\/","title":{"rendered":"\u4e0d\u8fde\u7eed\u6027\u7684\u7c7b\u578b"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u5b58\u5728\u54ea\u4e9b\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u6240\u6709\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\u7684\u793a\u4f8b\uff0c\u5e76\u4e14\u80fd\u591f\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u51fd\u6570\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<p><strong><\/strong><\/p>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><strong> <\/strong><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcuales-son-todos-los-tipos-de-discontinuidades\"><\/span>\u4ec0\u4e48\u662f\u6240\u6709\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e0d\u8fde\u7eed\u6027\u5206\u4e3a\u4e09\u79cd\u7c7b\u578b\uff0c\u5373\uff1a<\/p>\n<ul>\n<li><strong>\u53ef\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027<\/strong>\uff1a\u51fd\u6570\u5728\u4e00\u70b9\u5904\u7684\u6a2a\u5411\u6781\u9650\u4e0e\u51fd\u6570\u7684\u503c\u4e0d\u91cd\u5408\u3002<\/li>\n<li><strong>\u4e0d\u53ef\u907f\u514d\u7684\u6709\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027<\/strong>\uff1a\u51fd\u6570\u5728\u4e00\u70b9\u5904\u7684\u6a2a\u5411\u6781\u9650\u662f\u4e0d\u540c\u7684\u3002<\/li>\n<li><strong>\u4e0d\u53ef\u907f\u514d\u7684\u65e0\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027<\/strong>\uff1a\u51fd\u6570\u7684\u6a2a\u5411\u6781\u9650\u4e4b\u4e00\u7ed9\u51fa\u65e0\u7a77\u5927\u6216\u4e0d\u5b58\u5728\u3002<\/li>\n<\/ul>\n<p>\u4e3a\u4e86\u5b8c\u6210\u5bf9\u8fd9\u4e9b\u6982\u5ff5\u7684\u7406\u89e3\uff0c\u6211\u4eec\u5c06\u66f4\u8be6\u7ec6\u5730\u89e3\u91ca\u6bcf\u79cd\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\uff0c\u5e76\u4e14\u6211\u4eec\u5c06\u770b\u5230\u5177\u6709\u4e09\u79cd\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\u7684\u51fd\u6570\u793a\u4f8b\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-evitable\"><\/span> \u53ef\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><strong> <\/strong><\/div>\n<\/div>\n<p><strong>\u53ef\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027<\/strong>\u662f\u4e00\u79cd\u4e0d\u8fde\u7eed\u6027\uff0c\u5982\u679c\u8be5\u70b9\u5b58\u5728\u8fb9\u754c\u4f46\u4e0e\u51fd\u6570\u7684\u503c\u4e0d\u91cd\u5408\u6216\u51fd\u6570\u7684\u56fe\u50cf\u4e0d\u5b58\u5728\uff0c\u5219\u8be5\u70b9\u5177\u6709\u51fd\u6570\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-c26b9be97568ba85e1f8f22b568a2354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\exists \\lim_{x \\to a} f(x) \\neq f(a) \\qquad | \\qquad \\displaystyle \\exists\\lim_{x \\to a} f(x) \\text{ y } \\ \\cancel{\\exists} \\ f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"367\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns are-vertically-aligned-top is-layout-flex wp-container-99\">\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow\">\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/discontinuite-evitable-d-une-fonction.webp\" alt=\"\u51fd\u6570\u7684\u53ef\u907f\u514d\u4e0d\u8fde\u7eed\u6027\" class=\"wp-image-1400\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p>\u8be5\u51fd\u6570\u7684\u6a2a\u5411\u6781\u9650\u5f7c\u6b64\u76f8\u7b49\uff0c\u4f46\u4e0e\u51fd\u6570\u5728\u8be5\u70b9\u7684\u503c\u4e0d\u540c\u3002\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5448\u73b0\u51fa\u53ef\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027\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-ac5bdc61d377477ddcc788b7230bcfbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l}\\displaystyle \\lim_{x \\to a^-} f(x) =b \\\\[3ex] \\displaystyle \\lim_{x \\to a^+} f(x)=b \\end{array} \\right\\} \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to a} f(x)=b\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"276\" 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-9f61efde161e83828572db200f128ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a} f(x)=b \\qquad f(a)=c\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"198\" 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-de211758fe99134c01f6eec8ea7c6348_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\exists \\lim_{x \\to a} f(x) \\neq f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"135\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow\">\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/discontinuite-evitable-d-une-fonction-sans-image.webp\" alt=\"\u6ca1\u6709\u56fe\u50cf\u7684\u51fd\u6570\u7684\u53ef\u907f\u514d\u4e0d\u8fde\u7eed\u6027\" class=\"wp-image-1401\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p class=\"has-text-align-left\">\u4e0a\u4f8b\u4e2d\u7684\u51fd\u6570\u5177\u6709\u53ef\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027\uff0c\u56e0\u4e3a x=a \u5904\u7684\u6a2a\u5411\u6781\u9650\u5177\u6709\u76f8\u540c\u7684\u503c\uff0c\u4f46\u6b64\u65f6\u51fd\u6570\u7684\u56fe\u50cf\u4e0d\u5b58\u5728\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-ac5bdc61d377477ddcc788b7230bcfbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l}\\displaystyle \\lim_{x \\to a^-} f(x) =b \\\\[3ex] \\displaystyle \\lim_{x \\to a^+} f(x)=b \\end{array} \\right\\} \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to a} f(x)=b\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"276\" 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-87531b3fbfb53b42e79af5a7305ffc37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a} f(x)=b \\qquad \\cancel{\\exists} \\ f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"181\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\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\/\u6a2a\u5411\u9650\u5236\/\">\u51fd\u6570\u7684\u6a2a\u5411\u6781\u9650<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-inevitable-de-salto-finito\"><\/span>\u6709\u9650\u8df3\u8dc3\u4e0d\u53ef\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p><strong>\u4e0d\u53ef\u907f\u514d\u7684\u6709\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027<\/strong>\u662f\u4e00\u79cd\u4e0d\u8fde\u7eed\u6027\uff0c\u5f53\u51fd\u6570\u5728\u8be5\u70b9\u7684\u6a2a\u5411\u6781\u9650\u4e0d\u76f8\u7b49\u65f6\uff0c\u8be5\u70b9\u5448\u73b0\u51fd\u6570\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-66fd7a55b2fad1a91622d738925d3304_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) \\neq \\lim_{x \\to a^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"175\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c\u4e0b\u4e00\u4e2a\u5206\u6bb5\u5b9a\u4e49\u7684\u51fd\u6570\u5728\u5b9a\u4e49\u6539\u53d8\u70b9\u5904\u7684\u6a2a\u5411\u6781\u9650\u662f\u4e0d\u540c\u7684\uff0c\u56e0\u6b64\u8be5\u51fd\u6570\u5728\u8be5\u70b9\u5904\u5177\u6709\u4e0d\u53ef\u907f\u514d\u7684\u6709\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/saut-fini-inevitable-discontinuite.webp\" alt=\"\u6709\u9650\u8df3\u8dc3\u4e0d\u53ef\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027\" class=\"wp-image-1406\" width=\"275\" height=\"258\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f7173f197ec50976b07e8ab608ec4aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=b \\qquad  \\lim_{x \\to a^+} f(x)=c\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"254\" style=\"vertical-align: -14px;\"><\/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-66fd7a55b2fad1a91622d738925d3304_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) \\neq \\lim_{x \\to a^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"175\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u8fd9\u79cd\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\u901a\u5e38\u51fa\u73b0\u5728\u5206\u6bb5\uff08\u6216\u5206\u6bb5\uff09\u5b9a\u4e49\u7684\u51fd\u6570\u4e2d\u3002<\/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\">\u5206\u6bb5\u51fd\u6570\u7684\u8fde\u7eed\u6027<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-inevitable-de-salto-infinito\"><\/span>\u65e0\u9650\u8df3\u8dc3 \u4e0d\u53ef\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-107\"><strong> <\/strong><\/div>\n<\/div>\n<p><strong>\u4e0d\u53ef\u907f\u514d\u7684\u65e0\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027<\/strong>\u662f\u4e00\u79cd\u4e0d\u8fde\u7eed\u6027\uff0c\u5982\u679c\u8be5\u70b9\u7684\u6a2a\u5411\u6781\u9650\u4e4b\u4e00\u662f\u65e0\u9650\u7684\u6216\u4e0d\u5b58\u5728\uff0c\u6709\u65f6\u5b83\u4f1a\u8d77\u4f5c\u7528\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-a67f3a84bbd7cc965e932b0cb681912a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) = \\pm \\infty \\qquad \\lim_{x \\to a^+} f(x)= \\pm \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"301\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-102\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p>\u4ee5\u4e0b\u51fd\u6570\u7684\u5de6\u6781\u9650\u7ed9\u51fa\u5b9e\u6570\uff0c\u4f46\u53f3\u6781\u9650\u7ed9\u51fa\u65e0\u7a77\u5927\u3002\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5448\u73b0\u51fa\u4e0d\u53ef\u907f\u514d\u7684\u65e0\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/saut-infini-discontinuite.webp\" alt=\"\u65e0\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027\" class=\"wp-image-1411\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e12509ad0839664b52f4224f0fc2e56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=b \\qquad \\lim_{x \\to a^+} f(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"277\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-left\">\u4e0b\u9762\u60a8\u53ef\u4ee5\u770b\u5230\u4e00\u4e2a\u56fe\u5f62\u51fd\u6570\uff0c\u5176\u4e24\u4fa7\u6781\u9650\u4e3a\u65e0\u7a77\u5927\uff0c\u56e0\u6b64\u8be5\u51fd\u6570\u5177\u6709\u4e0d\u53ef\u907f\u514d\u7684\u65e0\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/discontinuite-infinie.webp\" alt=\"\u65e0\u9650\u4e0d\u8fde\u7eed\u6027\" class=\"wp-image-1412\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-99099617bca8a79ef975169f06f5c14e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=-\\infty \\qquad \\lim_{x \\to a^+} f(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"301\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p>\u8fd9\u79cd\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\u901a\u5e38\u53d1\u751f\u5728<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6709\u7406\u51fd\u6570\/\">\u6709\u7406\uff08\u6216\u5206\u6570\uff09\u51fd\u6570<\/a><\/span>\u4e2d\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-tipos-de-discontinuidades\"><\/span>\u89e3\u51b3\u4e86\u6709\u5173\u4e0d\u8fde\u7eed\u6027\u7c7b\u578b\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601 <\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-108\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p>\u786e\u5b9a\u4ee5\u4e0b\u5206\u6bb5\u51fd\u6570\u5728\u70b9 x=3 \u5904\u7684\u4e0d\u8fde\u7eed\u7c7b\u578b\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-8185827ad36ab3921bb96eb5a6da21a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left\\{ \\begin{array}{lcl} -2x+1 &amp;  \\text{si} &amp;  x\\leq 3 \\\\[2ex] 4x - 5 &amp; \\text{si} &amp; x > 3 \\end{array} \\right.&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;65&#8243; width=&#8221;232&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/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\">\u51fd\u6570\u7b2c\u4e00\u4e2a\u5143\u7d20\u7684\u5b9a\u4e49\u57df\uff0c<\/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-490b7f67d1b8735fc34485932796cef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -2px;\"><\/p>\n<p>\u548c\u7b2c\u4e8c\u6bb5\u4e00\u6837\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82dafeb4abb94d9f10e1603d00cc3d59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x-5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<p> \uff0c\u90fd\u662f\u5b9e\u6570\uff0c\u56e0\u4e3a\u5b83\u4eec\u662f\u591a\u9879\u5f0f\u51fd\u6570\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u51fd\u6570\u53ef\u80fd\u4e0d\u8fde\u7eed\u7684\u552f\u4e00\u70b9\u662f\u5206\u6bb5\u51fd\u6570\u7684\u505c\u6b62\u70b9\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u5728\u6b64\u9636\u6bb5\u8ba1\u7b97\u6a2a\u5411\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-e5aa03a9198a249e6cb09793b67754f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to 3^-} f(x)=\\lim_{x \\to 3} (-2x+1) = -2\\cdot 3+1=-5\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"349\" style=\"vertical-align: -14px;\"><\/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-c8e29ea20c018b8936dca674ada7590a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to 3^+} f(x)=\\lim_{x \\to 3}(4x-5)=4\\cdot 3-5=7\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"308\" style=\"vertical-align: -14px;\"><\/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-ffa1cc3d456b55bfef8f4a5999e072e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x) \\neq \\lim_{x \\to 3^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"174\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> x=3 \u5904\u7684\u4e24\u4e2a\u6a2a\u5411\u6781\u9650\u7ed9\u51fa\u4e86\u4e0d\u540c\u7684\u7ed3\u679c\u3002\u56e0\u6b64\uff0cx=3\u70b9\u662f\u4e0d\u53ef\u907f\u514d\u7684\u6709\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u70b9\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>\u627e\u51fa\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u5728\u4e0d\u5c5e\u4e8e\u5176\u5b9a\u4e49\u57df\u7684\u70b9\u5904\u5448\u73b0\u54ea\u79cd\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\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-44d5d873cde7d3365fc55943c61e78f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= \\cfrac{x^2-4}{x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"109\" 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\">\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u8981\u89e3\u51b3\u6b64\u7ec3\u4e60\uff0c\u60a8\u5fc5\u987b\u9996\u5148\u627e\u5230\u51fd\u6570\u7684\u57df\u3002\u56e0\u6b64\uff0c\u7531\u4e8e\u8fd9\u662f\u4e00\u4e2a\u6709\u7406\u51fd\u6570\uff0c\u6211\u4eec\u5c06\u5206\u6bcd\u8bbe\u7f6e\u4e3a 0 \u5e76\u6c42\u89e3\u6240\u5f97\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-24e301fa7ea2e8d9f0041192d9a84927_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"73\" 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-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" 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-fbd5fe607cd89a42b4db6e52bc047c56_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=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u9664\u4e86 x=-2 \u4e4b\u5916\uff0c\u8be5\u51fd\u6570\u5728\u6240\u6709\u70b9\u4e0a\u90fd\u662f\u8fde\u7eed\u7684\uff0c\u6240\u4ee5\u8ba9\u6211\u4eec\u770b\u770b x=-2 \u70b9\u662f\u4ec0\u4e48\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\u51fd\u6570\u5728\u8be5\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-bf6f3ceb66dcd630224097f54365ef24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} \\cfrac{x^2-4}{x+2} = \\cfrac{ (-2)^2-4}{-2+2}= \\cfrac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"227\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4f46\u662f\u6211\u4eec\u5728\u96f6\u4e4b\u95f4\u83b7\u5f97\u96f6\u4e0d\u786e\u5b9a\u6027\uff0c\u56e0\u6b64\u6211\u4eec\u5bf9\u5206\u5b50\u548c\u5206\u6bcd\u7684\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u5e76\u7b80\u5316\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-e939f4fee6ac399b046fa809daab31c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} \\cfrac{x^2-4}{x+2}=\\lim_{x \\to -2} \\cfrac{ (x-2)\\cancel{(x+2)}}{\\cancel{x+2}}  =\\lim_{x \\to -2} (x-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"385\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\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-5e05e20f45a4d8b2fbe26bb0d3ae5091_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} (x-2) =-2-2=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"217\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u51fd\u6570\u5728\u70b9 x=-2 \u5904\u7684\u6781\u9650\u786e\u5b9e\u5b58\u5728\u5e76\u7ed9\u51fa -4\u3002\u73b0\u5728\u6211\u4eec\u68c0\u67e5\u4e00\u4e0b\u5b83\u662f\u5426\u5b58\u5728<\/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-80b84d482e50cebc375313e005736c97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\"><\/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-c58a37ec90f203b24b790c7cfacaf2c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)=\\cfrac{(-2)^2-4}{-2+2}= \\cfrac{4-4}{0} = \\cfrac{0}{0} \\quad \\bm{\\longrightarrow} \\quad \\cancel{\\exists} \\ f(2)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"359\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8ba1\u7b97\u51fd\u6570\u7684\u56fe\u50cf\u65f6\uff0c\u4e0d\u5b9a\u5f0f0\/0\u65e0\u6cd5\u7b80\u5316\u4e14\u65e0\u89e3\u3002\u6240\u4ee5<\/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-7ee53c0d0a8e84c09c63d946334cd34b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u4e0d\u5b58\u5728\u3002<\/p>\n<p class=\"has-text-align-left\">\u603b\u4e4b\uff0c\u51fd\u6570\u5728 x=-2 \u5904\u7684\u6781\u9650\u5b58\u5728\uff0c\u4f46\u662f<\/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-7ee53c0d0a8e84c09c63d946334cd34b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u4e0d\u4f1a\u3002\u56e0\u6b64\uff0cx=-2 \u662f\u53ef\u4ee5\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027\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><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-110\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p>\u5206\u6790\u4ee5\u4e0b\u6709\u7406\u51fd\u6570\u7684\u8fde\u7eed\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-59ee18262fd6f3427ebab6ceabb22868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\frac{2}{x-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"101\" 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\">\u8981\u5224\u65ad\u5b83\u662f\u5426\u662f\u8fde\u7eed\u51fd\u6570\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u8ba1\u7b97\u5b83\u7684\u5b9a\u4e49\u57df\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u6709\u7406\u51fd\u6570\u7684\u5206\u6bcd\u8bbe\u7f6e\u4e3a\u96f6\uff0c\u4ee5\u67e5\u770b\u54ea\u4e9b\u70b9\u4e0d\u5c5e\u4e8e\u8be5\u57df\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-845b4cbd750afedb8e09b0ed6a9809c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" 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-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" 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-96a28ea816d10d62e90dd13ad1aa79c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{5\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u9664\u4e86 x=5 \u4e4b\u5916\uff0c\u8be5\u51fd\u6570\u5728\u6240\u6709\u70b9\u4e0a\u90fd\u662f\u8fde\u7eed\u7684\u3002\u90a3\u4e48\u6211\u4eec\u901a\u8fc7\u8ba1\u7b97\u6b64\u65f6\u7684\u6781\u9650\u6765\u770b\u770b x=5 \u662f\u4ec0\u4e48\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\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-976747f92d549df73e0cf24ee4ff2953_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5} \\frac{2}{x-5} = \\frac{2}{5-5} = \\frac{2}{0} = \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u53d1\u73b0\u6570\u5b57\u9664\u4ee5 0 \u5177\u6709\u4e0d\u786e\u5b9a\u6027\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\u51fd\u6570\u5728 x=5 \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-98edca328c2637f8b7ae59dde1789f44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5^{-}} \\frac{2}{x-5}=\\frac{2}{4,999-5}=\\frac{2}{-0}= \\bm{-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"292\" style=\"vertical-align: -16px;\"><\/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-378f3bdf00d4375069e68f4fc8547ca0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5^{+}} \\frac{2}{x-5}=\\frac{2}{5,001-5}=\\frac{2}{+0}=\\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"292\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> x=5 \u5904\u51fd\u6570\u7684\u5de6\u6781\u9650\u7ed9\u51fa\u8d1f\u65e0\u7a77\u5927\uff0c\u53f3\u6781\u9650\u7ed9\u51fa\u6b63\u65e0\u7a77\u5927\u3002\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5728 x = 5 \u5904\u5177\u6709\u4e0d\u53ef\u907f\u514d\u7684\u65e0\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027\uff0c\u56e0\u4e3a\u6b64\u65f6\u81f3\u5c11\u6709\u4e00\u4e2a\u6a2a\u5411\u6781\u9650\u8d8b\u4e8e\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\u4e604<\/h3>\n<p>\u786e\u5b9a\u4e0b\u56fe\u4e2d\u6240\u793a\u5206\u6bb5\u51fd\u6570\u7684\u6240\u6709\u4e0d\u8fde\u7eed\u70b9\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-discontinuites-de-fonctions.webp\" alt=\"\u8fd0\u52a8\u89e3\u51b3\u4e86\u529f\u80fd\u7684\u4e0d\u8fde\u7eed\u6027\" class=\"wp-image-1433\" width=\"400\" height=\"344\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\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\">\u8981\u7ed8\u5236\u8be5\u51fd\u6570\uff0c\u60a8\u5fc5\u987b\u5728 x=-2\u3001x=1 \u548c x=4 \u5904\u4e3e\u8d77\u94c5\u7b14\u3002\u56e0\u6b64\u8be5\u51fd\u6570\u5728\u8fd9\u4e09\u4e2a\u70b9\u5904\u662f\u4e0d\u8fde\u7eed\u7684\u3002<\/p>\n<p class=\"has-text-align-left\">\u5728 x=-2 \u5904\uff0c\u5de6\u4fa7\u6781\u9650\u4e3a +\u221e\uff0c\u53f3\u4fa7\u6781\u9650\u4e3a 3\u3002\u56e0\u6b64\uff0c\u7531\u4e8e\u4e00\u4fa7\u6781\u9650\u4e3a\u65e0\u7a77\u5927\uff0c\u56e0\u6b64\u8be5\u51fd\u6570\u5728 x=-2 \u5904\u4e0d\u53ef\u907f\u514d\u5730\u5b58\u5728\u65e0\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027\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-eff79ace33659ceb8203e6e27f38fe35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2^-} f(x) = +\\infty \\ \\neq \\ \\lim_{x \\to -2^+} f(x) = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"296\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> x=1 \u5904\u51fd\u6570\u7684\u6781\u9650\u4e3a 0\uff0c\u53e6\u4e00\u65b9\u9762\uff0cx=1 \u5904\u51fd\u6570\u7684\u503c\u7b49\u4e8e 2\u3002\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5728 x=1 \u5904\u5448\u73b0\u53ef\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027\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-3a616cc5210984ffeed3525a219dd53a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1^-} f(x) =   \\lim_{x \\to 1^+} f(x) = 0 \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to 1} f(x) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"350\" style=\"vertical-align: -14px;\"><\/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-9a3aea29db1a67d08d91d510033ffd1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1} f(x) =  0 \\neq  f(1) = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"187\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5f53 x = 4 \u65f6\uff0c\u5de6\u4fa7\u6781\u9650\u4e3a -3\uff0c\u53f3\u4fa7\u6781\u9650\u4e3a 1\u3002\u56e0\u6b64\uff0c\u7531\u4e8e\u4e24\u4fa7\u6781\u9650\u4e0d\u540c\u4e14\u5747\u4e0d\u7ed9\u51fa\u65e0\u7a77\u5927\uff0c\u56e0\u6b64\u8be5\u51fd\u6570\u5728 x = 4 \u5904\u4e0d\u53ef\u907f\u514d\u5730\u5b58\u5728\u6709\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027\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-b758745a987f927350b2d885009c3a87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 4^-} f(x) = -3 \\ \\neq \\ \\lim_{x \\to 4^+} f(x) = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"265\" style=\"vertical-align: -14px;\"><\/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>\u627e\u51fa\u4e0b\u56fe\u4e2d\u8868\u793a\u7684\u51fd\u6570\u7684\u6240\u6709\u6e10\u8fd1\u7ebf\u548c\u4e0d\u8fde\u7eed\u70b9\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-types-de-discontinuites-d-une-fonction.webp\" alt=\"\u89e3\u51b3\u4e86\u51fd\u6570\u4e0d\u8fde\u7eed\u7c7b\u578b\u7684\u7ec3\u4e60\" class=\"wp-image-1435\" width=\"537\" height=\"453\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\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\"><strong><span style=\"text-decoration: underline;\">\u6e10\u8fd1\u7ebf<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\">\u8be5\u51fd\u6570\u975e\u5e38\u63a5\u8fd1\u5782\u76f4\u7ebf x=3\uff0c\u4f46\u4ece\u672a\u89e6\u53ca\u5b83\u3002\u53e6\u5916\uff0cx=3 \u5904\u7684\u5de6\u4fa7\u6781\u9650\u4e3a+\u221e\uff0c\u53f3\u4fa7\u6781\u9650\u4e3a-\u221e\u3002\u56e0\u6b64\uff0cx=3 \u662f\u5782\u76f4\u6e10\u8fd1\u7ebf\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-89bdb1598b6153cec4e9efce7b0927b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x)=+\\infty \\qquad \\lim_{x \\to 3^+} f(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"300\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u540c\u6837\u7684\u60c5\u51b5\u4e5f\u53d1\u751f\u5728\u6c34\u5e73\u7ebf y=-1 \u4e0a\uff0c\u51fd\u6570\u975e\u5e38\u63a5\u8fd1 y=-1\uff0c\u4f46\u4ece\u672a\u7a7f\u8fc7\u5b83\u3002\u6b64\u5916\uff0c\u5f53 x \u63a5\u8fd1 + \u65e0\u7a77\u5927\u548c &#8211; \u65e0\u7a77\u5927\u65f6\uff0c\u51fd\u6570\u7684\u6781\u9650\u4e3a -1\u3002\u56e0\u6b64\uff0cy=-1 \u662f\u6c34\u5e73\u6e10\u8fd1\u7ebf\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-d0f0ee09aaa4a3bfa4fcb77ecc84640a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} f(x)=-1 \\qquad \\lim_{x \\to -\\infty} f(x)=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"297\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong><span style=\"text-decoration: underline;\">\u4e0d\u8fde\u7eed\u6027<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\">\u5f53 x=6 \u65f6\uff0c\u51fd\u6570\u56e0\u5b58\u5728\u5f00\u8def\u70b9\u800c\u4e2d\u65ad\u3002 x \u63a5\u8fd1 6 \u65f6\u7684\u6781\u9650\u662f -1.4\uff0c\u4f46 f(6)=1\u3002\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5728 x=6 \u5904\u5177\u6709\u53ef\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027\uff0c\u56e0\u4e3a\u6781\u9650\u503c\u4e0e\u51fd\u6570\u503c\u4e0d\u4e00\u81f4\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-33612be383c71fea04c8c886710f7f10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l} \\displaystyle \\lim_{x \\to 6^-} f(x)=-1,4\\\\[3ex] \\displaystyle \\lim_{x \\to 6^+} f(x)=-1,4 \\end{array} \\right\\} \\bm{\\longrightarrow} \\lim_{x \\to 6} f(x)=-1,4\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"326\" 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-647b9aea6cc8b605d7e8bc7d5e83ee64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 6} f(x)=-1,4 \\neq f(6)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"217\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5f53 x=-3 \u65f6\uff0c\u6a2a\u5411\u6781\u9650\u4e0d\u91cd\u5408\uff0c\u5e76\u4e14\u6ca1\u6709\u7ed9\u51fa\u65e0\u7a77\u5927\u3002\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5728 x=-3 \u5904\u5177\u6709\u4e0d\u53ef\u907f\u514d\u7684\u6709\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027\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-3f7d2a2c7abbc525adfcc7576b449f1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -3^-} f(x)=-2 \\neq \\lim_{x \\to -3^+} f(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"275\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u8be5\u51fd\u6570\u5728 x = 3 \u5904\u5b58\u5728\u4e0d\u53ef\u907f\u514d\u7684\u65e0\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027\uff0c\u56e0\u4e3a\u6b64\u65f6\u81f3\u5c11\u6709\u4e00\u4e2a\u6a2a\u5411\u6781\u9650\u4f1a\u5bfc\u81f4\u65e0\u7a77\u5927\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-89bdb1598b6153cec4e9efce7b0927b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x)=+\\infty \\qquad \\lim_{x \\to 3^+} f(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"300\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u5b58\u5728\u54ea\u4e9b\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u6240\u6709\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\u7684\u793a\u4f8b\uff0c\u5e76\u4e14\u80fd\u591f\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u51fd\u6570\u7c7b\u578b &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e4%b8%8d%e8%bf%9e%e7%bb%ad%e6%80%a7%e7%9a%84%e7%b1%bb%e5%9e%8b\/\"> <span class=\"screen-reader-text\">\u4e0d\u8fde\u7eed\u6027\u7684\u7c7b\u578b<\/span> \u67e5\u770b\u5168\u6587 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