{"id":24,"date":"2023-09-17T11:06:22","date_gmt":"2023-09-17T11:06:22","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e8%bf%9e%e7%bb%ad%e5%87%bd%e6%95%b0-%e5%87%bd%e6%95%b0%e7%9a%84%e8%bf%9e%e7%bb%ad%e6%80%a7\/"},"modified":"2023-09-17T11:06:22","modified_gmt":"2023-09-17T11:06:22","slug":"%e8%bf%9e%e7%bb%ad%e5%87%bd%e6%95%b0-%e5%87%bd%e6%95%b0%e7%9a%84%e8%bf%9e%e7%bb%ad%e6%80%a7","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e8%bf%9e%e7%bb%ad%e5%87%bd%e6%95%b0-%e5%87%bd%e6%95%b0%e7%9a%84%e8%bf%9e%e7%bb%ad%e6%80%a7\/","title":{"rendered":"\u8fde\u7eed\u51fd\u6570\uff08\u51fd\u6570\u7684\u8fde\u7eed\u6027\uff09"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u4ec0\u4e48\u662f\u8fde\u7eed\u51fd\u6570\u4ee5\u53ca\u5982\u4f55\u786e\u5b9a\u51fd\u6570\u5728\u4e00\u70b9\u5904\u662f\u5426\u8fde\u7eed\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u53d1\u73b0\u8fde\u7eed\u51fd\u6570\u7684\u5c5e\u6027\u4ee5\u53ca\u6700\u5e38\u89c1\u51fd\u6570\u7684\u8fde\u7eed\u6027\u5206\u6790\u3002\u6700\u540e\uff0c\u60a8\u53ef\u4ee5\u901a\u8fc7\u8fde\u7eed\u51fd\u6570\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\uff0c\u4ee5\u5145\u5206\u7406\u89e3\u8be5\u6982\u5ff5\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-continua\"><\/span>\u4ec0\u4e48\u662f\u8fde\u7eed\u51fd\u6570\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u51fd\u6570\u7684\u8fde\u7eed\u6027\u53ef\u4ee5\u7528\u56fe\u5f62\u6765\u7814\u7a76\u3002<strong>\u8fde\u7eed\u51fd\u6570\u662f\u65e0\u9700\u4ece\u7eb8\u4e0a\u53d6\u4e0b\u94c5\u7b14\u5373\u53ef\u5728\u56fe\u5f62\u4e0a\u8868\u793a\u7684\u51fd\u6570\u3002<\/strong><\/p>\n<p class=\"has-text-align-center has-medium-font-size\"><u style=\"text-decoration-color:#FF9B28;\"><strong>\u8fde\u7eed\u529f\u80fd<\/strong><\/u><\/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\/fonction-continue.webp\" alt=\"\u8fde\u7eed\u51fd\u6570\" class=\"wp-image-1491\" width=\"354\" height=\"255\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p>\u4e0a\u8ff0\u529f\u80fd\u662f\u8fde\u7eed\u7684\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u4e00\u7b14\u753b\u51fa\u6765\uff0c\u800c\u65e0\u9700\u5c06\u624b\u4ece\u7eb8\u4e0a\u79fb\u5f00\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5f53\u5148\u524d\u7684\u8fde\u7eed\u6027\u6761\u4ef6\u6ca1\u6709\u653e\u5165\u51fd\u6570\u4e2d\u65f6\uff0c\u5219\u79f0\u8be5\u51fd\u6570\u4e3a<strong>\u4e0d\u8fde\u7eed\u51fd\u6570<\/strong>\u3002<\/p>\n<p class=\"has-text-align-center has-medium-font-size\"><u style=\"text-decoration-color:#FF9B28;\"><strong>\u95f4\u65ad\u51fd\u6570<\/strong><\/u><\/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\/fonction-pointillee.webp\" alt=\"\u4e0d\u8fde\u7eed\u51fd\u6570\" class=\"wp-image-1495\" width=\"354\" height=\"262\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p>\u524d\u4e00\u4e2a\u51fd\u6570\u662f\u4e0d\u8fde\u7eed\u7684\uff0c\u56e0\u4e3a\u8981\u8868\u793a\u5b83\uff0c\u60a8\u5fc5\u987b\u7528\u94c5\u7b14\u753b\u4e24\u6761\u7ebf\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u51fd\u6570\u5728 x=3 \u5904\u4e0d\u518d\u8fde\u7eed\uff0c\u56e0\u6b64\u6211\u4eec\u8bf4 x=3 \u662f<strong>\u4e0d\u8fde\u7eed\u70b9<\/strong>\u3002<\/p>\n<p>\u6b64\u5916\uff0c<strong>\u4e0d\u8fde\u7eed\u6027\u8fd8\u5206\u4e3a\u4e09\u79cd\u7c7b\u578b<\/strong>\uff1a\u53ef\u907f\u514d\u7684\u4e0d\u8fde\u7eed\u6027\u3001\u4e0d\u53ef\u907f\u514d\u7684\u6709\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027\u548c\u4e0d\u53ef\u907f\u514d\u7684\u65e0\u9650\u8df3\u8dc3\u4e0d\u8fde\u7eed\u6027\u3002\u5728\u4ee5\u4e0b\u94fe\u63a5\u4e2d\uff0c\u60a8\u53ef\u4ee5\u4e86\u89e3\u6bcf\u79cd\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\u7684\u5916\u89c2\u4ee5\u53ca\u6bcf\u79cd\u4e0d\u8fde\u7eed\u6027\u7684\u4e0d\u540c\u4e4b\u5904\uff1a<\/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\/\u4e0d\u8fde\u7eed\u6027\u7684\u7c7b\u578b\/\">\u4e0d\u8fde\u7eed\u6027\u7684\u7c7b\u578b<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"continuidad-de-una-funcion-en-un-punto\"><\/span>\u51fd\u6570\u5728\u4e00\u70b9\u7684\u8fde\u7eed\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u770b\u5230\u8fde\u7eed\u51fd\u6570\u7684\u56fe\u5f62\u662f\u4ec0\u4e48\u6837\u5b50\uff0c\u6211\u4eec\u5c31\u4f1a\u770b\u770b\u5982\u4f55\u901a\u8fc7\u89e3\u6790\u6765\u5224\u65ad\u51fd\u6570\u662f\u5426\u8fde\u7eed\u3002<\/p>\n<p>\u6570\u5b66\u4e0a\uff0c<strong>\u5982\u679c\u6ee1\u8db3\u4ee5\u4e0b\u4e09\u4e2a\u6761\u4ef6\uff0c\u51fd\u6570\u5728\u4e00\u70b9\u8fde\u7eed\uff1a<\/strong><\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;border:\">\n<li style=\"margin-bottom:15px\"><span style=\"color:#101010;font-weight: normal;\">\u6b64\u65f6\u51fd\u6570\u5b58\u5728\uff0c\u5373\u8be5\u70b9\u7684\u56fe\u50cf\u5b58\u5728\u3002<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e7292d399b69758819eab74a2aa9afd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\exists \\ f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"48\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u6b64\u65f6\u529f\u80fd\u5df2\u53d7\u5230\u9650\u5236\u3002\u56e0\u6b64\uff0c\u6b64\u65f6\u51fd\u6570\u7684\u5de6\u53f3\u4fa7\u6781\u9650\u76f8\u7b49\u3002<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7c4c9431d93839b2511a56583101db46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) = \\lim_{x \\to a^+} f(x)  \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black} \\quad \\exists \\lim_{x \\to a} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"413\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:15px\"><span style=\"color:#101010;font-weight: normal;\">\u8be5\u70b9\u7684\u56fe\u50cf\u4e0e\u51fd\u6570\u5728\u8be5\u70b9\u7684\u6781\u9650\u91cd\u5408\u3002<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da2902aa458fe8a9c8234e2be38336c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(a)=\\lim_{x \\to a} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"123\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/ol>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u51fd\u6570\u7684\u6240\u6709\u70b9\u90fd\u6ee1\u8db3\u4e09\u4e2a\u8fde\u7eed\u6027\u6761\u4ef6\uff0c\u5219\u8be5\u51fd\u6570\u662f\u8fde\u7eed\u7684\u3002<\/p>\n<p>\u4f5c\u4e3a\u4f8b\u5b50\uff0c\u6211\u4eec\u5c06\u5206\u6790\u4ee5\u4e0b\u5206\u6bb5\u51fd\u6570\u7684\u8fde\u7eed\u6027\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\/continuite-dune-fonction-definie-par-morceaux.webp\" alt=\"\u5206\u6bb5\u5b9a\u4e49\u51fd\u6570\u7684\u8fde\u7eed\u6027\" class=\"wp-image-201\" width=\"440\" height=\"306\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p>\u5373\u4f7f\u4f60\u6539\u53d8\u4e86\u90e8\u5206\uff0c\u5728\u8fd9\u4e00\u70b9\u4e0a<\/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>\u8be5\u51fd\u6570\u662f\u8fde\u7eed\u7684\uff0c\u56e0\u4e3a\u8be5\u70b9\u5904\u51fd\u6570\u7684\u6a2a\u5411\u6781\u9650\u76f8\u7b49\u5e76\u4e14\u4e0e\u8be5\u70b9\u5904\u51fd\u6570\u7684\u503c\u66f4\u4e00\u81f4\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-3f659d88902824c6a762a5ebe2d6db14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{x \\to -2^-} f(x)=\\lim\\limits_{x \\to -2^+} f(x)= f(-2)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"300\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u51fd\u6570\u5728\u8be5\u70b9\u4e0d\u8fde\u7eed<\/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-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u56e0\u4e3a\u4e24\u4e2a\u6a2a\u5411\u6781\u9650\u4e0d\u540c\uff0c\u56e0\u6b64\u6b64\u65f6\u51fd\u6570\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-5f9d62d0c5ddcefe8cc4cbe2daaf6d57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{x \\to 4^-} f(x)=3 \\neq \\lim\\limits_{x \\to 4^+} f(x)= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"240\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u7531\u5206\u6bb5\u5b9a\u4e49\u7684\u51fd\u6570\u5728\u6240\u6709\u5b9e\u6570\u4e2d\u90fd\u662f\u8fde\u7eed\u7684\uff0c\u9664\u4e86<\/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-9ad850560a1ff3e3bb4386cf732d0220_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=4,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5b58\u5728\u4e0d\u8fde\u7eed\u6027\u7684\u5730\u65b9\u3002<\/p>\n<p>\u6211\u4eec\u8fd8\u53ef\u4ee5\u9a8c\u8bc1\u8be5\u51fd\u6570\u662f\u4e0d\u8fde\u7eed\u7684<\/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-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u56e0\u4e3a\u8981\u4ee5\u56fe\u5f62\u65b9\u5f0f\u8868\u793a\u5b83\uff0c\u6b64\u65f6\u5fc5\u987b\u5c06\u94c5\u7b14\u4ece\u7eb8\u4e0a\u79fb\u5f00\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"continuidad-de-funciones-elementales\"><\/span>\u521d\u7b49\u51fd\u6570\u7684\u8fde\u7eed\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u67d0\u4e9b\u7c7b\u578b\u7684\u51fd\u6570\u56e0\u5176\u7279\u5f81\u800c\u8fde\u7eed\uff1a<\/p>\n<ul>\n<li><strong>\u5e38\u6570\u51fd\u6570<\/strong>\u5728\u6240\u6709\u5b9e\u6570\u4e2d\u90fd\u662f\u8fde\u7eed\u7684\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-252f9958e223f77bf50cb3b92a7c3e35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u591a\u9879\u5f0f\u51fd\u6570<\/strong>\u5bf9\u4e8e\u6240\u6709\u5b9e\u6570\u90fd\u662f\u8fde\u7eed\u7684\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3094a01ff9b10acb7c44349cda083025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=a_0+a_1x+a_2x^2+a_3x^3+\\dots+a_nx^n\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"338\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u6709\u7406\uff08\u6216\u5206\u6570\uff09\u51fd\u6570<\/strong>\u5728\u6240\u6709\u5b9e\u6570\u4e2d\u90fd\u662f\u8fde\u7eed\u7684\uff0c\u9664\u4e86\u62b5\u6d88\u5206\u6570\u5206\u6bcd\u7684\u503c\u4e4b\u5916\uff0c\u5728\u8fd9\u4e9b\u70b9\u4e0a\u51fd\u6570\u5448\u73b0\u4e0d\u8fde\u7eed\u6027\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6cc33f4306e45701e8bc92457779201d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{p(x)}{q(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"93\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u6307\u6570\u51fd\u6570<\/strong>\u5728\u6240\u6709\u5b9e\u6570\u4e0a\u8fde\u7eed\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-73aa6cf687ce5e8c2f9faf41f5614e53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=a^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u5bf9\u6570\u51fd\u6570<\/strong>\u5728\u4f7f\u5176\u8bba\u8bc1\u4e3a\u6b63\u7684\u6240\u6709\u70b9\u4e0a\u90fd\u662f\u8fde\u7eed\u7684\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d94badc2befa1e0c57a867970b1040aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a (x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u65e0\u7406\u51fd\u6570<\/strong>\u6216\u6709\u6839\u51fd\u6570\u7684\u8fde\u7eed\u6027\u53d6\u51b3\u4e8e\u6839\u5f0f (n) \u7684\u6307\u6570\u3002\u5982\u679c\u7d22\u5f15\u662f\u5076\u6570\uff0c\u5219\u8fd9\u4e9b\u5728\u6240\u6709\u70b9\u4e0a\u90fd\u662f\u8fde\u7eed\u51fd\u6570\uff0c\u4f7f\u6839\u53c2\u6570\u7b49\u4e8e\u6216\u5927\u4e8e\u96f6\u3002\u4f46\u5982\u679c\u7d22\u5f15\u662f\u5947\u6570\uff0c\u5219\u5b83\u4eec\u662f\u6240\u6709\u5b9e\u6570\u4e0a\u7684\u8fde\u7eed\u51fd\u6570\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca6c3302aac609e9214e62444cfec2bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u4e09\u89d2\u51fd\u6570<\/strong>\u7684\u8fde\u7eed\u6027\u53d6\u51b3\u4e8e\u51fd\u6570\u7684\u7c7b\u578b\u3002\u6b63\u5f26\u51fd\u6570\u548c\u4f59\u5f26\u51fd\u6570\u5728\u5b9e\u6570\u96c6\u5408\u4e0a\u8fde\u7eed\uff0c\u4f46\u6b63\u5207\u51fd\u6570\u5728\u70b9\u4e0a\u4e0d\u8fde\u7eed\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0c1c82b94111254bf0771af43a5b4411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x=\\frac{\\pi}{2}+k\\pi\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"91\" style=\"vertical-align: -12px;\"><\/p>\n<p>\uff08\u5176\u4e2d<em>k<\/em>\u662f\u6574\u6570\uff09\u3002 <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a42292efae266c09baade046e8a3cb76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=sen(x)\\qquad f(x)=cos(x)\\qquad f(x)=tg(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-las-funciones-continuas\"><\/span>\u8fde\u7eed\u51fd\u6570\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8096\u6069<\/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-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a5054ad96fb0978182340eb214bb125_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u4e24\u4e2a\u8fde\u7eed\u51fd\u6570\u5728\u8be5\u70b9<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c20f4d749ca0651113257e1f1ea66b02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=a,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u4e0b\u4e00\u4e2a\uff1a<\/p>\n<ul>\n<li>\u4e00\u70b9\u4e0a<strong>\u7684\u4e24\u4e2a\u8fde\u7eed\u51fd\u6570\u7684\u548c<\/strong>\u662f\u8be5\u70b9\u4e0a\u7684\u53e6\u4e00\u4e2a\u8fde\u7eed\u51fd\u6570\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c566932a59271b6e33a784bcf81ee749_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)+g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u4e24\u4e2a\u8fde\u7eed\u51fd\u6570<\/strong>\u5728\u67d0\u4e00\u70b9\u7684\u4e58\u79ef\u7b49\u4e8e\u8be5\u70b9\u7684\u53e6\u4e00\u4e2a\u8fde\u7eed\u51fd\u6570\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d47b381826b8c5e901bf202b6d4b14c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\cdot g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u53ea\u8981\u8be5\u70b9\u4e0d\u53d6\u6d88\u9664\u6cd5<strong>\u51fd\u6570\uff0c\u5728\u4e00\u70b9\u5904\u9664\u4ee5\u4e24\u4e2a<\/strong>\u8fde\u7eed\u51fd\u6570\u5c31\u4f1a\u5728\u8be5\u70b9\u5f97\u5230\u53e6\u4e00\u4e2a\u8fde\u7eed\u51fd\u6570\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5962b35380c55e0089deeac0a98b01fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{f(x)}{g(x)}\\qquad g(a)\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li><strong>\u4e24\u4e2a\u8fde\u7eed\u51fd\u6570\u5728\u4e00\u70b9\u7684\u590d\u5408<\/strong>\u4f1a\u5728\u540c\u4e00\u70b9\u4ea7\u751f\u8fde\u7eed\u51fd\u6570\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ba04f43c8995b3659a05f370a10485a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\circ g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/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\/\u51fd\u6570\u7684\u590d\u5408-\u590d\u5408\u51fd\u6570\/\">\u4ec0\u4e48\u662f\u590d\u5408\u51fd\u6570\uff1f<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-continuidad-de-una-funcion\"><\/span>\u89e3\u51b3\u4e86\u51fd\u6570\u8fde\u7eed\u6027\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u627e\u51fa\u4e0b\u56fe\u4e2d\u6240\u793a\u51fd\u6570\u7684\u4e0d\u8fde\u7eed\u70b9\u3002\u8fd8\u8981\u786e\u5b9a\u5b83\u662f\u4ec0\u4e48\u7c7b\u578b\u7684\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\/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<p><strong>\u6ce8\u610f\uff1a<\/strong>\u8981\u8fdb\u884c\u6b64\u7ec3\u4e60\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u9996\u5148\u4e86\u89e3\u4e0d\u540c\u7c7b\u578b\u7684\u4e0d\u8fde\u7eed\u6027\u4ee5\u53ca\u5982\u4f55\u8bc6\u522b\u5b83\u4eec\u3002\u60a8\u53ef\u4ee5\u53c2\u9605<u style=\"text-decoration-color:#FF9B28;\">\u4e0d\u8fde\u7eed\u7c7b\u578b<\/u>\u539f\u7406\u94fe\u63a5\u4e2d\u7684\u89e3\u91ca\u3002 <\/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\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-61593bab94da601722d6ae7aedfdb172_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1} f(x) =  0 \\neq  f(0) = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"187\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728 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\u4e602<\/h3>\n<p>\u786e\u5b9a\u4e0b\u56fe\u4e2d\u6240\u793a\u51fd\u6570\u4e0d\u8fde\u7eed\u7684\u70b9\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\/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=\"515\" height=\"434\" 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\">\u5728\u70b9 x=6 \u5904\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<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\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\">\u6709\u7406\u51fd\u6570\u5728\u5176\u6574\u4e2a\u57df\u4e2d\u662f\u8fde\u7eed\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u9664\u4e86\u62b5\u6d88\u5206\u6bcd\u7684\u503c\u4e4b\u5916\u7684\u6240\u6709\u5b9e\u6570\u4e2d\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u6709\u7406\u51fd\u6570\u7684\u5206\u6bcd\u8bbe\u7f6e\u4e3a\u96f6\uff0c\u770b\u770b\u54ea\u4e9b\u70b9\u4e0d\u5c5e\u4e8e\u5b9a\u4e49\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<\/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>\u5206\u6790\u4ee5\u4e0b\u5206\u6bb5\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-a18e6289d268e6ea9fe1ee3ea14d31fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left\\{ \\begin{array}{lcl} 5x-2 &amp; \\text{si} &amp;  x < 1 \\\\[2ex] x^2+2 &amp; \\text{si} &amp; x \\geq 1 \\end{array} \\right.\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"218\" style=\"vertical-align: 0px;\"><\/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\">\u8be5\u51fd\u6570\u5728\u7b2c\u4e00\u90e8\u5206\u4e2d\u4e5f\u662f\u8fde\u7eed\u7684\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-e05d9a74362639e610acff0ab2d83b16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<p> \uff0c\u5982\u7b2c\u4e8c\u90e8\u5206\u6240\u793a\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-79baa9dfae33805a8e2362cc182fd867_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"47\" style=\"vertical-align: -2px;\"><\/p>\n<p> \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\u51fd\u6570\u5206\u6bb5\u4e2d\u65ad\u7684\u70b9\u3002\u90a3\u4e48\u6211\u4eec\u6765\u8ba1\u7b97\u6b64\u65f6\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-3c84a263e22011d5c8d67c9ee977f98e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1^-} f(x) = \\lim_{x \\to 1} (5x-2)=5\\cdot 1-2=\\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"309\" 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-a1d1b6f5e109c06114b9e36af6f7078a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1^+} f(x) = \\lim_{x \\to 1} (x^2+2)=1^2+2=\\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"293\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u4e24\u4e2a\u6a2a\u5411\u6781\u9650\u91cd\u5408\uff0c\u5f53 x \u8d8b\u4e8e 1 \u65f6\u51fd\u6570\u7684\u6781\u9650\u7b49\u4e8e 3\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-a621c7ef999aae5418c2f71da1da67f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1^-} f(x) = \\lim_{x \\to 1^+} f(x) = 3 \\ \\bm{\\longrightarrow} \\ \\exists \\lim_{x \\to 1} f(x) = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"360\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b64\u5916\uff0cx=1\u7684\u56fe\u50cf\u4e5f\u662f3\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-61f3e46233f15d71b39af62ae6bfb4eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=1^2+2=\\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u7531\u4e8e\u51fd\u6570\u5728 x=1 \u5904\u7684\u6781\u9650\u7b49\u4e8e\u8be5\u70b9\u7684\u56fe\u50cf\uff0c\u56e0\u6b64\u8be5\u51fd\u6570\u5728\u70b9 x=1 \u5904\u8fde\u7eed\u3002\u56e0\u6b64\u5b83\u5728\u6240\u6709\u5b9e\u6570\u4e2d\u90fd\u662f\u8fde\u7eed\u7684\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-8cb4559dfddcda3b3c68a5d64eeadcee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(1)=\\lim_{x \\to 1} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"122\" 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\u4e605<\/h3>\n<p>\u7814\u7a76\u4ee5\u4e0b\u65e0\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-c43021550a231793494acc2b6eea24d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{2x+6}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\"><\/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\">\u5b83\u662f\u4e00\u4e2a\u5076\u6570\u4e0b\u6807\u7684\u6839\u5f0f\u51fd\u6570\uff0c\u56e0\u6b64\u53ea\u8981\u6839\u5f0f\u7684\u81ea\u53d8\u91cf\u5927\u4e8e 0\uff0c\u8be5\u51fd\u6570\u5c31\u662f\u8fde\u7eed\u7684\uff08\u56e0\u4e3a\u8d1f\u6570\u7684\u5e73\u65b9\u6839\u4e0d\u5b58\u5728\uff09\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-d54da4e00c0cc48d43914e9e34b1c1d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+6\\ge 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u89e3\u51b3\u4e0d\u7b49\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-7739f2163d650971be01af6f5a93ae25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x\\ge -6\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"66\" style=\"vertical-align: -3px;\"><\/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-db29954e4e5815cd2bf4bcbfe4c53145_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\ge \\cfrac{-6}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"67\" 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-dfc84780b14328431bcc372ff904772d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\ge -3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u89e3\u7531\u6240\u6709\u5927\u4e8e\u6216\u7b49\u4e8e-3 \u7684\u6570\u5b57\u7ec4\u6210\u3002\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5728\u5176\u5b9a\u4e49\u57df\u7684\u533a\u95f4\u4e0a\u662f\u8fde\u7eed\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-1d2a6678926adfe02dc663e155ec573f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{Dom } \\ \\bm{f = [-3,+\\infty) }\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e606<\/h3>\n<p>\u5206\u6790\u4ee5\u4e0b\u5bf9\u6570\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-e2c2073b5212610fcc153bdb47eacccf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_3 (-3x+6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" style=\"vertical-align: -5px;\"><\/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\">\u8fd9\u662f\u4e00\u4e2a\u5bf9\u6570\u51fd\u6570\uff0c\u65e2\u6ca1\u6709\u8d1f\u6570\u7684\u5bf9\u6570\uff0c\u4e5f\u6ca1\u67090\u7684\u5bf9\u6570\u3002\u56e0\u6b64\uff0c\u53ea\u8981\u5bf9\u6570\u7684\u53c2\u6570\u4e3a\u6b63\uff08\u5927\u4e8e\u96f6\uff09\uff0c\u8be5\u51fd\u6570\u5c31\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-53c23d1b367425e8cfb94fb36235b8f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3x+6>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;95&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u89e3\u51b3\u4e0d\u7b49\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-d0183470903eba7ebd08dfcdbf49287e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3x>-6&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;78&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/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-9c67175fd587232ef7d927f7dfca725f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x<\\cfrac{-6}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"67\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8bf7\u8bb0\u4f4f\uff0c\u5f53\u60a8\u5c06\u8d1f\u6570\u9664\u4ee5\u4e0d\u7b49\u5f0f\u7684\u53e6\u4e00\u8fb9\u65f6\uff0c\u5fc5\u987b\u53cd\u8f6c\u4e0d\u7b49\u5f0f\u7684\u7b26\u53f7\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-88de95669c546ef6d18c28d0579fbe0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x<2\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"42\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u89e3\u7531\u6240\u6709\u5c0f\u4e8e 2 \u7684\u6570\u5b57\u7ec4\u6210\u3002\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u4e3a\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-505dcdf16c80fdf012163a8800d92836_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{Dom } \\ \\bm{f = (-\\infty,2) }\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8be5\u51fd\u6570\u5728\u5176\u57df\u5185\u7684\u6bcf\u4e2a\u70b9\u90fd\u662f\u8fde\u7eed\u7684\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e607<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\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-66e02ab966f87bc29b3791246fbf8032_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{4x-2}{\\sqrt{-2x-8}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"139\" 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\">\u5728\u5206\u6570\u7684\u5206\u6bcd\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u5177\u6709\u5076\u6570\u7d22\u5f15\u7684\u6839\u5f0f\uff0c\u56e0\u6b64\u53ea\u8981\u6839\u7684\u5185\u5bb9\u7b49\u4e8e\u6216\u5927\u4e8e\u96f6\uff0c\u8be5\u51fd\u6570\u5c31\u4f1a\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-042efdf7af54fcbec527f0ee83e1b007_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x-8\\geq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u800c\u4e14\uff0c\u6839\u5728\u5206\u6570\u7684\u5206\u6bcd\u4e2d\uff0c\u800c\u5206\u6570\u7684\u5206\u6bcd\u6c38\u8fdc\u4e0d\u53ef\u80fd\u4e3a 0\u3002\u56e0\u6b64\uff0c\u53ea\u6709\u5f53\u6839\u7684\u5185\u5bb9\u4e25\u683c\u5927\u4e8e 0 \u65f6\uff0c\u8be5\u51fd\u6570\u624d\u4f1a\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-62002e9d71e0718d04d6d9db08d0e04b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x-8> 0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;95&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u89e3\u51b3\u4e0d\u7b49\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-336543c46271685f7d069786d2cf4e12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x>8&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;64&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/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-3e4a2af9f53dd0a356211660f770666e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x<\\cfrac{8}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"59\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8bf7\u8bb0\u4f4f\uff0c\u5f53\u6211\u4eec\u901a\u8fc7\u4e58\u6216\u9664\u4e0d\u7b49\u5f0f\u6765\u6539\u53d8\u8d1f\u6570\u7684\u4e24\u8fb9\u65f6\uff0c\u6211\u4eec\u8fd8\u5fc5\u987b\u65cb\u8f6c\u4e0d\u7b49\u53f7\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-ee1c9c50b3c39064f9670f06f9bdc8fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x<-4\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"57\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7ed3\u679c\u662f\u6240\u6709\u5c0f\u4e8e-4 \u7684\u6570\u5b57\u3002\u56e0\u6b64\uff0c\u51fd\u6570\u7684\u57df\u53ca\u5176\u8fde\u7eed\u6027\u7531\u4ee5\u4e0b\u533a\u95f4\u5b9a\u4e49\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-00cfb1cb63133c3092854bb810abfce8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbf{Dom } \\ \\bm{f = (-\\infty,-4) }\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e608<\/h3>\n<p>\u8ba1\u7b97<em>k<\/em>\u7684\u503c\uff0c\u4f7f\u51fd\u6570\u59cb\u7ec8\u8fde\u7eed<\/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-6a134e3092861eafea1239dba23bea40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathbb{R} .\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" 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-f7d8f0d6e0730c139c3baff0989a8fe7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left\\{ \\begin{array}{lcl} kx-1 &amp; \\text{si} &amp;  x \\leq 2 \\\\[2ex] 3x^2 - 5  &amp; \\text{si} &amp; x > 2 \\end{array} \\right.&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;65&#8243; width=&#8221;225&#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\">\u4e3a\u4e86\u4f7f\u51fd\u6570\u8fde\u7eed\uff0c\u65ad\u70b9\u5904\u7684\u4e24\u4e2a\u6a2a\u5411\u6781\u9650\u5fc5\u987b\u7ed9\u51fa\u76f8\u540c\u7684\u7ed3\u679c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u6ca1\u6709<em>k<\/em>\u7684\u96f6\u4ef6\u65ad\u88c2\u70b9\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-7eff7d699bc801340c66f4fd95c30b2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2^+} f(x) = \\lim_{x \\to 2} (3x^2 - 5) = 3\\cdot 2^2-5=\\bm{7}\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"324\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8981\u4f7f\u5206\u6bb5\u51fd\u6570\u8fde\u7eed\uff0c\u53e6\u4e00\u8fb9\u6781\u9650\u4e5f\u5fc5\u987b\u7b49\u4e8e 7\u3002<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c1d\u8bd5\u8ba1\u7b97\u53e6\u4e00\u4e2a\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-1fc80cd47e7fd6cf50b2f2de57c4b40f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2^-} f(x) = \\lim_{x \\to 2} (kx-1) = k\\cdot2 -1= 2k-1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"350\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e3a\u4e86\u4f7f\u51fd\u6570\u8fde\u7eed\uff0c\u4efb\u4f55\u70b9\u7684\u4e24\u4e2a\u6a2a\u5411\u6781\u9650\u5fc5\u987b\u7ed9\u51fa\u76f8\u540c\u7684\u7ed3\u679c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u4ece\u6781\u9650\u5f97\u5230\u7684\u8868\u8fbe\u5f0f\u8bbe\u7f6e\u4e3a 7\uff08\u53e6\u4e00\u4e2a\u6a2a\u5411\u6781\u9650\u7684\u7ed3\u679c\uff09\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-8b99f2f508e7c3f7ab4ebaa9f30638a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2k -1= 7\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u6c42\u89e3\u6240\u5f97\u65b9\u7a0b\u4ee5\u627e\u5230<em>k<\/em>\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-c591d3bbba83f012852966634d0d8234_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2k-1 = 7\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" 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-747038396badd9b1d5e6336cf463fe13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2k = 7 +1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" 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-fa5cd6bc10e8ce9c34542635d995323c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2k = 8\" 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-1009397e0b35416230f2a5a3d307755a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k = \\cfrac{8}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"44\" 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-ffe7f00b80fc8f5c4961250446632d6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{k =4}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/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\u4ec0\u4e48\u662f\u8fde\u7eed\u51fd\u6570\u4ee5\u53ca\u5982\u4f55\u786e\u5b9a\u51fd\u6570\u5728\u4e00\u70b9\u5904\u662f\u5426\u8fde\u7eed\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u53d1\u73b0\u8fde\u7eed\u51fd\u6570\u7684\u5c5e\u6027\u4ee5\u53ca\u6700\u5e38\u89c1\u51fd &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e8%bf%9e%e7%bb%ad%e5%87%bd%e6%95%b0-%e5%87%bd%e6%95%b0%e7%9a%84%e8%bf%9e%e7%bb%ad%e6%80%a7\/\"> <span class=\"screen-reader-text\">\u8fde\u7eed\u51fd\u6570\uff08\u51fd\u6570\u7684\u8fde\u7eed\u6027\uff09<\/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-24","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized 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