{"id":27980,"date":"2024-08-17T13:00:51","date_gmt":"2024-08-17T13:00:51","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27980"},"modified":"2024-08-18T06:57:41","modified_gmt":"2024-08-18T06:57:41","slug":"%e5%8d%95%e4%be%a7%e6%9e%81%e9%99%90%ef%bc%9a%e5%ae%9a%e4%b9%89%e3%80%81%e5%8f%91%e5%b1%95%e4%b8%8e%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e5%8d%95%e4%be%a7%e6%9e%81%e9%99%90%ef%bc%9a%e5%ae%9a%e4%b9%89%e3%80%81%e5%8f%91%e5%b1%95%e4%b8%8e%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u5355\u4fa7\u6781\u9650\uff1a\u5b9a\u4e49\u3001\u53d1\u5c55\u4e0e\u7ec3\u4e60"},"content":{"rendered":"<p><center><\/p>\n<h1>\u5355\u4fa7\u6781\u9650\uff1a\u5b9a\u4e49\u3001\u53d1\u5c55\u4e0e\u7ec3\u4e60<\/h1>\n<p><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n\u672c\u6587\u89e3\u91ca\u4e86\u5fae\u79ef\u5206\u4e2d\u7684\u5355\u4fa7\u6781\u9650\u548c\u53cc\u4fa7\u6781\u9650\uff0c\u5c55\u793a\u4e86\u5b83\u4eec\u5982\u4f55\u76f4\u89c2\u5730\u548c\u5f62\u5f0f\u5316\u5730\u5b9a\u4e49\u548c\u5e94\u7528\u3002\u672c\u6587\u63d0\u4f9b\u4e86\u56fe\u5f62\u548c\u4ee3\u6570\u793a\u4f8b\uff0c\u8ba8\u8bba\u4e86\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\u4f7f\u7528\u6781\u9650\u4ee3\u6570\u7684\u6761\u4ef6\uff0c\u5e76\u5305\u542b\u4e86\u89e3\u7b54\u7ec3\u4e60\uff0c\u4ee5\u52a0\u5f3a\u7406\u89e3\u3002\u672c\u6587\u65e8\u5728\u63d0\u4f9b\u5bf9\u8fd9\u4e9b\u5fae\u79ef\u5206\u57fa\u7840\u6982\u5ff5\u7684\u6e05\u6670\u7b80\u660e\u7684\u7406\u89e3\u3002<\/em><\/p>\n<p><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5728\u672c\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ul style=\"text-align:left;\">\n<li><strong>\u7406\u89e3<\/strong>\u5355\u4fa7\u6781\u9650\u548c\u53cc\u4fa7\u6781\u9650\u4e4b\u95f4\u7684\u533a\u522b\u3002<\/li>\n<li><strong>\u6b63\u5f0f\u5b9a\u4e49<\/strong>\u53f3\u4fa7\u548c\u5de6\u4fa7\u7684\u5355\u4fa7\u6781\u9650\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u5355\u4fa7\u6781\u9650\u7684\u5b9a\u4e49\u4e8e\u5fae\u79ef\u5206\u95ee\u9898\u4e2d\u3002<\/li>\n<li><strong>\u56fe\u5f62\u5316\u89e3\u91ca<\/strong>\u5355\u4fa7\u6781\u9650\u548c\u53cc\u4fa7\u6781\u9650\u3002<\/li>\n<li><strong>\u8bc6\u522b<\/strong>\u53cc\u4fa7\u6781\u9650\u5b58\u5728\u7684\u5fc5\u8981\u6761\u4ef6\u3002<\/li>\n<li><strong>\u5728\u5355\u4fa7\u6781\u9650\u60c5\u5883\u4e0b\u4f7f\u7528<\/strong>\u6781\u9650\u4ee3\u6570\u3002<\/li>\n<li><strong>\u89e3\u51b3<\/strong>\u4e0e\u5355\u4fa7\u6781\u9650\u76f8\u5173\u7684\u5fae\u79ef\u5206\u7ec3\u4e60\u3002<\/li>\n<\/ul>\n<p><strong>\u5185\u5bb9\u76ee\u5f55\uff1a<\/strong><br \/>\n<a href=\"#1\">\u4ecb\u7ecd<\/a><br \/>\n<a href=\"#2\">\u5355\u4fa7\u6781\u9650\u548c\u53cc\u4fa7\u6781\u9650\u7684\u76f4\u89c2\u6982\u5ff5<\/a><br \/>\n<a href=\"#3\">\u5355\u4fa7\u6781\u9650\u7684\u6b63\u5f0f\u5b9a\u4e49<\/a><br \/>\n<a href=\"#4\">\u6781\u9650\u4ee3\u6570\u7684\u6761\u4ef6<\/a><br \/>\n<a href=\"#5\">\u5efa\u8bae\u548c\u89e3\u7b54\u7ec3\u4e60<\/a><\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/8lkvxEHsF6c\" title=\"YouTube\u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u4ecb\u7ecd<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=138s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5f53\u6211\u4eec\u9047\u5230\u53ea\u80fd\u4ece\u5de6\u4fa7\u6216\u53f3\u4fa7\u5b58\u5728\u7684\u6781\u9650\u65f6\uff0c<\/span><\/strong><\/a> \u5c31\u4f1a\u51fa\u73b0\u5355\u4fa7\u6781\u9650\uff0c\u800c\u4e0d\u662f\u4ece\u4e24\u4fa7\u90fd\u5b58\u5728\u7684\u6781\u9650\u3002\u6211\u4eec\u5230\u76ee\u524d\u4e3a\u6b62\u6240\u7814\u7a76\u7684\u6b63\u662f\u540e\u4e00\u79cd\u7c7b\u578b\uff1a\u51fd\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u5f53 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to x_0<\/span><\/span> \u65f6\u7684\u6781\u9650\u5b58\u5728\uff0c\u8981\u6c42 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u7684\u4e24\u4fa7\u90fd\u5b9a\u4e49\u826f\u597d\uff1b\u5982\u679c\u6ca1\u6709\u53d1\u751f\u8fd9\u79cd\u60c5\u51b5\uff0c\u90a3\u4e48\u6781\u9650\u7684\u5b9a\u4e49\u5c06\u65e0\u6cd5\u6210\u7acb\u3002\u7531\u4e8e\u8fd9\u79cd\u7c7b\u578b\u7684\u6781\u9650\u51fa\u73b0\u7684\u60c5\u51b5\u5f88\u9891\u7e41\uff0c\u56e0\u6b64\u9700\u8981\u627e\u5230\u4e00\u79cd\u65b9\u6cd5\u6765\u5904\u7406\u5b83\u4eec\u3002\u8fd9\u901a\u8fc7\u6b63\u5f0f\u5b9a\u4e49\u6765\u89e3\u51b3\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u5355\u4fa7\u6781\u9650\u548c\u53cc\u4fa7\u6781\u9650\u7684\u76f4\u89c2\u6982\u5ff5<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=279s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u51fd\u6570\u6781\u9650\u5b58\u5728\u7684\u6761\u4ef6<\/span><\/strong><\/a> \u662f\uff0c\u5f53 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to x_0<\/span><\/span> \u65f6\uff0c\u51fd\u6570\u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u7684\u4e24\u4fa7\u90fd\u5b9a\u4e49\u826f\u597d\u3002\u5982\u679c\u8fd9\u79cd\u60c5\u51b5\u53d1\u751f\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u8ba8\u8bba\u53cc\u4fa7\u6781\u9650\u3002\u800c\u5982\u679c\u8be5\u6781\u9650\u7684\u7ed3\u679c\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">L<\/span><\/span>\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5199<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0}f(x) = L<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u73b0\u5728\uff0c\u5047\u8bbe\u6211\u4eec\u91cd\u65b0\u5b9a\u4e49\u8fd9\u4e2a\u51fd\u6570\uff0c\u4f7f\u5176\u5b9a\u4e49\u57df\u4ec5\u5305\u542b\u5927\u4e8e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u7684\u503c\u3002\u5982\u679c\u6211\u4eec\u8fd9\u6837\u505a\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\u6781\u9650\u4e0d\u518d\u5b58\u5728\uff08\u56e0\u4e3a\u4f1a\u6709 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u7684\u503c\u6ca1\u6709\u610f\u4e49\uff09\uff1b\u7136\u800c\uff0c\u56fe\u5f62\u4e0a\u6211\u4eec\u4ecd\u7136\u53ef\u4ee5\u8bf4\uff0c\u5f53 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to x_0<\/span><\/span> \u65f6\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u4ecd\u7136\u8d8b\u5411\u4e8e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">L<\/span><\/span>\u3002\u6211\u4eec\u5728\u8fd9\u91cc\u4ea7\u751f\u7684\u76f4\u89c2\u6982\u5ff5\u662f\u53f3\u4fa7\u6781\u9650\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e66\u5199\u8868\u793a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0^+}f(x) = L<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u540c\u6837\u7684\uff0c\u6211\u4eec\u5c06\u5f97\u5230\u5de6\u4fa7\u6781\u9650<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0^-}f(x) = L<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\uff0c\u5f53\u5de6\u53f3\u6781\u9650\u90fd\u5b58\u5728\u4e14\u76f8\u7b49\u65f6\uff0c\u53cc\u4fa7\u6781\u9650\u624d\u4f1a\u5b58\u5728<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0^-}f(x) = \\lim_{x\\to x_0}f(x) = \\lim_{x\\to x_0^-}f(x)<\/span><\/span><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u5355\u4fa7\u6781\u9650\u7684\u6b63\u5f0f\u5b9a\u4e49<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=438s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6b63\u5f0f\u5b9a\u4e49\u5355\u4fa7\u6781\u9650\u65f6\uff0c\u53ea\u9700<\/span> <\/strong><\/a>\u5bf9\u539f\u59cb\u6781\u9650\u5b9a\u4e49\u8fdb\u884c\u5c0f\u5e45\u4fee\u6539\u3002<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} f(x) = L := \\left(\\forall \\epsilon\\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\exist \\delta \\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\right.<\/span><\/span> <span style=\"background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\lt|x-x_0|\\lt\\delta <\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left.\\rightarrow |f(x)-L|\\lt\\epsilon \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5bf9\u4e8e\u53f3\u4fa7\u6781\u9650\uff0c\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall \\epsilon\\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\exist \\delta \\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\right.<\/span><\/span> <span style=\"background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0 \\lt x \\lt x_0 + \\delta <\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left.\\rightarrow |f(x)-L|\\lt\\epsilon \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5bf9\u4e8e\u5de6\u4fa7\u6781\u9650\uff0c\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall \\epsilon\\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\exist \\delta \\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\right.<\/span><\/span> <span style=\"background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0 - \\delta \\lt x \\lt x_0<\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left.\\rightarrow |f(x)-L|\\lt\\epsilon \\right)<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u6781\u9650\u4ee3\u6570\u7684\u6761\u4ef6<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=801s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u8fd9\u4e9b\u5b9a\u4e49\u7684\u6709\u8da3\u4e4b\u5904\u5728\u4e8e\u5b83\u4eec\u90fd\u5305\u542b\u5728<\/span><\/strong><\/a> \u4f20\u7edf\u6781\u9650\u5b9a\u4e49\u4e2d\uff0c\u8fd9\u5f88\u91cd\u8981\uff0c\u56e0\u4e3a\u8fd9\u4f7f\u6211\u4eec\u514d\u4e8e\u91cd\u65b0\u8bc1\u660e\u6211\u4eec\u5df2\u7ecf\u8bc1\u660e\u7684\u6240\u6709\u53cc\u4fa7\u6781\u9650\u6027\u8d28\u3002\u53ea\u8981\u6d89\u53ca\u7684\u6781\u9650\u6027\u8d28\u76f8\u540c\uff08\u90fd\u662f\u4ece\u5de6\u4fa7\u6216\u90fd\u662f\u4ece\u53f3\u4fa7\uff0c\u4ece\u4e0d\u6df7\u5408\uff09\u3001\u6307\u5411\u540c\u4e00\u70b9\u5e76\u5b58\u5728\u4e8e\u8be5\u70b9\uff0c\u6240\u6709\u7684\u6781\u9650\u4ee3\u6570\u90fd\u5c06\u5982\u6211\u4eec\u4e4b\u524d\u7684\u8bfe\u7a0b\u4e2d\u6240\u89c1\u7684\u90a3\u6837\u8fd0\u4f5c\u3002<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u5efa\u8bae\u548c\u89e3\u7b54\u7ec3\u4e60<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to {\\frac{1}{2}}^- } \\sqrt{\\dfrac{x+2}{x+1}} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=994s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 1^+} \\sqrt{\\dfrac{x-1}{x+2}} <\/span><\/span><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1058s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"> <strong>[\u89e3\u7b54]<\/strong><\/span><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2^+} \\left(\\dfrac{x}{x+1} \\right) \\left(\\dfrac{2x+5}{x^2+x} \\right)<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1058s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u7b54]<\/strong><\/span><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 1^-} \\left(\\dfrac{1}{x+1} \\right) \\left(\\dfrac{x+6}{x} \\right) \\left(\\dfrac{3-x}{x} \\right) <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1102s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u7b54]<\/strong><\/span><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{h\\to 0^+ } \\dfrac{\\sqrt{h^2 + 4h +5} - \\sqrt{5}}{h} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1168s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u7b54]<\/strong><\/span><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{h\\to 0^-} \\dfrac{\\sqrt{6} - \\sqrt{5h^2 + 11h +6}}{h}<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1276s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li>\n<table>\n<tbody>\n<tr style=\"text-align: justify;\">\n<td>a. <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -2^+} (x+3)\\dfrac{|x+2|}{x+2}\n\n<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>b. <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -2^-} (x+3)\\dfrac{|x+2|}{x+2}\n\n<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1378s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li>\n<table>\n<tbody>\n<tr style=\"text-align: justify;\">\n<td>a. <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 1^+} \\dfrac{\\sqrt{2x}(x-1)}{|x-1|}\n\n<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>b. <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 1^-}\\dfrac{\\sqrt{2x}(x-1)}{|x-1|}\n\n<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1655s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u5355\u4fa7\u6781\u9650\uff1a\u5b9a\u4e49\u3001\u53d1\u5c55\u4e0e\u7ec3\u4e60 \u6458\u8981\uff1a \u672c\u6587\u89e3\u91ca\u4e86\u5fae\u79ef\u5206\u4e2d\u7684\u5355\u4fa7\u6781\u9650\u548c\u53cc\u4fa7\u6781\u9650\uff0c\u5c55\u793a\u4e86\u5b83\u4eec\u5982\u4f55\u76f4\u89c2\u5730\u548c\u5f62\u5f0f\u5316\u5730\u5b9a\u4e49\u548c\u5e94\u7528\u3002\u672c\u6587\u63d0\u4f9b\u4e86\u56fe\u5f62\u548c\u4ee3\u6570\u793a\u4f8b\uff0c\u8ba8\u8bba\u4e86\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\u4f7f\u7528\u6781\u9650\u4ee3\u6570\u7684\u6761\u4ef6\uff0c\u5e76\u5305\u542b\u4e86\u89e3\u7b54\u7ec3\u4e60\uff0c\u4ee5\u52a0\u5f3a\u7406\u89e3\u3002\u672c\u6587\u65e8\u5728\u63d0\u4f9b\u5bf9\u8fd9\u4e9b\u5fae\u79ef\u5206\u57fa\u7840\u6982\u5ff5\u7684\u6e05\u6670\u7b80\u660e\u7684\u7406\u89e3\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5728\u672c\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u7406\u89e3\u5355\u4fa7\u6781\u9650\u548c\u53cc\u4fa7\u6781\u9650\u4e4b\u95f4\u7684\u533a\u522b\u3002 \u6b63\u5f0f\u5b9a\u4e49\u53f3\u4fa7\u548c\u5de6\u4fa7\u7684\u5355\u4fa7\u6781\u9650\u3002 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[&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27972,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":42,"footnotes":""},"categories":[858,575],"tags":[],"class_list":["post-27980","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-858","category-575"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u5355\u4fa7\u6781\u9650\uff1a\u5b9a\u4e49\u3001\u53d1\u5c55\u4e0e\u7ec3\u4e60 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u8be6\u7ec6\u89e3\u91ca\u5355\u4fa7\u6781\u9650\u548c\u53cc\u4fa7\u6781\u9650\uff0c\u5305\u542b\u6b63\u5f0f\u5b9a\u4e49\u3001\u5b9e\u9645\u4f8b\u5b50\u548c\u89e3\u7b54\u7ec3\u4e60\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link 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