{"id":10383,"date":"2023-07-17T23:55:19","date_gmt":"2023-07-17T15:55:19","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=10383"},"modified":"2025-04-06T22:12:55","modified_gmt":"2025-04-06T14:12:55","slug":"%e6%b1%82%e6%9e%81%e9%99%90%e7%9a%84%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=10383","title":{"rendered":"\u6781\u9650"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_83 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#1_%E6%9E%81%E9%99%90%E6%80%A7%E8%B4%A8\" >1 \u6781\u9650\u6027\u8d28<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#11_%E6%9C%89%E7%95%8C%E6%80%A7\" >1.1 \u6709\u754c\u6027<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#111_%E6%95%B0%E5%88%97\" >1.1.1 \u6570\u5217<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#112_%E5%87%BD%E6%95%B0\" >1.1.2 \u51fd\u6570<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#12_%E4%BF%9D%E5%8F%B7%E6%80%A7\" >1.2 \u4fdd\u53f7\u6027<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#121_%E6%95%B0%E5%88%97\" >1.2.1 \u6570\u5217<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#122_%E5%87%BD%E6%95%B0\" >1.2.2 \u51fd\u6570<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#2_%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90%E7%9A%84%E5%85%B3%E7%B3%BB\" >2 \u51fd\u6570\u6781\u9650\u548c\u6570\u5217\u6781\u9650\u7684\u5173\u7cfb<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#21_%E6%B5%B7%E6%B6%85%E5%AE%9A%E7%90%86\" >2.1 \u6d77\u6d85\u5b9a\u7406<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#3_%E6%9E%81%E9%99%90%E8%AE%A1%E7%AE%97\" >3 \u6781\u9650\u8ba1\u7b97<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#31_%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97\" >3.1 \u56db\u5219\u8fd0\u7b97<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#32_%E9%87%8D%E8%A6%81%E6%9E%81%E9%99%90%E5%92%8C%E7%AD%89%E4%BB%B7%E6%97%A0%E7%A9%B7%E5%B0%8F\" >3.2 \u91cd\u8981\u6781\u9650\u548c\u7b49\u4ef7\u65e0\u7a77\u5c0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#33_%E6%B4%9B%E5%BF%85%E8%BE%BE%E6%B3%95%E5%88%99\" >3.3 \u6d1b\u5fc5\u8fbe\u6cd5\u5219<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#%E6%8E%A8%E5%B9%BF\" >\u63a8\u5e7f<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#34_%E5%A4%B9%E9%80%BC%E5%87%86%E5%88%99\" >3.4 \u5939\u903c\u51c6\u5219<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#35_%E5%8D%95%E8%B0%83%E6%9C%89%E7%95%8C%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90%E5%87%86%E5%88%99\" >3.5 \u5355\u8c03\u6709\u754c\u6570\u5217\u6781\u9650\u51c6\u5219<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#36_%E6%97%A0%E7%A9%B7%E5%B0%8F%E6%80%A7%E8%B4%A8\" >3.6 \u65e0\u7a77\u5c0f\u6027\u8d28<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#37_%E5%87%BD%E6%95%B0%E7%9A%84%E8%BF%9E%E7%BB%AD%E6%80%A7\" >3.7 \u51fd\u6570\u7684\u8fde\u7eed\u6027<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#38_%E6%B3%B0%E5%8B%92%E5%85%AC%E5%BC%8F\" >3.8 \u6cf0\u52d2\u516c\u5f0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/blog.iyatt.com\/?p=10383\/#39_%E5%AF%BC%E6%95%B0%E5%AE%9A%E4%B9%89\" >3.9 \u5bfc\u6570\u5b9a\u4e49<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"1_%E6%9E%81%E9%99%90%E6%80%A7%E8%B4%A8\"><\/span>1 \u6781\u9650\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"11_%E6%9C%89%E7%95%8C%E6%80%A7\"><\/span>1.1 \u6709\u754c\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"111_%E6%95%B0%E5%88%97\"><\/span>1.1.1 \u6570\u5217<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5982\u679c\u6570\u5217<code class=\"katex-inline\">\\{x_n\\}<\/code>\u6536\u655b\uff0c\u90a3\u4e48\u6570\u5217<code class=\"katex-inline\">\\{x_n\\}<\/code>\u4e00\u5b9a\u6709\u754c\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"112_%E5%87%BD%E6%95%B0\"><\/span>1.1.2 \u51fd\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u82e5<code class=\"katex-inline\">\\lim_{x\\to x_0}f(x)<\/code>\u5b58\u5728\uff0c\u5219<code>f(x)<\/code>\u5728<code class=\"katex-inline\">x_0<\/code>\u7684\u67d0\u53bb\u5fc3\u90bb\u57df\u6709\u754c\uff08\u5c40\u90e8\u6709\u754c\uff09\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"12_%E4%BF%9D%E5%8F%B7%E6%80%A7\"><\/span>1.2 \u4fdd\u53f7\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"121_%E6%95%B0%E5%88%97\"><\/span>1.2.1 \u6570\u5217<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u8bbe<code class=\"katex-inline\">\\lim_{n\\to\\infty}x_n=A<\/code><br \/>\n\u5982\u679c<code class=\"katex-inline\">A\\gt0<\/code>\u6216<code class=\"katex-inline\">A\\lt0<\/code>\uff0c\u5219<code class=\"katex-inline\">\\exists N\\gt0<\/code>\uff0c\u5f53<code class=\"katex-inline\">n\\gt N<\/code>\u65f6\uff0c<code class=\"katex-inline\">x_n\\gt0<\/code>\u6216<code class=\"katex-inline\">x_n\\lt0<\/code>\u3002<br \/>\n\u5982\u679c<code class=\"katex-inline\">\\exists N\\gt0<\/code>\uff0c<code class=\"katex-inline\">n\\gt N<\/code>\u65f6\uff0c<code class=\"katex-inline\">x_n\\ge0<\/code>\u6216<code class=\"katex-inline\">x_n\\le0<\/code>\uff0c\u5219<code class=\"katex-inline\">A\\ge0<\/code>\u6216<code class=\"katex-inline\">A\\le0<\/code>\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"122_%E5%87%BD%E6%95%B0\"><\/span>1.2.2 \u51fd\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u8bbe<code class=\"katex-inline\">\\lim_{x\\to x_0}f(x)=A<\/code><br \/>\n\u5982\u679c<code class=\"katex-inline\">A\\gt0<\/code>\u6216<code class=\"katex-inline\">A\\lt0<\/code>\uff0c\u5219<code class=\"katex-inline\">\\exists\\delta\\gt0<\/code>\uff0c\u5f53<code class=\"katex-inline\">x\\in\\mathring{U}(x_0,\\delta)<\/code>\u65f6\uff0c<code class=\"katex-inline\">f(x)\\gt0<\/code>\u6216<code class=\"katex-inline\">f(x)\\lt0<\/code>\u3002<br \/>\n\u5982\u679c<code class=\"katex-inline\">\\exists\\delta\\gt0<\/code>\uff0c\u5f53<code class=\"katex-inline\">x\\in\\mathring{U}(x_0,\\delta)<\/code>\u65f6\uff0c<code class=\"katex-inline\">f(x)\\ge0<\/code>\u6216<code class=\"katex-inline\">f(x)\\le0<\/code>\uff0c\u90a3\u4e48<code class=\"katex-inline\">A\\ge0<\/code>\u6216<code class=\"katex-inline\">A\\le0<\/code>\u3002<\/p>\n<h1><span class=\"ez-toc-section\" id=\"2_%E5%87%BD%E6%95%B0%E6%9E%81%E9%99%90%E5%92%8C%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90%E7%9A%84%E5%85%B3%E7%B3%BB\"><\/span>2 \u51fd\u6570\u6781\u9650\u548c\u6570\u5217\u6781\u9650\u7684\u5173\u7cfb<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"21_%E6%B5%B7%E6%B6%85%E5%AE%9A%E7%90%86\"><\/span>2.1 \u6d77\u6d85\u5b9a\u7406<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u82e5<code class=\"katex-inline\">\\lim_{x\\to x_0}f(x)=A<\/code>\uff0c\u5219\u5bf9\u4efb\u610f\u6570\u5217<code class=\"katex-inline\">\\{x_n\\}<\/code>\uff0c<code class=\"katex-inline\">\\lim_{n\\to\\infty}x_n=x_0<\/code>\uff0c\u4e14<code class=\"katex-inline\">x_n\\ne=x_0<\/code>\uff0c\u90fd\u6709<code class=\"katex-inline\">\\lim_{n\\to\\infty}f(x_n)=A<\/code><\/p>\n<h1><span class=\"ez-toc-section\" id=\"3_%E6%9E%81%E9%99%90%E8%AE%A1%E7%AE%97\"><\/span>3 \u6781\u9650\u8ba1\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"31_%E5%9B%9B%E5%88%99%E8%BF%90%E7%AE%97\"><\/span>3.1 \u56db\u5219\u8fd0\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u82e5<code class=\"katex-inline\">\\lim f(x)=a\uff0c\\lim g(x)=b<\/code>\uff0c\u5219<br \/>\n(1) <code class=\"katex-inline\">\\lim[f(x)\\pm g(x)]=\\lim f(x)\\pm \\lim g(x)=a\\pm b<\/code><br \/>\n(2) <code class=\"katex-inline\">\\lim[f(x)g(x)]=\\lim f(x) \\cdot\\lim g(x)=ab<\/code><br \/>\n(3) <code class=\"katex-inline\">\\lim\\frac{f(x)}{g(x)}=\\frac{\\lim f(x)}{\\lim g(x)}=\\frac{a}{b}\\ (b\\ne0)<\/code><\/p>\n<p>\u63a8\u8bba<br \/>\n(1) <code class=\"katex-inline\">\\lim cf(x)=c\\lim f(x)=ca\\ (c\u4e3a\u5e38\u6570)<\/code><br \/>\n(2) <code class=\"katex-inline\">\\lim [f(x)]^n=[\\lim f(x)]^n=a^n\\ (n\u4e3a\u6b63\u6574\u6570)<\/code><\/p>\n<p>\u6ce8<br \/>\n(1) <code class=\"katex-inline\">\u5b58\u5728\\pm\u4e0d\u5b58\u5728=\u4e0d\u5b58\u5728<\/code><br \/>\n(2) <code class=\"katex-inline\">\u4e0d\u5b58\u5728\\pm\u4e0d\u5b58\u5728=\u4e0d\u4e00\u5b9a<\/code><br \/>\n(3) <code class=\"katex-inline\">\u5b58\u5728\\times(\\div)\u4e0d\u5b58\u5728=\u4e0d\u4e00\u5b9a<\/code><br \/>\n(4) <code class=\"katex-inline\">\u4e0d\u5b58\u5728\\times(\\div)\u4e0d\u5b58\u5728=\u4e0d\u4e00\u5b9a<\/code><\/p>\n<h2><span class=\"ez-toc-section\" id=\"32_%E9%87%8D%E8%A6%81%E6%9E%81%E9%99%90%E5%92%8C%E7%AD%89%E4%BB%B7%E6%97%A0%E7%A9%B7%E5%B0%8F\"><\/span>3.2 \u91cd\u8981\u6781\u9650\u548c\u7b49\u4ef7\u65e0\u7a77\u5c0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7b49\u4ef7\u65e0\u7a77\u5c0f\u66ff\u6362\u5b9a\u7406\uff1a<br \/>\n\u8bbe<code class=\"katex-inline\">f_1(x)\\sim f_2(x)\uff0cg_1(x)\\sim g_2(x)\uff0c\u4e14\\lim\\frac{f_2(x)}{g_2(x)}\u5b58\u5728\uff0c\u5219 \\\\ \\lim\\frac{f_1(x)}{g_1(x)}=\\lim\\frac{f_2(x)}{g_2(x)}=(\u63a8\u5e7f)\\lim\\frac{f_1(x)}{g_2(x)}=\\lim\\frac{f_2(x)}{g_1(x)}<\/code><\/p>\n<p>\u548c\u5dee\u5173\u7cfb\u5728\u6ee1\u8db3\u4e00\u5b9a\u6761\u4ef6\u4e0b\u53ef\u4ee5\u4f5c\u7b49\u4ef7\u66ff\u6362<br \/>\n(1) <code class=\"katex-inline\">\u82e5\\lim\\frac{f_1(x)}{g_1(x)}\\ne1\uff0c\u5219\\lim[f_1(x)-g_1(x)]=\\lim[f_2(x)-g_2(x)]<\/code><br \/>\n(2) <code class=\"katex-inline\">\u82e5\\lim\\frac{f_1(x)}{g_2(x)}\\ne-1\uff0c\u5219\\lim[f_1(x)+g_1(x)]=\\lim[f_2(x)+g_2(x)]<\/code><\/p>\n<p>\u5e38\u89c1\u7b49\u4ef7\u65e0\u7a77\u5c0f\u548c\u91cd\u8981\u6781\u9650\u8be6\u89c1\uff1a<a href=\"https:\/\/blog.iyatt.com\/?p=10351\">https:\/\/blog.iyatt.com\/?p=10351<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"33_%E6%B4%9B%E5%BF%85%E8%BE%BE%E6%B3%95%E5%88%99\"><\/span>3.3 \u6d1b\u5fc5\u8fbe\u6cd5\u5219<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u82e5<br \/>\n(1) <code class=\"katex-inline\">\\lim_{x\\rightarrow x_0}f(x)=\\lim_{x\\rightarrow x_0}f(x)=0\uff08\u6216\\infty\uff09<\/code><br \/>\n(2) <code class=\"katex-inline\">f(x)\u548cg(x)\u5728x_0\u7684\u67d0\u53bb\u5fc3\u90bb\u57df\u5185\u53ef\u5bfc\uff0c\u4e14g'(x)\\ne0<\/code><br \/>\n(3) <code class=\"katex-inline\">\\lim\\frac{f'(x)}{g'(x)}\u5b58\u5728<\/code><br \/>\n\u5219<br \/>\n<code class=\"katex-inline\">\\lim_{x\\rightarrow x_0}\\frac{f(x)}{g(x)}=\\lim_{x\\rightarrow x_0}\\frac{f'(x)}{g'(x)}<\/code><\/p>\n<p>\u4e00\u822c\u7528\u4e8e<code class=\"katex-inline\">\\frac{0}{0}\u3001\\frac{\\infty}{\\infty}\u3001\\infty\\pm\\infty\u30010\\cdot\\infty\u30011^\\infty\u3001\\infty^0\u30010^0<\/code>\uff0c\u524d\u4e24\u79cd\u76f4\u63a5\u4f7f\u7528\uff0c\u540e\u4e94\u79cd\u5316\u4e3a\u524d\u4e24\u79cd<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E6%8E%A8%E5%B9%BF\"><\/span>\u63a8\u5e7f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u53ea\u8981\u5206\u6bcd\u8d8b\u8fd1\u4e8e\u65e0\u7a77\uff0c\u4e14\u5206\u6bcd\u5bfc\u6570\u4e0d\u4e3a 0\uff0c\u5219\u540c\u6837\u53ef\u7528<\/p>\n<h2><span class=\"ez-toc-section\" id=\"34_%E5%A4%B9%E9%80%BC%E5%87%86%E5%88%99\"><\/span>3.4 \u5939\u903c\u51c6\u5219<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u82e5\u51fd\u6570f(x)\u3001g(x)\u3001h(x)\u6ee1\u8db3\uff1a<br \/>\n(1) <code class=\"katex-inline\">g(x)\\le f(x)\\le h(x)<\/code><br \/>\n(2) <code class=\"katex-inline\">\\lim_{x\\rightarrow x_0}g(x)=\\lim_{x\\rightarrow x_0}h(x)=A<\/code><br \/>\n\u5219<br \/>\n<code class=\"katex-inline\">\\lim_{x\\rightarrow x_0}f(x)=A<\/code><\/p>\n<h2><span class=\"ez-toc-section\" id=\"35_%E5%8D%95%E8%B0%83%E6%9C%89%E7%95%8C%E6%95%B0%E5%88%97%E6%9E%81%E9%99%90%E5%87%86%E5%88%99\"><\/span>3.5 \u5355\u8c03\u6709\u754c\u6570\u5217\u6781\u9650\u51c6\u5219<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5355\u8c03\u6709\u754c\u6570\u5217\u5fc5\u6709\u6781\u9650<\/p>\n<p>\u4e00\u822c\u65b9\u6cd5\uff1a<br \/>\n(1) \u8bc1\u660e\u6570\u5217\u5355\u8c03\u6709\u754c\uff08\u591a\u7528\u5f52\u7eb3\u6cd5\uff09<br \/>\n(2) \u4ee4<code class=\"katex-inline\">\\lim_{x\\rightarrow\\infty}x_n=a<\/code>\uff0c\u5bf9\u7ed9\u5b9a\u7684\u5173\u7cfb\u5f0f\u4e24\u8fb9\u6c42\u6781\u9650\uff0c\u89e3\u51fa a<\/p>\n<h2><span class=\"ez-toc-section\" id=\"36_%E6%97%A0%E7%A9%B7%E5%B0%8F%E6%80%A7%E8%B4%A8\"><\/span>3.6 \u65e0\u7a77\u5c0f\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u65e0\u7a77\u5c0f\u548c\u6709\u754c\u91cf\u4e58\u79ef\u4ecd\u4e3a\u65e0\u7a77\u5c0f<\/p>\n<h2><span class=\"ez-toc-section\" id=\"37_%E5%87%BD%E6%95%B0%E7%9A%84%E8%BF%9E%E7%BB%AD%E6%80%A7\"><\/span>3.7 \u51fd\u6570\u7684\u8fde\u7eed\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>(1) <code class=\"katex-inline\">\u82e5f(x)\u5728x=x_0\u70b9\u8fde\u7eed\uff0c\u5219\\lim_{x\\rightarrow x_0}f(x)=f(x_0\uff09<\/code><br \/>\n(2) <code class=\"katex-inline\">\u82e5f(x)\uff0c\\phi(x)\u4e3a\u8fde\u7eed\u51fd\u6570\uff0c\u5219\\lim_{x\\rightarrow x_0}f[\\phi(x)]=f[\\lim_{x\\rightarrow x_0]}\\phi(x)]<\/code><br \/>\n(3) <code class=\"katex-inline\">\u82e5\\lim f(x)=A>0\uff0c\\lim g(x)=B\uff0c\u5219 \\\\ \\lim f(x)^{g(x)}=[lim f(x)]^{\\lim g(x)}=A^B<\/code><\/p>\n<h2><span class=\"ez-toc-section\" id=\"38_%E6%B3%B0%E5%8B%92%E5%85%AC%E5%BC%8F\"><\/span>3.8 \u6cf0\u52d2\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8be6\u89c1\uff1a<a href=\"https:\/\/blog.iyatt.com\/?p=10375\">https:\/\/blog.iyatt.com\/?p=10375<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"39_%E5%AF%BC%E6%95%B0%E5%AE%9A%E4%B9%89\"><\/span>3.9 \u5bfc\u6570\u5b9a\u4e49<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>(1) <code class=\"katex-inline\">\\lim_{\\Delta x\\to0}\\frac{f(x_0+a\\Delta x)-f(x_0)}{\\Delta x}=a\\lim_{\\Delta x\\to0}\\frac{f(x_0+a\\Delta x)-f(x_0)}{a\\Delta x}=af'(x_0)<\/code><br \/>\n(2) <code class=\"katex-inline\">\\lim_{\\Delta x\\to0}\\frac{f(x_0)-f(x_0+b\\Delta x)}{\\Delta x}=-b\\lim_{\\Delta x\\to0}\\frac{f(x_0+b\\Delta x)-f(x_0)}{b\\Delta x}=-bf'(x_0)<\/code><br \/>\n(3) <code class=\"katex-inline\">\\lim_{\\Delta x\\to0}\\frac{f(x_0+a\\Delta x)-f(x_0+b\\Delta x)}{\\Delta x}=\\lim_{\\Delta x\\to0}\\frac{[f(x_0+a\\Delta x)-f(x_0)]-[f(x_0+b\\Delta x)-f(x_0)]}{\\Delta x}=a\\lim_{\\Delta x\\to0}\\frac{f(x_0+a\\Delta x)-f(x_0)}{a\\Delta x}-b\\lim_{\\Delta x\\to0}\\frac{f(x_0+b\\Delta x)-f(x_0)}{b\\Delta x}=(a-b)f'(x_0)<\/code><\/p>\n","protected":false},"excerpt":{"rendered":"<p>1 \u6781\u9650\u6027\u8d28 1.1 \u6709\u754c\u6027 1.1.1 \u6570\u5217 \u5982\u679c\u6570\u5217\\{x_n\\}\u6536\u655b\uff0c\u90a3\u4e48\u6570\u5217\\{x_n\\}\u4e00\u5b9a\u6709\u754c\u3002  [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"_lmt_disableupdate":"no","_lmt_disable":"no","footnotes":""},"categories":[1,612],"tags":[],"class_list":["post-10383","post","type-post","status-publish","format-standard","hentry","category-all","category-612"],"modified_by":"IYATT-yx","_links":{"self":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/10383","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10383"}],"version-history":[{"count":1,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/10383\/revisions"}],"predecessor-version":[{"id":19832,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/10383\/revisions\/19832"}],"wp:attachment":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}