{"id":10351,"date":"2023-07-04T01:35:02","date_gmt":"2023-07-03T17:35:02","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=10351"},"modified":"2025-03-26T12:24:39","modified_gmt":"2025-03-26T04:24:39","slug":"%e5%b8%b8%e8%a7%81%e7%ad%89%e4%bb%b7%e6%97%a0%e7%a9%b7%e5%b0%8f%e5%92%8c%e9%87%8d%e8%a6%81%e6%9e%81%e9%99%90","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=10351","title":{"rendered":"\u5e38\u89c1\u7b49\u4ef7\u65e0\u7a77\u5c0f\u548c\u91cd\u8981\u6781\u9650"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 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-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.iyatt.com\/?p=10351\/#%E5%B8%B8%E8%A7%81%E7%AD%89%E4%BB%B7%E6%97%A0%E7%A9%B7%E5%B0%8F\" >\u5e38\u89c1\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-2\" href=\"https:\/\/blog.iyatt.com\/?p=10351\/#%E9%87%8D%E8%A6%81%E6%9E%81%E9%99%90\" >\u91cd\u8981\u6781\u9650<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E5%B8%B8%E8%A7%81%E7%AD%89%E4%BB%B7%E6%97%A0%E7%A9%B7%E5%B0%8F\"><\/span>\u5e38\u89c1\u7b49\u4ef7\u65e0\u7a77\u5c0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5f53 <code class=\"katex-inline\">x\\rightarrow0<\/code> \u65f6<\/p>\n<p><code class=\"katex-inline\">\\sin x\\sim \\arcsin x\\sim \\tan x \\sim \\arctan x \\sim \\ln(1+x) \\sim e^x-1 \\sim x<\/code><br \/>\n<code class=\"katex-inline\">a^x-1\\sim x\\ln a<\/code><br \/>\n<code class=\"katex-inline\">(1+x)^a-1\\sim ax<\/code><br \/>\n<code class=\"katex-inline\">1-\\cos^ax\\sim \\frac{a}{2}x^2<\/code><br \/>\n<code class=\"katex-inline\">x-\\sin x\\sim \\frac{1}{6}x^3<\/code><br \/>\n<code class=\"katex-inline\">x-\\arcsin x \\sim -\\frac{1}{6}x^3<\/code><br \/>\n<code class=\"katex-inline\">x-\\tan x\\sim -\\frac{1}{3}x^3<\/code><br \/>\n<code class=\"katex-inline\">x-\\arctan x\\sim \\frac{1}{3}x^3<\/code><br \/>\n<code class=\"katex-inline\">x-\\ln(1+x)\\sim\\frac{1}{2}x^2<\/code><br \/>\n<code class=\"katex-inline\">\\tan x - \\sin x=\\frac{1}{2}x^3<\/code><br \/>\n<code class=\"katex-inline\">\\arctan x - \\arcsin x=-\\frac{1}{2}x^3<\/code><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E9%87%8D%E8%A6%81%E6%9E%81%E9%99%90\"><\/span>\u91cd\u8981\u6781\u9650<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><code class=\"katex-inline\">\\lim_{x\\to0}\\frac{sinx}{x}=1<\/code><br \/>\n<code class=\"katex-inline\">\\lim_{x\\to0}(1+x)^\\frac{1}{x}=e<\/code><\/p>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\Rightarrow\n\\lim_{x\\rightarrow0}(1+ax)^\\frac{b}{x}=e^{ab} \\\\\n\\Rightarrow\n\\lim_{x\\rightarrow\\infty}(1+\\frac{a}{x})^{bx}=e^{ab} \\\\\n\\Rightarrow\n\u82e5\\lim\\alpha(x)=0\uff0c\\lim\\beta(x)=\\infty\uff0c\u4e14\\lim\\alpha(x)\\beta(x)=A \\\\\n\u5219\u6709\\lim[1+\\alpha(x)]^{\\beta(x)}=e^A\n\\end{array}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u5e38\u89c1\u7b49\u4ef7\u65e0\u7a77\u5c0f \u5f53 x\\rightarrow0 \u65f6 \\sin x\\sim \\arcsin x\\sim \\tan [&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-10351","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\/10351","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=10351"}],"version-history":[{"count":1,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/10351\/revisions"}],"predecessor-version":[{"id":19699,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/10351\/revisions\/19699"}],"wp:attachment":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10351"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10351"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}