https://cn-sunisalex-pages.zh-cn.edgeone.cool/tags/%E5%B8%B8%E7%94%A8%E6%8A%80%E5%B7%A7/Recent content in 常用技巧 on ∇Alex的实验室Hugozh-CNThu, 05 Mar 2026 20:54:13 +0800https://cn-sunisalex-pages.zh-cn.edgeone.cool/posts/math/lnx-approximation/Thu, 05 Mar 2026 20:54:13 +0800https://cn-sunisalex-pages.zh-cn.edgeone.cool/posts/math/lnx-approximation/<h1 id="泰勒展开">泰勒展开</h1> <p><span class="math math-inline"> $ \ln (1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \cdots + (-1)^{n-1} \frac{x^n}{n} + o(x^n) $ </span> 需要注意的是,此公式具有收敛半径<span class="math math-inline"> $R=1$ </span>,仅适用于<span class="math math-inline"> $x\approx 0$ </span>的情况.</p> <p>具体内容,可以见<a href="https://www.sunisalex.org/posts/math/taylor-expansion/">浅谈泰勒展开与高考数学</a>.</p> <h1 id="帕德逼近">帕德逼近(※)</h1> <p>以下是<a href="https://zh.wikipedia.org/zh-sg/%E5%B8%95%E5%BE%B7%E8%BF%91%E4%BC%BC">维基百科</a>给出的简介,这里不加赘述. <figure class="img-wrapper"> <a href="https://cn-sunisalex-pages.zh-cn.edgeone.cool/posts/math/lnx-approximation/AgACAgEAAyEGAATlvtEQAAMeaal9j4ifvzXpCZbNC-5wPK-cSREAAukLaxuKrkhFJmRRegg0MOEBAAMCAAN3AAM6BA.png" target="_blank" rel="noopener"> <div class="loading-spinner"></div> <img alt="图片" loading="lazy" src="https://cn-sunisalex-pages.zh-cn.edgeone.cool/posts/math/lnx-approximation/AgACAgEAAyEGAATlvtEQAAMeaal9j4ifvzXpCZbNC-5wPK-cSREAAukLaxuKrkhFJmRRegg0MOEBAAMCAAN3AAM6BA.png"style="opacity: 0; transition: opacity 0.4s ease;" onload="this.style.opacity='1'; if (this.previousElementSibling &amp;&amp; this.previousElementSibling.classList.contains('loading-spinner')) { this.previousElementSibling.style.display='none'; }"> </a></figure> </p>