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a/advanced-math/exercise/1-limit/limit.tex +++ b/advanced-math/exercise/1-limit/limit.tex @@ -132,6 +132,8 @@ $\therefore\lim\limits_{n\to\infty}n^2\left(\arctan\dfrac{2}{n}-\arctan\dfrac{2} 且一般只有麦克劳林公式表上的基本初等函数才会使用倒泰勒公式,复合函数最好不要使用。 +一般遇到$0-0$型会用到这个公式,其他方式没办法解出。 + \textbf{例题:}求极限$\lim\limits_{x\to 0}\dfrac{\arcsin x-\arctan x}{\sin x-\tan x}$。\medskip 分析:该题目使用洛必达法则会比较麻烦且难以计算,所以先考虑是否能用泰勒展开。