From f2a840ed742bc2c32ebf961359281e00279dd5a2 Mon Sep 17 00:00:00 2001 From: Didnelpsun <2675350965@qq.com> Date: Tue, 16 Aug 2022 23:02:34 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- advanced-math/exercise/1-limit/limit.pdf | Bin 188192 -> 190485 bytes advanced-math/exercise/1-limit/limit.tex | 8 +++++++- 2 files changed, 7 insertions(+), 1 deletion(-) diff --git a/advanced-math/exercise/1-limit/limit.pdf b/advanced-math/exercise/1-limit/limit.pdf index d176d0be503a31bebb714cfde68abbddd568e50a..ca87f01849eff26424219c89d508326492e5a4b7 100644 GIT binary patch delta 139968 zcmY(KLwGJsw5(%e$F^|p+G-ek(fZL$9ez57PvCJ!?^i!$gpMg&d->Hxp5xe+2zm*;!_ zHDHdV8z{Doa@|4QKtm7h4lTi&`;31|RDMzjft4BA5dJ)q>Uo`@jEny_quTV(_x&6i5jox_asK zTIBKh6&1bv0psi$dL2_?d;!$X&o93qqdT^@pnu1uwV{ViF(j8gM&m&j zYB#}&75+#p+5>?T`eQ~%{oNwHX9$8hoUgl34dy}fVGX#- zqgZk7QzyGDEZvLN-|)8%iU|zUR?xy%OhDnt{`;%JvUsFqV`i=3V4xiUj#c2J($Pc$ 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对于无法直接得出变换式子的,可以对对应参数进行凑,以达到目标的可替换的等价无穷小。 @@ -371,6 +371,10 @@ $=-1+\lim\limits_{x\to 0}\dfrac{-\dfrac{1}{2}(\cos 2x-1)+\sqrt{\cos 2x}(1-\sqrt[ $=-1+\lim\limits_{x\to 0}\dfrac{-\dfrac{1}{2}(-\dfrac{4x^2}{2})+\left(-\dfrac{1}{3}\right)\left(-\dfrac{9x^2}{2}\right)}{-\dfrac{x^2}{2}}=-6$ +\subsection{脱帽法} + +即函数中有$f(x)$,且$f(x)$无法转换出常数项。则将$f(x)$利用已知的极限值转换为一个函数加上高阶无穷小的形式。 + \section{极限计算形式} 极限相关计算形式主要分为下面六种: @@ -505,6 +509,8 @@ $\therefore a=1;b=-\dfrac{5}{2}$。 \subsubsection{无穷小} +求无穷小阶数时,注意低阶吸收高阶,即面对多项式的无穷小,其阶数为幂次最低的那个,逼近0速度最慢的那个的阶数。 + \paragraph{等价无穷小} \leavevmode \medskip 等价无穷小一般不会使用$\lim\dfrac{f(x)}{g(x)}=1$的方式来求参数,而是直接求没有参数的极限,然后对比求出参数。

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