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a/advanced-math/knowledge/3-applications-of-derivatives/applications-of-derivatives.tex +++ b/advanced-math/knowledge/3-applications-of-derivatives/applications-of-derivatives.tex @@ -127,6 +127,8 @@ $\text{罗尔定理}\xrightleftharpoons[\text{特例:}f(a)=f(b)]{\text{泛化 \section{洛必达法则} +\subsection{定理} + 若当$x\to a$或$x\to\infty$时两个函数$f(x)F(x)$都趋向0或无穷大,那么极限$\lim\limits_{x\to \frac{a}{\infty}}\dfrac{f(x)}{F(x)}$可能存在,也可能不存在,这种极限就是不定式。\medskip \textcolor{aqua}{\textbf{定理:}} @@ -138,7 +140,7 @@ $\text{罗尔定理}\xrightleftharpoons[\text{特例:}f(a)=f(b)]{\text{泛化 \item $\lim\limits_{x\to a}\dfrac{f(x)}{g(x)}=\lim\limits_{x\to a}\dfrac{f'(x)}{g'(x)}$或$\lim\limits_{x\to\infty}\dfrac{f(x)}{g(x)}=\lim\limits_{x\to\infty}\dfrac{f'(x)}{g'(x)}$。 \end{enumerate} -\textcolor{orange}{注意:} +\subsection{注意事项} \begin{enumerate} \item 如果函数比值不为$\dfrac{0}{0}$或$\dfrac{\infty}{\infty}$型,则不能使用洛必达法则。