LaTeX Templates Nội dung sách tuyệt đẹp 1

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%%%%%%%%%%%%%%%%%%%
\begin{document}
 \tableofcontents
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{\chap\chapter{Les fonctions logarithmiques} 
 \vspace*{-1cm}
 \begin{mybox}{{\large  Logarithme Népérien : $\ln$}}
 \begin{boite}{Définition}
 \begin{itemize}
 \item [\bccrayon] 
 Le logarithme népérien est la primitive de la fonction $ x \mapsto \frac{1}{x}$  sur l'intervalle $] 0,+\infty[$ et qui s'annule en $ 1$ . On la note $ \ln$ .
 \end{itemize} 
 \end{boite}
 \begin{boite}{Conséquences}
 \begin{itemize} 
 \item [\bclampe]$\text { Le domaine de définition de } \ln \text { est }] 0,+\infty[. \qquad\ln (1)=0$
 \item [\bclampe] $\ln \text { est une fonction dérivable sur } ] 0,+\infty[\text { et on a : } \quad(\forall x \in] 0,+\infty[): \ln ^{\prime}(x)=\frac{1}{x}. $
 \item [\bclampe]$\ln \text { est strictement croissante sur }] 0,+\infty[$. 
 \item [\bclampe] $\text { Pour tous } a \text { et } b \text { de }] 0,+\infty[: \quad a<b \Longleftrightarrow \ln (a)<\ln (b)$
 \item [\bclampe] $\begin{array}{lcc}\star \text { Pour tous } a \text { et } b \text { de }] 0,+\infty[: & a<b \Longleftrightarrow \ln (a)<\ln (b) & \ln (a)=\ln (b) \Leftrightarrow a=b . \\ \star \ln (x)=0 \Leftrightarrow x=1 & \ln (x)>0 \Leftrightarrow x>1 & \ln (x)<0 \Leftrightarrow 0<x<1 .\end{array}$
 \end{itemize} 
 \end{boite}
 \begin{boite}{Une proprièté fondamentale :}
 Pour tous $a$ et $b$ de $]0,+\infty[$ : $\ln(ab) = \ln(a) + \ln(b).$
 \end{boite}
 \begin{boite}{Proposition}
 Pour tous $a$ et $b$ de $] 0,+\infty[$ et $r \in \mathbb{Q}$ on a :
 {\small  $
 \begin{array}{ll}
 \bcplume \ln \left(\frac{1}{a}\right)=-\ln (a) & \bcplume \ln \left(\frac{a}{b}\right)=\ln (a)-\ln (b) \\
 \bcplume \ln (\sqrt{a})=\frac{1}{2} \ln (a) & \bcplume \ln \left(a^{r}\right)=r \ln (a)
 \end{array}
 $}
 \end{boite}
 \begin{boite}{Proposition:Limites Fondamentales}
 $\begin{array}{lll}
 {\tiny \bcetoile } \lim _{x \rightarrow+\infty} \ln (x)=+\infty & \bcetoile \lim _{x \rightarrow 0^{+}} \ln (x)=-\infty & \bcetoile \lim _{x \rightarrow 1} \frac{\ln (x)}{x-1}=1 \\
 \bcetoile \lim _{x \rightarrow 0} \frac{\ln (1+x)}{x}=1 & \bcetoile \lim _{x \rightarrow+\infty} \frac{\ln (x)}{x}=0 & \bcetoile \lim _{x \rightarrow 0^{+}} x \cdot \ln (x)=0 \\
 \bcetoile \lim _{x \rightarrow+\infty} \frac{\ln (x)}{x^{n}}=0 & \bcetoile \lim _{x \rightarrow 0^{+}} x^{n} \cdot \ln (x)=0 & \left(\forall n \in \mathbb{N}^{*}\right)
 \end{array}$
 \end{boite}
 \end{mybox}
\newpage
{\chap\chapter{Les fonctions exponentielles}
{\chap\chapter{Arithmétique}
\end{document}

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