Commit 62c0a3e9 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent c9537e63
Pipeline #14634 canceled with stage
...@@ -91,12 +91,14 @@ RÉSUMÉ<br> ...@@ -91,12 +91,14 @@ RÉSUMÉ<br>
&\Longrightarrow\quad\big[\,ln\,|N|\,\big]_{N(t_1)}^{N(t_2)}= r \,\big[\,t\,\big]_{t_1}^{t_2}\\ &\Longrightarrow\quad\big[\,ln\,|N|\,\big]_{N(t_1)}^{N(t_2)}= r \,\big[\,t\,\big]_{t_1}^{t_2}\\
\\ \\
&\Longrightarrow\quad\underbrace{ln\,|N(t_2)|-\,ln\,|N(t_1)|}_{ &\Longrightarrow\quad\underbrace{ln\,|N(t_2)|-\,ln\,|N(t_1)|}_{
N>0 \Longrightarrow|N|=N} = r\,(t_2 - t_1)\\ N>0 \;\Longrightarrow\;|N|\,=\,N} = r\,(t_2 - t_1)\\
\\ \\
&\Longrightarrow\quad ln\,N(t_2) = ln\,N(t_2) + r\,(t_2 - t_1)\\ &\Longrightarrow\quad ln\,N(t_2) = ln\,N(t_1) + r\,(t_2 - t_1)\\
\\ \\
&\Longrightarrow\quad \underbrace{exp\big[ln\,N(t_2)\big]}_{exp(ln x)=x} &\Longrightarrow\quad \underbrace{exp\big[ln\,N(t_2)\big]}_{exp(ln\,x)\;=\;x}
=\underbrace{exp\big[ln\,N(t_2) + r\,(t_2 - t_1)]}_{exp (a+b)= exp a\cdot exp b} =\underbrace{exp\big[ln\,N(t_1) + r\,(t_2 - t_1)]}_{exp (a+b)\;=\;exp\,a\times exp\,b}\\
\\
&\Longrightarrow\quad N(t_2)=N(t_1)\,exp\,[r\,(t_2 - t_1)]
\end{align}`$ \end{align}`$
......
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