MacBookPro.lan 2025-6-22:13:31:34

This commit is contained in:
oskar
2025-06-22 13:31:34 +02:00
parent 8b46f5af46
commit d73ea25b05
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"obsidian-git",
"wikilinks-to-mdlinks-obsidian",
"obsidian-daily-note-outline",
"mysnippets-plugin",
"github-sync",
"extended-graph"
"contribution-graph",
"obsidian-tasks-plugin",
"quickadd"
]

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{
"id": "contribution-graph",
"name": "Contribution Graph",
"version": "0.10.0",
"minAppVersion": "1.3.0",
"description": "Generate a interactive heatmap graph to visualize and track your productivity",
"author": "vran",
"authorUrl": "https://github.com/vran-dev",
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"fundingUrl": "https://www.buymeacoffee.com/vran"
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---
aliases:
tags:
up:
---
# EXERCICE 1 (6 points )
(Commun à tous les candidats)
## Partie A
On considère la fonction $f$ définie sur lensemble $\mathbb{R}$ des nombres réels par :
$f (x) = \frac{7}{2} - \frac{1}{2}(e^{ x } - e^{ -x })$
### 1)
#### a) Déterminer la limite de la fonction $f$ en $+\infty$
On a :
$\begin{align} \lim\limits_{ x \to \infty } f(x) &= \lim\limits_{ x \to \infty } \left( \frac{7}{2} - \frac{1}{2}(e^{ x } - e^{ -x }) \right) \\&= \frac{7}{2} - \frac{1}{2}\lim\limits_{ x \to \infty } e^{ ^{x} } - e^{ -x } \\&= \frac{7}{2} - \infty \\&= -\infty\end{align}$
#### b) Montrer que la fonction $f$ est strictement décroissante sur lintervalle $[0 ; +∞[$
On sait que $x \mapsto e^{ x }$ est croissante sur cet intervalle, et supérieure à 1
#### c) Montrer que léquation $f (x) = 0$ admet, sur lintervalle $[0 ; +∞[$, une unique solution, que lon note $\alpha$.
### 2) En remarquant que, pour tout réel $x$, $f (x) = f (x)$, justifier que léquation $f (x) = 0$ admet exactement deux solutions dans $\mathbb{R}$ et quelles sont opposées

16
daily/2025-06-22.md Normal file
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# Todo
# I did
> [!smallquery]- Modified files
> ```dataview
> LIST file.mtime
> where file.mtime > date(this.file.name) and file.mtime < (date(this.file.name) + dur(1 day)) sort file.mtime asc
> ```
```tasks
done 2025-06-22
short mode
```
# I am gratefull to