Willis Ward
05/26/2024 · Primary School
Exercice 1 : Soit \( f \) la fonction définie par : \( \left\{\begin{array}{l}f(x)=\frac{1-\cos (x)}{x}, \text { si } x \neq 0 \\ f(0)=0\end{array}\right. \) 1) Montrer que \( f \) est continue en 0 2) a- Etudier la dérivabilité de \( f \) en 0 b- Ecrire l'équation de la tangente \( (T) \) à la courbe \( \left(C_{f}\right) \) au point d'abscisse 0 3) Déterminer \( f^{\prime}(x) \) pour tout \( x \in I R \)
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1. \( f \) est continue en 0.
2. \( f \) est dérivable en 0 avec \( f'(0) = 0 \), l'équation de la tangente est \( y = 0 \).
3. Pour \( x \neq 0 \), \( f'(x) = \frac{x \sin(x) - (1 - \cos(x))}{x^2} \).
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