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Author(s) Philippe Delsarte, Manon Oreins
Deadline No deadline
Submission limit No limitation
Category tags Fct, limite

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Fonctions - Q23

Sans utiliser la règle de l’Hospital, calculer les limites suivantes :

Question 1:
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\begin{equation*} \lim_{x \rightarrow 0} \, \frac{\cos 2x - \cos x}{\sin 2x - \sin x} \end{equation*}
Question 2:
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\begin{equation*} \lim_{x \rightarrow \frac{\pi}{6}} \frac{\sin \left( x - \frac{\pi}{6} \right)}{1 - 2 \sin x} \end{equation*}
Question 3:
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\begin{equation*} \lim_{x \rightarrow \frac{\pi}{2}} \frac{\cos^2 x \left( \tan \frac{x}{2} - 1 \right)} {\left( x - \frac{\pi}{2} \right) \sin 2x \left( \sqrt{2} - 2 \cos \frac{x}{2} \right)} \end{equation*}
Question 4:
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\begin{equation*} \lim_{x \rightarrow \pm \infty} x \left( 1 - \sqrt[3]{1 - \sin \frac{1}{x}} \right) \end{equation*}