All subjects

\LARGE \lim\limits_{x \rightarrow-\infty}x^{3} \mathrm{e}^{x}=?

\LARGE 0

\LARGE \lim\limits_{x \rightarrow+\infty}\left(\frac{1}{x}+x^{2}\right)=?

\LARGE +\infty

\Large \text{Si}\lim\limits_{x \rightarrow+\infty} f(x)=L

,

\Large \text{alors la droite}

\Large \text{d'équation } y=L \text{ est :}

\Large \text{Asymptote horizontale }

\Large \text{à la courbe}

\Large \text{de la fonction } f \text{ en} +\infty

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\Large\text{Comment note-t-on}

\Large\text{que f admet }

\Large\text{pour limite} -\infty \text{ en} +\infty ?

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\Large\lim\limits_{x \rightarrow+\infty} f(x)=-\infty .

\Large \text{Une fonction }f

\Large \text{qui tend vers }+\infty \text{ en } +\infty

\Large \text{est-elle }

\Large \text{forcément croissante ?}

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\Large \text{Existe-t-il des fonctions}

\Large \text{n'ayant pas}

\Large \text{de limite en l'infini,}

\Large \text{ni finie ni infinie ?}

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\LARGE \lim\limits_{x \rightarrow-\infty}x^{7} =?

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\Large \text{La droite d'équation }

\Large y=A

\Large \text{est asymptote verticale}

\Large \text{à la courbe de } f \text{ si :}

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\Large\text{Comment note-t-on}

\Large\text{que la limite de }f

\Large\text{à gauche de }0

\Large\text{est } +\infty \text{ ?}

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\LARGE \text{Soit }n \in\N

,

\LARGE\lim\limits_{x \rightarrow +\infty}\frac{e^x}{x^n}=?

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