Bonsoir s'il vous plaît aidez moi à calculer cette limite !.... Pergunta de ideia deBluenoodles

Bluenoodles @Bluenoodles

May 2019 1 80 Report

Bonsoir s'il vous plaît aidez moi à calculer cette limite !

$\lim_{x \to +\infty} 1 - \frac{x}{4} \sqrt{ (x-2)^{2} }$

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Commentaires Bonjour Bluenoodles

Il n'y a aucune indétermination.

$\lim\limits_{x\to+\infty}\dfrac{x}{4}=+\infty\ \ et\ \ \lim\limits_{x\to+\infty}\sqrt{(x-2)^{2}}=+\infty\\\\\\\Longrightarrow\boxed{\lim\limits_{x\to+\infty}\dfrac{x}{4}\sqrt{(x-2)^{2}}=+\infty}$

Donc

$\lim\limits_{x\to+\infty}[1-\dfrac{x}{4}\sqrt{(x-2)^{2}}]=1-(+\infty)\\\\\\\Longrightarrow\boxed{ \lim\limits_{x\to+\infty}[1-\dfrac{x}{4}\sqrt{(x-2)^{2}}]=-\infty}$

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