Вычислить предел: [tex]\lim_{x \to \infty} (\sqrt{x+2} -\sqrt{x-2} )[/tex]. Created by vicasavronova. matematika-ru

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$\lim_{x \to \infty} (\sqrt{x+2} -\sqrt{x-2} )=\lim_{x \to \infty}\dfrac{(\sqrt{x+2} -\sqrt{x-2} )(\sqrt{x+2} +\sqrt{x-2} )}{(\sqrt{x+2} +\sqrt{x-2} )}=\lim_{x \to \infty}\dfrac{x+2-(x-2)}{(\sqrt{x+2} +\sqrt{x-2} )}=\lim_{x \to \infty}\dfrac{4}{(\sqrt{x+2} +\sqrt{x-2} )}=0$

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Namib

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Пошаговое объяснение:

$\lim_{x \to \infty} (\sqrt{x+2} -\sqrt{x-2} ) = \\ = \lim_{x \to \infty} \frac{(\sqrt{x+2} -\sqrt{x-2} )(\sqrt{x+2} + \sqrt{x-2} )}{(\sqrt{x+2} + \sqrt{x-2} )} = \\ = \lim_{x \to \infty} \frac{(x+2)-(x-2)}{(\sqrt{x+2} + \sqrt{x-2} )} = \\ = \lim_{x \to \infty} \frac{4}{(\sqrt{x+2} + \sqrt{x-2} )} = 0$

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