Question

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Answer 1

Ответ:

Объяснение:

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Answer 2

Ответ:

$\lim\limits _{x \to 0}\, \dfrac{\sqrt{x^2+2}-\sqrt2}{\sqrt{x^2+1}-1}=\lim\limits _{x \to 0}\, \dfrac{(\sqrt{x^2+2}-\sqrt2)(\sqrt{x^2+2}+\sqrt2)(\sqrt{x^2+1}+1)}{(\sqrt{x^2+1}-1)(\sqrt{x^2+1}+1)(\sqrt{x^2+2}+\sqrt2)}=\\\\\\=\lim\limits _{x \to 0}\, \dfrac{(x^2+2-2)(\sqrt{x^2+1}+1)}{(x^2+1-1)(\sqrt{x^2+2}+\sqrt2)}=\lim\limits _{x \to 0}\, \dfrac{x^2(\sqrt{x^2+1}+1)}{x^2(\sqrt{x^2+2}+\sqrt2)}=$

$=\lim\limits _{x \to 0}\, \dfrac{\sqrt{x^2+1}+1}{\sqrt{x^2+2}+\sqrt2}=\dfrac{1+1}{\sqrt2+\sqrt2}=\dfrac{2}{2\sqrt2}=\dfrac{1}{\sqrt2}=\dfrac{\sqrt2}{2}$