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Решите задачу:

$\lim\limits_{n \to \infty} ( \sqrt{(n^2+1)(n^2+2)}- \sqrt{(n^2-1)(n^2-2)} )=\\\\= \lim\limits _{n \to \infty}\frac{(n^2+1)(n^2+2)-(n^2-1)(n^2-2)}{ \sqrt{(n^2+1)(n^2+2)}+\sqrt{(n^2-1)(n^2-2)}}=\\\\= \lim\limits _{n \to \infty} \frac{n^4+3n^2+2-(n^4-3n^2+2)}{\sqrt{n^4+3n^2+2}+\sqrt{n^2-3n^2+2}} =\Big [\frac{:n^2}{:n^2}\Big ]=\\\\= \lim\limits _{n \to \infty}\frac{\frac{6n^2}{n^2}}{\sqrt{1+\frac{3}{n^2}+\frac{2}{n^4}}+\sqrt{1-\frac{3}{n^2}+\frac{2}{n^4}}}=\frac{6}{\sqrt1+\sqrt1}=\frac{6}{2}=3$