$lim x \to \infty x^{2} (1 - c o s \frac{2}{x})$

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Solution

$lim x \to \infty x^{2} (1 - cos \frac{2}{x}) = lim x \to \infty \frac{2 {sin}^{2} \frac{1}{x}}{\frac{1}{x^{2}}} = 2$

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