помогите [tex] \lim_{x \to \infty} ( \frac{ x^{4} }{ x^{2} -2}- \frac{ x^{4} }{ x^{2} +2} )[/tex]. Created by Poppii. matematika-ru

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[tex] \lim_{x \to \infty} ( \frac{ x^{4} }{ x^{2} -2}- \frac{ x^{4} }{ x^{2} +2} )[/tex]

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kmike21

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

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