A.\(\mathop {\lim }\limits_{x \to  \pm \infty } x\left( {\sqrt {{x^2} + 1}  - \sqrt {{x^2} - 3} } \right) =- 2\)
B.\(\mathop {\lim }\limits_{x \to  \pm \infty } x\left( {\sqrt {{x^2} + 1}  - \sqrt {{x^2} - 3} } \right) = 2\)
C.\(\begin{array}{l}\mathop {\lim }\limits_{x \to + \infty } x\left( {\sqrt {{x^2} + 1} - \sqrt {{x^2} - 3} } \right) = -2\\\mathop {\lim }\limits_{x \to - \infty } x\left( {\sqrt {{x^2} + 1} - \sqrt {{x^2} - 3} } \right) =  2\end{array}\)
D.\(\begin{array}{l}\mathop {\lim }\limits_{x \to + \infty } x\left( {\sqrt {{x^2} + 1} - \sqrt {{x^2} - 3} } \right) = 2\\\mathop {\lim }\limits_{x \to - \infty } x\left( {\sqrt {{x^2} + 1} - \sqrt {{x^2} - 3} } \right) = - 2\end{array}\)

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