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

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