$\begin{matrix}\lim _{x\to \infty }\frac{(\sqrt{3x+1}+\sqrt{3x-1}{)}^{6}+(\sqrt{3x+1}-\sqrt{3x-1}{)}^{6}}{{\left(x+\sqrt{{x}^{2}-1}\right)}^{6}+{\left(x-\sqrt{{x}^{2}-1}\right)}^{6}}{x}^{3} \ \text{ }\end{matrix}$ [JEE Main 2023, 31 Jan (Shift 2)]

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\(\begin{matrix}\lim _{x\to \infty }\frac{(\sqrt{3x+1}+\sqrt{3x-1}{)}^{6}+(\sqrt{3x+1}-\sqrt{3x-1}{)}^{6}}{{\left(x+\sqr…

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