jee-main 2023 Q71

jee-main · India · session1_31jan_shift2 Taylor series Limit evaluation using series expansion or exponential asymptotics

$\lim_{x \rightarrow \infty} \frac{(\sqrt{3x+1} + \sqrt{3x-1})^6 + (\sqrt{3x+1} - \sqrt{3x-1})^6}{\left(x + \sqrt{x^2-1}\right)^6 + \left(x - \sqrt{x^2-1}\right)^6} x^3$
(1) is equal to $\frac{27}{2}$
(2) is equal to 9
(3) does not exist
(4) is equal to 27

$\lim_{x \rightarrow \infty} \frac{(\sqrt{3x+1} + \sqrt{3x-1})^6 + (\sqrt{3x+1} - \sqrt{3x-1})^6}{\left(x + \sqrt{x^2-1}\right)^6 + \left(x - \sqrt{x^2-1}\right)^6} x^3$\\
(1) is equal to $\frac{27}{2}$\\
(2) is equal to 9\\
(3) does not exist\\
(4) is equal to 27

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