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Limits Continuity and Differentiability question

2023 · 25 Jan · Shift 1 · Q28

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JEE Main
Mathematics
Limits Continuity and Differentiability
2023 · 25 Jan · Shift 1 · Q28

Limits Continuity and Differentiability question

2023 · 25 Jan · Shift 1 · Q28

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

The value of

\mathop {\lim }\limits_{n \to \infty } {{1 + 2 - 3 + 4 + 5 - 6\, + \,.....\, + \,(3n - 2) + (3n - 1) - 3n} \over {\sqrt {2{n^4} + 4n + 3} - \sqrt {{n^4} + 5n + 4} }}

is :

A
${3 \over {2\sqrt 2 }}$
B
${3 \over 2}(\sqrt 2 + 1)$
C
$3(\sqrt 2 + 1)$
D
${{\sqrt 2 + 1} \over 2}$

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