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Limits Continuity and Differentiability question

2024 · Shift 2 · Q22

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2024 · Shift 2 · Q22

Limits Continuity and Differentiability question

2024 · Shift 2 · Q22

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −2

Let

S

be the set of all

(\alpha, \beta) \in \mathbb{R} \times \mathbb{R}

such that

\lim\limits_{x \rightarrow \infty} \frac{\sin \left(x^2\right)\left(\log _e x\right)^\alpha \sin \left(\frac{1}{x^2}\right)}{x^{\alpha \beta}\left(\log _e(1+x)\right)^\beta}=0 .

Then which of the following is (are) correct?

A
$(-1,3) \in S$
B
$(-1,1) \in S$
C
$(1,-1) \in S$
D
$(1,-2) \in S$

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