Let S be the set of all (α, β) ∈ R × R such that lim_x → ∞ fracsin(x^2)(log_e x)^α sin (1/(x^2) )x^αβ(log_e(1+x))^β = 0. Then which of the following is (are) correct?

Let S be the set of all (α, β) ∈ R × R such that lim_x → ∞… — JEE Advanced 2024 Mathematics PYQ

JEE Advanced 2024 · Paper 2 · one or more correct

Let

S

be the set of all

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

such that

\lim_{x \to \infty} \frac{\sin(x^2)(\log_e x)^\alpha \sin\left(\dfrac{1}{x^2}\right)}{x^{\alpha\beta}(\log_e(1+x))^\beta} = 0.

Then which of the following is (are) correct?

Show answer

Correct options: B, C

[JEE Advanced 2024 · Paper 2]

Practise Limits Continuity and Differentiability the way it is asked

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