Let S be the set of all (α, β) ∈ × such that _ x (x^ 2 ) ( _ e x )^ ( 1 x^ 2 ) x^ ( _ e…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let S be the set of all (α, β) ∈
× such that
\[\lim _{x \rightarrow \infty} \frac{\sin \left(x^{2}\right)\left(\log _{e} x\right)^{\alpha} \sin \left(\frac{1}{x^{2}}\right)}{x^{\alpha \beta}\left(\log _{e}(1+x)\right)^{\beta}}=0\]
Then which of the following is (are) correct?
× such that \[\lim _{x \rightarrow \infty} \frac{\sin \left(x^{2}\right)\left(\log _{e} x\right)^{\alpha} \sin \left(\frac{1}{x^{2}}\right)}{x^{\alpha \beta}\left(\log _{e}(1+x)\right)^{\beta}}=0\]
Then which of the following is (are) correct?
- (−1, 3) ∈S
- (−1, 1) ∈S
- (1, –1) ∈S
- (1, –2) ∈S
Answer
(A) (−1, 3) ∈ S
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