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Question:
Let S be the set of all \((α, β) ∈ \R\times\R\) such that
\(\lim\limits_{x\rightarrow\infin}\frac{\sin(x^2)(\log_ex)^\alpha\sin(\frac{1}{x^2})}{x^{αβ}(\log_e(1+x))^β}=0\)
Then which of the following is (are) correct ?
Let S be the set of all \((α, β) ∈ \R\times\R\) such that
\(\lim\limits_{x\rightarrow\infin}\frac{\sin(x^2)(\log_ex)^\alpha\sin(\frac{1}{x^2})}{x^{αβ}(\log_e(1+x))^β}=0\)
Then which of the following is (are) correct ?
\(\lim\limits_{x\rightarrow\infin}\frac{\sin(x^2)(\log_ex)^\alpha\sin(\frac{1}{x^2})}{x^{αβ}(\log_e(1+x))^β}=0\)
Then which of the following is (are) correct ?
Updated On: Aug 17, 2024
- (-1, 3) ∈ S
- (-1, 1) ∈ S
- (1, -1) ∈ S
- (1, -2) ∈ S
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The Correct Option is B, C
Solution and Explanation
The correct option is (B): (-1, 1) ∈ S and (C): (1, -1) ∈ S.
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