JEE MATHEMATICS MCQ: LIMITS

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\lim _{x \rightarrow 0} \frac{\alpha e^x+\beta e^{-x}+\gamma \sin x}{x \sin ^2 x}=\frac{2}{3}

, where

\alpha, \beta, \gamma \in \mathbf{R}

, then which of the following is NOT correct?

View answer and explanation

Correct option: C

\alpha \beta^2+\beta \gamma^2+\gamma \alpha^2+3=0

Option C (

\alpha \beta^2+\beta \gamma^2+\gamma \alpha^2+3=0

) is NOT correct because after finding the values of

\alpha

\beta

, and

\gamma

, substituting them into the expression does not result in 0.

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