If $\lim\limits_{x \rightarrow 0} \frac{\alpha \mathrm{e}^{x}+\beta \mathrm{e}^{-x}+\gamma \sin x}{x \sin ^{2} x}=\frac{2}{3}$, where $\alpha, \beta, \gamma \in \mathbf{R}$, then which of the following is NOT correct?

Question

$\alpha^{2}+\beta^{2}+\gamma^{2}=6$

$\alpha \beta+\beta \gamma+\gamma \alpha+1=0$

$\alpha\beta^{2}+\beta \gamma^{2}+\gamma \alpha^{2}+3=0$

$\alpha^{2}-\beta^{2}+\gamma^{2}=4$

Solution

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