JEE Main 202229 Jul, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002If limx→0αex+βe−x+γsinxxsin2x=23\lim\limits_{x \rightarrow 0} \frac{\alpha \mathrm{e}^{x}+\beta \mathrm{e}^{-x}+\gamma \sin x}{x \sin ^{2} x}=\frac{2}{3}x→0limxsin2xαex+βe−x+γsinx=32, where α,β,γ∈R\alpha, \beta, \gamma \in \mathbf{R}α,β,γ∈R, then which of the following is NOT correct?AOption A. α2+β2+γ2=6\alpha^{2}+\beta^{2}+\gamma^{2}=6α2+β2+γ2=6BOption B. αβ+βγ+γα+1=0\alpha \beta+\beta \gamma+\gamma \alpha+1=0αβ+βγ+γα+1=0COption C. αβ2+βγ2+γα2+3=0\alpha\beta^{2}+\beta \gamma^{2}+\gamma \alpha^{2}+3=0αβ2+βγ2+γα2+3=0DOption D. α2−β2+γ2=4\alpha^{2}-\beta^{2}+\gamma^{2}=4α2−β2+γ2=4CheckSkip · show solution
