If \lim_{x \to 0} { {\e}^x+\beta {\e}^{-x}+\gamma \sin x}/{x \sin ^2 x}=\frac{2}{3}, where \alpha, \beta, \gamma \in R, then which of the following is NOT correct? [29-Jul-2022-Shift-1]

Correct Answer is : αβ2+βγ2+γα2+3=0

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

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

Limits, Continuity and Differentiability Part 2

Section: Mathematics

Question : 17 of 100

Marks: +1, -0

lim

x→0

‌

ex+βe−x+γ‌sin‌x

xsin2x

=‌

, where α,β,γ∈R, then which of the following is NOT correct?

[29-Jul-2022-Shift-1]

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