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If the local maximum value of the function \(f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^2 x}, x \in\left(0, \f…

Q1

If the local maximum value of the function \(f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^2 x}, x \in\left(0, \frac{\pi}{2}\right)\) is \(\frac{k}{e}\), then \(\left(\frac{k}{e}\right)^8+\frac{k^8}{e^5}+k^8\) is equal to

a

\(e^5+e^6+e^{11}\)

b

\(e^3+e^5+e^{11}\)

c

\(e^3+e^6+e^{11}\)

d

\(e^3+e^6+e^{10}\)

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