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The value of \(\lim _{x\to 0}\frac{{\log }_{e}\left(\sec \left(ex\right)⋅\sec \left({e}^{2}x\right)⋅\ldots ⋅\sec \left({…

Q1

The value of \(\lim _{x\to 0}\frac{{\log }_{e}\left(\sec \left(ex\right)⋅\sec \left({e}^{2}x\right)⋅\ldots ⋅\sec \left({e}^{10}x\right)\right)}{{e}^{2}−{e}^{2\cos x}}\) is equal to

a

\(\frac{\left({e}^{10}−1\right)}{2\left({e}^{2}−1\right)}\)

b

\(\frac{\left({e}^{10}−1\right)}{2{e}^{2}\left({e}^{2}−1\right)}\)

c

\(\frac{\left({e}^{20}−1\right)}{2{e}^{2}\left({e}^{2}−1\right)}\)

d

\(\frac{\left({e}^{20}−1\right)}{2\left({e}^{2}−1\right)}\)

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