Limit of Logarithmic Expression (Jee Mains)

Evaluation of Limits

Hard

Limit of Logarithmic Expression

The value of
$\mathop {\lim }\limits_{x \to 0} \frac{{{{\log }_e}\left( {\sec (ex).\sec \left( {{e^2}x} \right) \cdot ... \cdot \sec \left( {{e^{10}}x} \right)} \right)}}{{{e^2} - {e^{2\cos x}}}}$
is equal to -

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