The value of lim x→0 loge(sec ... | Limits

JEE MAIN 2026

28-1-2026 S1

Question

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

Select the correct option:

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

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

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

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

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Easy

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