Let f: (-π/2, π/2) → ℝ be a differentiable function such that f(0… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 30 January, Shift 1Limits

Let $f : \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \to \mathbb{R}$ be a differentiable function such that $f(0) = \frac{1}{2}$ . If $\lim_{x \to 0} \frac{x \int_{0}^{x} f(t) \, dt}{e^{x^2} - 1} = \alpha$ , then $8\alpha^2$ is equal to:

A
$16$
B
$2$
C
$1$
D
$4$

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