List of top Mathematics Questions on Differentiability asked in KEAM

Let $f(x) = \int_{1}^{x} \sin^2 \left(\frac{t}{2}\right) dt$. Then the value of $\lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x}$ is equal to:

Let \( f(x) = \int_{1^{x} \sin^2 \left( \frac{t}{2} \right) dt \). Then the value of \( \lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x} \) is equal to:}

Let \( f(x) = \int_{1^{x} \sin^2 \left( \frac{t}{2} \right) dt \). Then the value of \( \lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x} \) is equal to:}