f(x)=\left\{\begin{array}{ll} \frac{\sin \frac{\pi x}{2}}{x} & x \neq 0 \\ 0 & x=0 \end{array}, \quad F(x)=\int_{0}^{3 x} f(x-t) d t\right. O Find the derivative F'(0). \text { Find the limit }

\lim _{n \rightarrow \infty} \frac{1}{n^{2}} \sum_{k=1} k f\left(\frac{\kappa}{n}\right)