Show that $\lim_{n \to \infty} \prod_{k=1}^{k=n} (1+ \frac{1}{n}f(\frac{k}{n})) = e^{\int_{0}^{1}f(x) dx}$
Help finding the limit of $\lim_{n \to \infty}\prod_{k=1}^{n}\left(1+\frac{1}{n}f\left(\frac{k}{n}\right)\right)$.