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Q.

If \(f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)} \quad \forall x, y \in R\) and \(f^{\prime}(1)\) exists, and area under the curve \(f(x)\) bounded by x-axis \(x=0\) and \(x = 1\) is \(\frac {1}{3}\), then find \(\lim _{n \rightarrow \infty} \sum_{r=1}^{n} e^{r / n} f\left(\frac{\sqrt{r}}{n}\right)\).