Let $f(x), x\in \left[0, 1\right]$, be any positive real valued continuous function. Then
$\displaystyle \lim_{n \rightarrow \infty} (n + 1) \int_{0}^{1} x^{n} f(x) \text{d}x$
equals.
- $\max_{x \in \left[0, 1\right]} f(x)$
- $\min_{x \in \left[0, 1\right]} f(x)$
- $f(0)$
- $f(1)$
- $\infty$