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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.

1. $\max_{x \in \left[0, 1\right]} f(x)$
2. $\min_{x \in \left[0, 1\right]} f(x)$
3. $f(0)$
4. $f(1)$
5. $\infty$
edited | 194 views
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Option D, we can take some sample f(x) and try..
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+1 vote