Question

Let \(f\), be a continuous function in \([0,1]\), then \(\lim _{n \rightarrow \infty} \sum_{j=0}^{n} \frac{1}{n} f\left(\frac{j}{n}\right)\) is
(A) \(\frac{1}{2} \int_{0}^{\frac{1}{2}} f(x) d x\)
(B) \(\int_{\frac{1}{2}}^{1} f(x) d x\)
(C) \(\int_{0}^{1} f(x) d x\)
(D) \(\int_{0}^{\frac{1}{2}} f(x) d x\)

Answer 1

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