Determine the value of limn→∞(1n2∑k=1nk⋅ek/n)\lim_{n \to \infty} \left( \frac{1}{n^2} \sum_{k=1}^n k \cdot e^{k/n} \right)limn→∞(n21∑k=1nk⋅ek/n) is NOT the intended form; consider limn→∞1n2∑k=1nk\lim_{n \to \infty} \frac{1}{n^2} \sum_{k=1}^n klimn→∞n21∑k=1nk. What is limn→∞1n2∑k=1nkcos(k/n)\lim_{n \to \infty} \frac{1}{n^2} \sum_{k=1}^n k \cos(k/n)limn→∞n21∑k=1nkcos(k/n)?
∫01xcos(x)dx\int_0^1 x \cos(x) dx∫01xcos(x)dx
∫01cos(x)dx\int_0^1 \cos(x) dx∫01cos(x)dx
000
1/21/21/2