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anonymous
 one year ago
Write the integral that produces the same value as\lim_{n \rightarrow \infty } \sum_{i=1}^{n}(3+i(5/n))^2)(5/n)
anonymous
 one year ago
Write the integral that produces the same value as\lim_{n \rightarrow \infty } \sum_{i=1}^{n}(3+i(5/n))^2)(5/n)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{n \rightarrow \infty}\sum_{i=1}^{n}(3+i(5/n))^2(5/n)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\dfrac{5}{n}\) suggests we're approximating an integral with \(n\) rectangles over the interval \([k,k+5]\), since \(\dfrac{5}{n}=\dfrac{k+5k}{n}\). Next, the fact that we're evaluating the square of some expression suggests, we're approximating the definite integral of \(f(x)=x^2\) over the interval above. When \(i=1\), you have the value of \(x\) is \(3+\dfrac{5}{n}\), which approaches \(3\) as \(n\to\infty\). This suggests the start of the interval is \(k=3\).
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