[Solution Library] Evaluate n→ ∞ lim (sin fracπ)/(n)+ sin (2pi)/(n)+....+ sin (nπ)/(n)n by interpreting it as the limit of Riemann sums
Question: Evaluate \(\underset{n\to \infty }{\mathop{\lim }}\,\frac{\sin \frac{\pi }{n}+\sin \frac{2\pi }{n}+....+\sin \frac{n\pi }{n}}{n}\) by interpreting it as the limit of Riemann sums for a continuous function f defined on [0, 1].
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![[All Steps] Given ∫_-2^4(|3-|3x||)dx, first sketch the](/images/solutions/MC-solution-library-35352.jpg "[All Steps] Given ∫_-2^4(|3-|3x||)dx, first sketch the graph")
[All Steps] Given ∫_-2^4(|3-|3x||)dx, first sketch the graph
Solution: Suppose that a tank initially contains 2000 gal of
[See Steps] Evaluate
![[Solution Library] Find an upper and lower](/images/solutions/MC-solution-library-35355.jpg "[Solution Library] Find an upper and lower bound for the integral ∫_0^1(1)/(x+2)dx")
[Solution Library] Find an upper and lower bound for the integral ∫_0^1(1)/(x+2)dx
(Solution Library) Apply the Fundamental Theorem of Calculus to find the
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