Question

lim_{n \to \infty} \left( \frac{\pi}{n} \left( \sin \left( \frac{\pi}{n} \right) + \sin \left( \frac{2\pi}{n} \right) + \sin \left( \frac{3\pi}{n} \right) + ... + \sin \left( \frac{n\pi}{n} \right) \right) \right) = \\ I. \lim_{n \to \infty} \sum_{k=1}^{n} \frac{\pi}{n} \sin \left( \frac{k\pi}{n} \right) \\ II. \int_{0}^{\pi} \sin(x)dx \\ III. 2 \\ A. I only \\ B. II only \\ C. III only \\ D. II and III only \\ E. I, II, and III

          lim_{n \to \infty} \left( \frac{\pi}{n} \left( \sin \left( \frac{\pi}{n} \right) + \sin \left( \frac{2\pi}{n} \right) + \sin \left( \frac{3\pi}{n} \right) + ... + \sin \left( \frac{n\pi}{n} \right) \right) \right) = \\
I. \lim_{n \to \infty} \sum_{k=1}^{n} \frac{\pi}{n} \sin \left( \frac{k\pi}{n} \right) \\
II. \int_{0}^{\pi} \sin(x)dx \\
III. 2 \\
A. I only \\
B. II only \\
C. III only \\
D. II and III only \\
E. I, II, and III

limn →∞ ( (π)/(n) ( sin( (π)/(n) ) + sin( (2π)/(n) ) + sin( (3π)/(n) ) + ... + sin( (nπ)/(n) ) ) ) =

I. limn →∞ ∑k=1^n (π)/(n) sin( (kπ)/(n) )

II. ∫0^π sin(x)dx

III. 2

A. I only

B. II only

C. III only

D. II and III only

E. I, II, and III

Added by Matthew M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/05/2023

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Hello. I have a question about calculus.Thank you. sin()+sin2 8 +sin(3)+...+sin( I. J^ sin(x)dx 1I1. 2 A. I only B. II only c. III only D. II and III only E. I, II, and III