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MC 2025 In-course Diagnostics for Undergraduate Mathematics MATH140 WP

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Which of the following are true?

Statement i:   If is increasing on , then the left Riemann sum for is an underestimate.

Statement ii:   If is increasing on and is decreasing on , then the left Riemann sum for

 Statement iii: If is concave down on , then the midpoint Riemann sum is an overestimate. 

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Given that f(x) is decreasing on [a,b] and A = , the left-hand endpoint Riemann Sum will: 

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(i) True or False?   If is continuous on , then the value of the Riemann Sum   does not depend on the choice of [, ] where

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