Explanation Proof: The left sum defined for n rectangles on [ a , b ] is ∑ k = 1 n f ( x k − 1 ) Δ x . Where, Δ x = b − a n , x k = a + k Δ x The right sum defined for n rectangles on [ a , b ] is ∑ k = 1 n f ( x k )

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 4.2, Problem 51P

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To prove: that if a function f is positive and increasing on [a,b] , then the left sum with n rectangles is less than or equal to the right sum with n rectangles.

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Chapter 4.2, Problem 50P

Chapter 4.2, Problem 52P

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To prove: that if a function f is positive and increasing on [ a , b ] , then the left sum with n rectangles is less than or equal to the right sum with n rectangles.

Solution Summary: The author proves that if a function f is positive and increasing on left[a,bright], then the left sum is less than or equal to the right sum.

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To prove: that if a function f is positive and increasing on [a,b] , then the left sum with n rectangles is less than or equal to the right sum with n rectangles.

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