Explanation Given: For any function f(x) on [a, b], R N − L N = b − a N ( f ( b ) − f ( a ) ) Calculation: For any f on I = [a, b], partition I into N equal subintervals. Let Δ x = b − a N and set x k = a + k Δ x , k = 0 , 1 , ... N . Then we have the following approximations to the area between the graph of f and the x -axis, the left endpoint approximation L N = Δ x ∑ k = 0 N − 1 f ( x k ) and right endpoint approximation R N = Δ x ∑ k = 1 N f ( x k ) . Accordingly, R N − L N = ( Δ x ∑ k = 1 N f ( x k ) ) − ( Δ x ∑ k = 0 N − 1 f ( x k ) ) &...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Question

Chapter 5.1, Problem 86E

To determine

To prove that $R_{N} - L_{N} = \frac{b - a}{N} (f (b) - f (a))$

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Chapter 5.1, Problem 85E

Chapter 5.1, Problem 87E

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Chapter 5 Solutions

Calculus - Standalone book

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