Explanation Assuming x k = a + k Δ x = − 1 + 5 k N , k = 1 , 2 , 3... , N are the end points of the N subintervals between 0 and 10, we apply R N = Δ x ∑ k = 1 N f ( x k ) and then apply limit N → ∞ to this which gives the solution Given: ∫ − 1 4 ( 4 x − 8 ) d x Calculation: Let N be a positive integer. Δ x = ( b − a ) N where b = 4 and a = − 1 , so Δ x = 5 N . If x k = a + k Δ x = − 1 + 5 k N , k = 1 , 2 , 3..... To determine (b) To draw a graph of the signed area represented by the integral given and then compute it using geometry

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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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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Question

Chapter 5.2, Problem 12E

To determine

(a)

To determine the value of the integral given using the limit theorem $\lim_{N \to \infty} R_{N}$

To determine

(b)

To draw a graph of the signed area represented by the integral given and then compute it using geometry

Expert Solution & Answer

Chapter 5 Solutions

Calculus - Standalone book

Ch. 5.1 - Prob. 1PQ Ch. 5.1 - Prob. 2PQ Ch. 5.1 - Prob. 3PQ Ch. 5.1 - Prob. 4PQ Ch. 5.1 - Prob. 5PQ Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E

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(a) To determine the value of the integral given using the limit theorem lim N → ∞ R N

Solution Summary: The author explains how to determine the value of the integral given using the limit theorem.

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(a)

To determine the value of the integral given using the limit theorem $\lim_{N \to \infty} R_{N}$

(b)

To draw a graph of the signed area represented by the integral given and then compute it using geometry

Chapter 5 Solutions

(a) To determine the value of the integral given using the limit theorem lim N → ∞ R N

Solution Summary: The author explains how to determine the value of the integral given using the limit theorem.

Concept explainers

Videos

(a) To determine the value of the integral given using the limit theorem limN→∞RN

(b) To draw a graph of the signed area represented by the integral given and then compute it using geometry

Chapter 5 Solutions

(a)

To determine the value of the integral given using the limit theorem $\lim_{N \to \infty} R_{N}$

(b)

To draw a graph of the signed area represented by the integral given and then compute it using geometry