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By computing the sum of these areas of the smaller rectangles (Lg) and the sum of the areas of the larger rectangles (R8), we obtain better lower and upper estimates for A: 0.5468750 < A < 0.7968750. So one possible answer to the question is to say that the true area lies somewhere between 0.5468750 and 0.7968750. We could obtain better estimates by increasing the number of strips. The table at the left shows the results of similar calculations (with a computer) using n rectangles whose heights are found with left endpoints (Ln) or right endpoints (Rn). In particular, we see by using 50 strips that the area lies between 0.6468 and 0.6868. With 1000 strips, we narrow it down even more: A lies between 0.6656670 and 0.6676670. A good estimate is obtained by averaging these numbers: A =

By computing the sum of these areas of the smaller rectangles (Lg) and the sum of the areas of the larger rectangles (R8), we obtain better lower and upper estimates for A: 0.5468750 < A < 0.7968750. So one possible answer to the question is to say that the true area lies somewhere between 0.5468750 and 0.7968750. We could obtain better estimates by increasing the number of strips. The table at the left shows the results of similar calculations (with a computer) using n rectangles whose heights are found with left endpoints (Ln) or right endpoints (Rn). In particular, we see by using 50 strips that the area lies between 0.6468 and 0.6868. With 1000 strips, we narrow it down even more: A lies between 0.6656670 and 0.6676670. A good estimate is obtained by averaging these numbers: A =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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y y (1, 2) (1, 2) y = 2 x? 1 1 8 (a) Using left endpoints (b) Using right endpoints By computing the sum of these areas of the smaller rectangles (L8) and the sum of the areas of the larger rectangles (R8), we obtain better lower and upper estimates for A: 0.5468750 < A < 0.7968750. So one possible answer to the question is to say that the true area lies somewhere between 0.5468750 and 0.7968750. We could obtain better estimates by increasing the number of strips. The table at the left shows the results of similar calculations (with a computer) using n rectangles whose heights are found with left endpoints (Ln) or right endpoints (Rn). In particular, we see by using 50 strips that the area lies between 0.6468 and 0.6868. With 1000 strips, we narrow it down even more: A lies between 0.6656670 and 0.6676670. A good estimate is obtained by averaging these numbers: A = HI CO
Transcribed Image Text:y y (1, 2) (1, 2) y = 2 x? 1 1 8 (a) Using left endpoints (b) Using right endpoints By computing the sum of these areas of the smaller rectangles (L8) and the sum of the areas of the larger rectangles (R8), we obtain better lower and upper estimates for A: 0.5468750 < A < 0.7968750. So one possible answer to the question is to say that the true area lies somewhere between 0.5468750 and 0.7968750. We could obtain better estimates by increasing the number of strips. The table at the left shows the results of similar calculations (with a computer) using n rectangles whose heights are found with left endpoints (Ln) or right endpoints (Rn). In particular, we see by using 50 strips that the area lies between 0.6468 and 0.6868. With 1000 strips, we narrow it down even more: A lies between 0.6656670 and 0.6676670. A good estimate is obtained by averaging these numbers: A = HI CO
Rn Ln 10 0.5700000 0.7700000 20 0.6175000 0.7175000 30 0.6337037 | 0.7003704 50 0.6468000 0.6868000 100 0.6567000 0.6767000 1000 0.6656670 | 0.6676670
Transcribed Image Text:Rn Ln 10 0.5700000 0.7700000 20 0.6175000 0.7175000 30 0.6337037 | 0.7003704 50 0.6468000 0.6868000 100 0.6567000 0.6767000 1000 0.6656670 | 0.6676670
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