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
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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
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

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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