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Suppose f(x) = 2. (a) The rectangles in the graph A illustrate f(x) on the interval 3 < x < 7. The area of all the rectangles is and it is an underestimate of v the area of the region enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and i 45 7. x = 7. Graph A Graph B (b) The rectangles in the graph B illustrate for f(x) on the interval 3

Suppose f(x) = 2. (a) The rectangles in the graph A illustrate f(x) on the interval 3 < x < 7. The area of all the rectangles is and it is an underestimate of v the area of the region enclosed by y = f(x), the x-axis, and the vertical lines x = 3 and i 45 7. x = 7. Graph A Graph B (b) The rectangles in the graph B illustrate for f(x) on the interval 3

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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8 8 Suppose f(x) 12 6 6 4 (a) The rectangles in the graph A illustrate f(x) on the interval 3 <x < 7. The area of all the rectangles is and it is 3 2 an underestimate of v the area of the region enclosed by y = f (x), the x-axis, and the vertical lines x = 3 and 1 2 4 5 6 7 8 1 2 3 4 5 6 7 7. Graph A Graph B (b) The rectangles in the graph B illustrate for f(x) on the interval 3 < x <7. The area of all the rectangles is and it is an overestimate of v the area of the region enclosed by y = f (x), the x-axis, and the vertical lines x 3 and x = 7. (c) To get a more accurate approximation of the area, the number of rectangles should: increase v rectangles. Note: Your objective is to find an approximation of the area under the curve on the interval 3 < x <7 using the areas of each of the sets of rectangles. Hint: Overestimate the area under the curve means that your area is larger than the area under the curve and underestimate the area under the curve means that your area is less than the area under the curve.
Transcribed Image Text:8 8 Suppose f(x) 12 6 6 4 (a) The rectangles in the graph A illustrate f(x) on the interval 3 <x < 7. The area of all the rectangles is and it is 3 2 an underestimate of v the area of the region enclosed by y = f (x), the x-axis, and the vertical lines x = 3 and 1 2 4 5 6 7 8 1 2 3 4 5 6 7 7. Graph A Graph B (b) The rectangles in the graph B illustrate for f(x) on the interval 3 < x <7. The area of all the rectangles is and it is an overestimate of v the area of the region enclosed by y = f (x), the x-axis, and the vertical lines x 3 and x = 7. (c) To get a more accurate approximation of the area, the number of rectangles should: increase v rectangles. Note: Your objective is to find an approximation of the area under the curve on the interval 3 < x <7 using the areas of each of the sets of rectangles. Hint: Overestimate the area under the curve means that your area is larger than the area under the curve and underestimate the area under the curve means that your area is less than the area under the curve.
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