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Q1:What is the limit of Riemann Sums as the number of rectangles (N) increases toward infinity?

Q1:What is the limit of Riemann Sums as the number of rectangles (N) increases toward infinity?

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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Q1:What is the limit of Riemann Sums as the number of rectangles (N) increases toward infinity?

Q2: A particle is moved along the x-axis by a force that measures F(x)=2x Newtons at each point x meters from the point x=0. Find the work done (in Newton-meters) when the particle is moved from  x=0 to x=8 meters.

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y = sin(x) π y = cos(x) Two students, S and T, considered this problem: Consider the region trapped between the graphs of y = sin x and y = 0≤x≤ 1/2 . This region is shaded in the figure included above. To find the area of the shaded region, Student S set up the following integral. TT/2 f (cos x - sin x) dx However, Student T says this won't find the correct value. What do you think? TT/2 = cos x, on the interval
Transcribed Image Text:y = sin(x) π y = cos(x) Two students, S and T, considered this problem: Consider the region trapped between the graphs of y = sin x and y = 0≤x≤ 1/2 . This region is shaded in the figure included above. To find the area of the shaded region, Student S set up the following integral. TT/2 f (cos x - sin x) dx However, Student T says this won't find the correct value. What do you think? TT/2 = cos x, on the interval
Student T is correct. Student S should include ² like this: 7T 2 π S² (sin x − cos x)² dx Student T is correct. A better integral expression is f (cos x - sin x) dx + f² (sin x − cos x) dx + S 4 Student T is incorrect. Student S has set up the integral correctly. Student T is correct. A better integral expression is ㅠ S² (cos x sin x) dx
Transcribed Image Text:Student T is correct. Student S should include ² like this: 7T 2 π S² (sin x − cos x)² dx Student T is correct. A better integral expression is f (cos x - sin x) dx + f² (sin x − cos x) dx + S 4 Student T is incorrect. Student S has set up the integral correctly. Student T is correct. A better integral expression is ㅠ S² (cos x sin x) dx
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