Homework Help is Here – Start Your Trial Now!
Math
Calculus
A particle is moving on a straight track.  You start your clock as it moves by your position.  The graph of the velocity as a function of time is shown by the blue curve in the diagram below.   To approximate the distance that the particle goes in the first 2.5 seconds, you construct the rectangles as shown. a)  Will this construction give an overestimate of the true distance, or will it give an underestimate of the true distance? b)  Is this a Left Sum, or is it a right sum? c)  What is the delta-t in this construction?   Options:  1. a)  Over estimate, b)  Right sum, c)  delta-t  =  0.25  2. a)  Under estimate, b)  Left sum, c)  delta-t  =  2.5  3.  a)  Under estimate, b)  Right sum, c)  delta-t  =  0.25

A particle is moving on a straight track.  You start your clock as it moves by your position.  The graph of the velocity as a function of time is shown by the blue curve in the diagram below.   To approximate the distance that the particle goes in the first 2.5 seconds, you construct the rectangles as shown. a)  Will this construction give an overestimate of the true distance, or will it give an underestimate of the true distance? b)  Is this a Left Sum, or is it a right sum? c)  What is the delta-t in this construction?   Options:  1. a)  Over estimate, b)  Right sum, c)  delta-t  =  0.25  2. a)  Under estimate, b)  Left sum, c)  delta-t  =  2.5  3.  a)  Under estimate, b)  Right sum, c)  delta-t  =  0.25

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...
See similar textbooks
icon
Related questions
Question

A particle is moving on a straight track.  You start your clock as it moves by your position.  The graph of the velocity as a function of time is shown by the blue curve in the diagram below.   To approximate the distance that the particle goes in the first 2.5 seconds, you construct the rectangles as shown.

a)  Will this construction give an overestimate of the true distance, or will it give an underestimate of the true distance?

b)  Is this a Left Sum, or is it a right sum?

c)  What is the delta-t in this construction?

 

Options: 

1. a)  Over estimate, b)  Right sum, c)  delta-t  =  0.25 

2. a)  Under estimate, b)  Left sum, c)  delta-t  =  2.5 

3.  a)  Under estimate, b)  Right sum, c)  delta-t  =  0.25 

 

The image displays a graph with a grid background, representing a mathematical function and its approximation using rectangular areas. The horizontal axis is labeled \( t \), while the vertical axis is labeled \( y = v(t) \). The graph includes: 1. **Curve**: A blue curve depicting the function \( v(t) \) that starts at a high value on the vertical axis and decreases as \( t \) increases. 2. **Rectangles**: A series of pink shaded rectangles underneath the curve, approximating the area under the curve. These rectangles are aligned vertically, with their tops touching the curve. The base of each rectangle is aligned along the horizontal axis. 3. **Intervals**: The rectangles are positioned between the integer values on the \( t \)-axis, specifically from \( t = 0 \) to \( t = 2 \). Each rectangle's height represents the value of the function at the left endpoint of the interval. The diagram visually represents the concept of Riemann sums, which are used to approximate the area under a curve as part of integral calculus. This approach essentially sums up the areas of the rectangles to estimate the total area under the curve \( v(t) \).
Transcribed Image Text:The image displays a graph with a grid background, representing a mathematical function and its approximation using rectangular areas. The horizontal axis is labeled \( t \), while the vertical axis is labeled \( y = v(t) \). The graph includes: 1. **Curve**: A blue curve depicting the function \( v(t) \) that starts at a high value on the vertical axis and decreases as \( t \) increases. 2. **Rectangles**: A series of pink shaded rectangles underneath the curve, approximating the area under the curve. These rectangles are aligned vertically, with their tops touching the curve. The base of each rectangle is aligned along the horizontal axis. 3. **Intervals**: The rectangles are positioned between the integer values on the \( t \)-axis, specifically from \( t = 0 \) to \( t = 2 \). Each rectangle's height represents the value of the function at the left endpoint of the interval. The diagram visually represents the concept of Riemann sums, which are used to approximate the area under a curve as part of integral calculus. This approach essentially sums up the areas of the rectangles to estimate the total area under the curve \( v(t) \).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS