Homework Help is Here – Start Your Trial Now!
Math
Calculus
Which of the following graphs is the slope field for = cos x? 2/4/20/10

Which of the following graphs is the slope field for = cos x? 2/4/20/10

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
**Question:** Which of the following graphs is the slope field for \(\frac{dy}{dx} = \cos x\)? **Explanation of Graphics:** There are four graphs provided, each with a blank circle next to them for selection purposes. 1. **Top-Left Graph:** - This graph shows a slope field on a grid from \(-5\) to \(5\) on both the x-axis and y-axis. - The vectors (slopes) form a series of vertical lines that follow an oscillating pattern in the y-direction. The slopes are positive where \(\cos(x)\) is positive (centered around \(x = 0, 2\pi, 4\pi\), etc.) and negative where \(\cos(x)\) is negative (centered around \(x = \pi, 3\pi, 5\pi\), etc.). 2. **Top-Right Graph:** - Similar in layout to the previous graph but the patterns of the vectors are different. - The vectors form diagonal lines and gradually change in slope as you move along the x-axis, not consistent with the behavior of \(\cos x\). 3. **Bottom-Left Graph:** - The layout extends from \(-5\) to \(5\) on both axes as well. - The vectors in this graph form horizontal lines indicating that the slopes are constant regardless of the x-coordinate which does not correspond to \(\frac{dy}{dx} = \cos x\). 4. **Bottom-Right Graph:** - This graph also follows the same grid setup. - The vectors show a repetitive pattern shifting from left to right, with reversals at points that are consistent with \(\cos x\) changes. The vertical slopes translate to horizontal oscillations characteristic of the \(\cos x\) function. **Answer:** Upon inspection, the **Top-Left Graph** represents the correct slope field for \(\frac{dy}{dx} = \cos x\). The vectors indicate a periodic pattern that mirrors the properties of the \(\cos x\) function, oscillating between positive and negative slopes at intervals corresponding to the function's behavior.
Transcribed Image Text:**Question:** Which of the following graphs is the slope field for \(\frac{dy}{dx} = \cos x\)? **Explanation of Graphics:** There are four graphs provided, each with a blank circle next to them for selection purposes. 1. **Top-Left Graph:** - This graph shows a slope field on a grid from \(-5\) to \(5\) on both the x-axis and y-axis. - The vectors (slopes) form a series of vertical lines that follow an oscillating pattern in the y-direction. The slopes are positive where \(\cos(x)\) is positive (centered around \(x = 0, 2\pi, 4\pi\), etc.) and negative where \(\cos(x)\) is negative (centered around \(x = \pi, 3\pi, 5\pi\), etc.). 2. **Top-Right Graph:** - Similar in layout to the previous graph but the patterns of the vectors are different. - The vectors form diagonal lines and gradually change in slope as you move along the x-axis, not consistent with the behavior of \(\cos x\). 3. **Bottom-Left Graph:** - The layout extends from \(-5\) to \(5\) on both axes as well. - The vectors in this graph form horizontal lines indicating that the slopes are constant regardless of the x-coordinate which does not correspond to \(\frac{dy}{dx} = \cos x\). 4. **Bottom-Right Graph:** - This graph also follows the same grid setup. - The vectors show a repetitive pattern shifting from left to right, with reversals at points that are consistent with \(\cos x\) changes. The vertical slopes translate to horizontal oscillations characteristic of the \(\cos x\) function. **Answer:** Upon inspection, the **Top-Left Graph** represents the correct slope field for \(\frac{dy}{dx} = \cos x\). The vectors indicate a periodic pattern that mirrors the properties of the \(\cos x\) function, oscillating between positive and negative slopes at intervals corresponding to the function's behavior.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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