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At the point C At the point A At the point B <>

At the point C At the point A At the point B <>

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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### Understanding Gradient Vectors in Contour Plots #### Contour Plot Overview The provided image displays a contour plot with labeled points A, B, and C. This plot is utilized to understand the concept of gradient vectors in a scalar field. #### Gradient Vector Directions Gradient vectors illustrate the direction and rate of the steepest ascent in a scalar field. In a contour plot, these vectors are perpendicular to the contour lines and point towards higher values. #### Multiple-Choice Questions Below the contour plot, there are multiple-choice questions aimed at determining the approximate direction of the gradient vector at each of the points A, B, and C. The directions of the gradient vectors are represented by combinations of unit vectors \(\vec{i}\) and \(\vec{j}\): 1. \(\vec{i}\) 2. \(-\vec{i}\) 3. \(\vec{j}\) 4. \(-\vec{j}\) 5. \(\vec{i} + \vec{j}\) 6. \(\vec{i} - \vec{j}\) 7. \(-\vec{i} + \vec{j}\) 8. \(-\vec{i} - \vec{j}\) #### Dropdown Menu for Selection Each labeled point on the contour plot (A, B, and C) has an associated dropdown menu where students can select the appropriate direction of the gradient vector: - **At point C:** [Dropdown menu with options 1 to 8] - **At point A:** [Dropdown menu with options 1 to 8] - **At point B:** [Dropdown menu with options 1 to 8] #### Analyzing the Plot Students are required to analyze the contour plot and determine the direction of the gradient vector at each point (A, B, C). They should keep in mind that: - **Gradient vectors** point perpendicularly to contour lines. - **Direction** of the gradient vectors is towards increasing values of the scalar field. This task helps reinforce the understanding of gradient vectors, contour plots, and their interrelation in representing scalar fields.
Transcribed Image Text:### Understanding Gradient Vectors in Contour Plots #### Contour Plot Overview The provided image displays a contour plot with labeled points A, B, and C. This plot is utilized to understand the concept of gradient vectors in a scalar field. #### Gradient Vector Directions Gradient vectors illustrate the direction and rate of the steepest ascent in a scalar field. In a contour plot, these vectors are perpendicular to the contour lines and point towards higher values. #### Multiple-Choice Questions Below the contour plot, there are multiple-choice questions aimed at determining the approximate direction of the gradient vector at each of the points A, B, and C. The directions of the gradient vectors are represented by combinations of unit vectors \(\vec{i}\) and \(\vec{j}\): 1. \(\vec{i}\) 2. \(-\vec{i}\) 3. \(\vec{j}\) 4. \(-\vec{j}\) 5. \(\vec{i} + \vec{j}\) 6. \(\vec{i} - \vec{j}\) 7. \(-\vec{i} + \vec{j}\) 8. \(-\vec{i} - \vec{j}\) #### Dropdown Menu for Selection Each labeled point on the contour plot (A, B, and C) has an associated dropdown menu where students can select the appropriate direction of the gradient vector: - **At point C:** [Dropdown menu with options 1 to 8] - **At point A:** [Dropdown menu with options 1 to 8] - **At point B:** [Dropdown menu with options 1 to 8] #### Analyzing the Plot Students are required to analyze the contour plot and determine the direction of the gradient vector at each point (A, B, C). They should keep in mind that: - **Gradient vectors** point perpendicularly to contour lines. - **Direction** of the gradient vectors is towards increasing values of the scalar field. This task helps reinforce the understanding of gradient vectors, contour plots, and their interrelation in representing scalar fields.
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