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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![### Question 11
If \(\nabla f = \vec{F}\), then \(\vec{F}\) is called a potential vector field, and \(f\) is called a conservative function.
- ⦿ True
- ⦿ False
---
This question evaluates your understanding of potential vector fields and conservative functions in the context of vector calculus. Specifically, the question states that if the gradient of a function \(f\) (denoted by \(\nabla f\)) is equal to a vector field \(\vec{F}\), then this vector field \(\vec{F}\) is called a potential vector field, and the function \(f\) is referred to as a conservative function.
**Terminologies:**
- **Potential Vector Field**: A vector field \(\vec{F}\) that can be expressed as the gradient of some scalar function \(f\).
- **Conservative Function**: A scalar function \(f\) whose gradient results in a vector field.
Answer options provided are:
- True
- False](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e343f85-ac09-4dac-ae1f-fa90b444949b%2F3ce24011-d32a-4033-8667-4821930495f2%2Ft60r77b_processed.png&w=3840&q=75)
Transcribed Image Text:### Question 11
If \(\nabla f = \vec{F}\), then \(\vec{F}\) is called a potential vector field, and \(f\) is called a conservative function.
- ⦿ True
- ⦿ False
---
This question evaluates your understanding of potential vector fields and conservative functions in the context of vector calculus. Specifically, the question states that if the gradient of a function \(f\) (denoted by \(\nabla f\)) is equal to a vector field \(\vec{F}\), then this vector field \(\vec{F}\) is called a potential vector field, and the function \(f\) is referred to as a conservative function.
**Terminologies:**
- **Potential Vector Field**: A vector field \(\vec{F}\) that can be expressed as the gradient of some scalar function \(f\).
- **Conservative Function**: A scalar function \(f\) whose gradient results in a vector field.
Answer options provided are:
- True
- False
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