For each of the following vector fields F, decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, V f = F) with f(0,0) = 0. If it is not conservative, type N. A. F(x, y) = (-12x + y)i + (x + 14y)j -0 f (x, y) = B. F(x, y) = -6yi - 5xj f (x, y) = C. F(x, y) = (-6 sin y)i + (2y - 6x cos y)j f (x, y) = -0 Note: Your answers should be either expressions of x and y (e.g. "3xy + 2y"), or the letter "N"
For each of the following vector fields F, decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, V f = F) with f(0,0) = 0. If it is not conservative, type N. A. F(x, y) = (-12x + y)i + (x + 14y)j -0 f (x, y) = B. F(x, y) = -6yi - 5xj f (x, y) = C. F(x, y) = (-6 sin y)i + (2y - 6x cos y)j f (x, y) = -0 Note: Your answers should be either expressions of x and y (e.g. "3xy + 2y"), or the letter "N"
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 4CR
Related questions
Question
![For each of the following vector fields F, decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f
(that is, V f = F) with ƒ(0,0) = 0. If it is not conservative, type N.
A. F (x, y) = (–12x + y)i + (x + 14y)j
f (x, y) =
B. F (x, y) = −6yi – 5xj
f (x, y) =
C. F (x, y) = (-6 sin y)i + (2y — 6x cos y)j
f (x, y)
=
Note: Your answers should be either expressions of x and y (e.g. "3xy + 2y"), or the letter "N"](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff60a9a8b-8f37-4a90-b833-69835617cf49%2F54d4deb7-cb4b-4adf-acd8-a7654168dce5%2Fsqgmjuv_processed.png&w=3840&q=75)
Transcribed Image Text:For each of the following vector fields F, decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f
(that is, V f = F) with ƒ(0,0) = 0. If it is not conservative, type N.
A. F (x, y) = (–12x + y)i + (x + 14y)j
f (x, y) =
B. F (x, y) = −6yi – 5xj
f (x, y) =
C. F (x, y) = (-6 sin y)i + (2y — 6x cos y)j
f (x, y)
=
Note: Your answers should be either expressions of x and y (e.g. "3xy + 2y"), or the letter "N"
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 5 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning