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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, Vf=F) with f(0,0) = 0. If it is not conservative, type N. A. F(x,y) = (12x - 4y)i +(-4z +16y)j f(x, y) = B. F (z,y) = 6yi +7zj f (x, y) = C.F(x, y) = (6 sin y)i + (-8y + 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"

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, Vf=F) with f(0,0) = 0. If it is not conservative, type N. A. F(x,y) = (12x - 4y)i +(-4z +16y)j f(x, y) = B. F (z,y) = 6yi +7zj f (x, y) = C.F(x, y) = (6 sin y)i + (-8y + 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"

Calculus For The Life Sciences
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
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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, Vf=F) with f(0,0) = 0. If it is not conservative, type N. A. F (x, y) = (12x - 4y)i +(-4x + 16y)j f (x,y)= B. F (x, y) = 6yi+7zj f(x, y) = C.F (x, y) = (6 sin y)i + (-8y + 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"
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, Vf=F) with f(0,0) = 0. If it is not conservative, type N. A. F (x, y) = (12x - 4y)i +(-4x + 16y)j f (x,y)= B. F (x, y) = 6yi+7zj f(x, y) = C.F (x, y) = (6 sin y)i + (-8y + 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"
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