For each of the following vector fields F, decide whether it is conservative or not by computing curl F. Type in a potential function f (that is, Vf = F). If it is not conservative, type N. A. F (x, y) = (16x – 6y) i+ (-6x + 2y)j f (x, y) = B. F (x, y) = 8yi + 9xj f (x, y) = C. F (2, y, z) : f (x, y, 2) = 8xi + 9yj +k %3D D. F (x, y) = (8 sin y) i+ (-12y+ 8x cos y)j f (1, y) = E. F (x, y, z) = 8x²i – 6y'j+ lz?k f (x, y, 2) = Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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For each of the following vector fields F, decide whether it is conservative or not by computing
curl F. Type in a potential function f (that is, Vf = F). If it is not conservative, type N.
A. F (x, y) = (16x – 6y) i+ (-6x + 2y)j
f (x, y) =
B. F (x, y) = 8yi + 9xj
f (x, y) =
C. F (2, y, z) :
f (x, y, 2) =
8xi + 9yj +k
%3D
D. F (x, y) = (8 sin y) i+ (-12y+ 8x cos y)j
f (1, y) =
E. F (x, y, z) = 8x²i – 6y'j+ lz?k
f (x, y, 2) =
Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"
Transcribed Image Text:For each of the following vector fields F, decide whether it is conservative or not by computing curl F. Type in a potential function f (that is, Vf = F). If it is not conservative, type N. A. F (x, y) = (16x – 6y) i+ (-6x + 2y)j f (x, y) = B. F (x, y) = 8yi + 9xj f (x, y) = C. F (2, y, z) : f (x, y, 2) = 8xi + 9yj +k %3D D. F (x, y) = (8 sin y) i+ (-12y+ 8x cos y)j f (1, y) = E. F (x, y, z) = 8x²i – 6y'j+ lz?k f (x, y, 2) = Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"
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