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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, ▼ ƒ = F). If it is not conservative, type N. A. F (x, y) = (−12x + 8y)i + (8x + 16y)j f (x, y) = B. F (x, y) = −6yi – 5xj f(x, y) = C. F (x, y, z) = −6xi — 5yj + k f (x, y, z) = D. F (x, y) = (-6 sin y)i + (16y — 6x cos y)j f (x, y) = E. F (x, y, z) = − 6x²i + 8y²j + 8z²k f (x, y, z) = Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"

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, ▼ ƒ = F). If it is not conservative, type N. A. F (x, y) = (−12x + 8y)i + (8x + 16y)j f (x, y) = B. F (x, y) = −6yi – 5xj f(x, y) = C. F (x, y, z) = −6xi — 5yj + k f (x, y, z) = D. F (x, y) = (-6 sin y)i + (16y — 6x cos y)j f (x, y) = E. F (x, y, z) = − 6x²i + 8y²j + 8z²k f (x, y, z) = Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"

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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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, V f = F). If it is not conservative, type N. (−12x + 8y)i + (8x + 16y)j A. F (x, y) f (x, y) = B. F (x, y) = −6yi — 5xj f(x, y) = C. F (x, y, z) = −6xi — 5yj + k f (x, y, z) = D. F (x, y) = (-6 sin y)i + (16y — 6x cos y)j f (x, y) = E. F (x, y, z) = − 6x²i+ 8y²j + 8z²k f (x, y, z) = 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, V f = F). If it is not conservative, type N. (−12x + 8y)i + (8x + 16y)j A. F (x, y) f (x, y) = B. F (x, y) = −6yi — 5xj f(x, y) = C. F (x, y, z) = −6xi — 5yj + k f (x, y, z) = D. F (x, y) = (-6 sin y)i + (16y — 6x cos y)j f (x, y) = E. F (x, y, z) = − 6x²i+ 8y²j + 8z²k f (x, y, z) = Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"
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