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(B) Do we have enough information to determine if F is a gradient vector field or not? Explain why or why not. If yes, then determine if it is a gradient vector field or not. (solution) (C) Do we have enough information to determine if F is a curl field or not? Explain why or why not. If yes, then determine if it is a curl field or not. (solution)

(B) Do we have enough information to determine if F is a gradient vector field or not? Explain why or why not. If yes, then determine if it is a gradient vector field or not. (solution) (C) Do we have enough information to determine if F is a curl field or not? Explain why or why not. If yes, then determine if it is a curl field or not. (solution)

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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Assume that div (x, y, z) = 0 and curlF (x, y, z) = 0. Let D(F) = R3 – {(0,0, k) such that any k is in R.}. (A) Answer the following questions and explain why briefly. Applicable? Test Yes/No Why? Curl Test Divergence Test (B) Do we have enough information to determine if F is a gradient vector field or not? Explain why or why not. If yes, then determine if it is a gradient vector field or not. (solution) (C) Do we have enough information to determine if F is a curl field or not? Explain why or why not. If yes, then determine if it is a curl field or not. (solution)
Transcribed Image Text:Assume that div (x, y, z) = 0 and curlF (x, y, z) = 0. Let D(F) = R3 – {(0,0, k) such that any k is in R.}. (A) Answer the following questions and explain why briefly. Applicable? Test Yes/No Why? Curl Test Divergence Test (B) Do we have enough information to determine if F is a gradient vector field or not? Explain why or why not. If yes, then determine if it is a gradient vector field or not. (solution) (C) Do we have enough information to determine if F is a curl field or not? Explain why or why not. If yes, then determine if it is a curl field or not. (solution)
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