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Calculate div F and curl F.

Calculate div F and curl F.

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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If F is a vector field on R with F = F¡i+ F2j + F3k then the curl of F is the new vector field given by curl F = Vx F i+ dz dz ´ƏF2 =)j+ k dy provided that these partial derivatives exist. In two dimensions, we often treat the curl as a scalar function: If F(r, y) = Fii+ F2j, then curl F 5. Here is a graph of the vector field F(x,y) = (x – y² + 2) i + (ry + y) j. 11 (a) Calculate div F and curl F. (b) Evaluate div F and curl F at the point (-1,1). Explain the meaning of each number. (c) Evaluate div F and curl F at the point (-1, –1). Explain the meaning of each number.
Transcribed Image Text:If F is a vector field on R with F = F¡i+ F2j + F3k then the curl of F is the new vector field given by curl F = Vx F i+ dz dz ´ƏF2 =)j+ k dy provided that these partial derivatives exist. In two dimensions, we often treat the curl as a scalar function: If F(r, y) = Fii+ F2j, then curl F 5. Here is a graph of the vector field F(x,y) = (x – y² + 2) i + (ry + y) j. 11 (a) Calculate div F and curl F. (b) Evaluate div F and curl F at the point (-1,1). Explain the meaning of each number. (c) Evaluate div F and curl F at the point (-1, –1). Explain the meaning of each number.
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