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Let F= r²i+ (2xy + x) j+zk. Let C be the circle x² + y² = 1 and S the disk a² + y² ≤ 1 within the plane = 0. (a) Determine the flux of F out of S. (b) Determine the circulation of F around C. (c) Find the flux of VX F. Verify Stokes' theorem directly in this case.

Let F= r²i+ (2xy + x) j+zk. Let C be the circle x² + y² = 1 and S the disk a² + y² ≤ 1 within the plane = 0. (a) Determine the flux of F out of S. (b) Determine the circulation of F around C. (c) Find the flux of VX F. Verify Stokes' theorem directly in this case.

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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4. Let F²i+ (2xy+xa) j+zk. Let C be the circle x² + y² = 1 and S the disk 2² + y² ≤ 1 within the plane z = 0. (a) Determine the flux of F out of S. (b) Determine the circulation of F around C. (c) Find the flux of VX F. Verify Stokes' theorem directly in this case.
Transcribed Image Text:4. Let F²i+ (2xy+xa) j+zk. Let C be the circle x² + y² = 1 and S the disk 2² + y² ≤ 1 within the plane z = 0. (a) Determine the flux of F out of S. (b) Determine the circulation of F around C. (c) Find the flux of VX F. Verify Stokes' theorem directly in this case.
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