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6. Let F = (4e" cos(4x), e sin(4x) + 2y) be a vector field and let C be a curve in the first quadrant that starts at (0, 3) and ends at (7/8,0) Use this to answer the following questions. (a) Use partial derivatives to show that is conservative. (b) Determine a potential function f(x, y) such that F =у. Evaluate [... F.dr.

6. Let F = (4e" cos(4x), e sin(4x) + 2y) be a vector field and let C be a curve in the first quadrant that starts at (0, 3) and ends at (7/8,0) Use this to answer the following questions. (a) Use partial derivatives to show that is conservative. (b) Determine a potential function f(x, y) such that F =у. Evaluate [... F.dr.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. Let F = (4e" cos(4x), e sin(4x) + 2y) be a vector field and let C be a curve in the first quadrant that starts at (0, 3) and ends at (7/8,0). Use this to answer the following questions. (a) Use partial derivatives to show that F is conservative. (b) Determine a potential function f(x, y) such that F = у. (c) Evaluate 1. F. dr.
Transcribed Image Text:6. Let F = (4e" cos(4x), e sin(4x) + 2y) be a vector field and let C be a curve in the first quadrant that starts at (0, 3) and ends at (7/8,0). Use this to answer the following questions. (a) Use partial derivatives to show that F is conservative. (b) Determine a potential function f(x, y) such that F = у. (c) Evaluate 1. F. dr.
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