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d) Use the curl test to determine if the following vector fields are conservative on R². If the test doesn't apply state so. If the curl test shows that the vector field is conservative find a potential function whose gradient gives the vector field. i) F¹ = (2xy³ – 3x²y², 3r²y² — 2r³y) ii) É = (-y², x²) iii) F = (x² + y²)i + 2xyj Y I iv) G = x² + y²¹ x² + y²

d) Use the curl test to determine if the following vector fields are conservative on R². If the test doesn't apply state so. If the curl test shows that the vector field is conservative find a potential function whose gradient gives the vector field. i) F¹ = (2xy³ – 3x²y², 3r²y² — 2r³y) ii) É = (-y², x²) iii) F = (x² + y²)i + 2xyj Y I iv) G = x² + y²¹ x² + y²

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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d) Use the curl test to determine if the following vector fields are conservative on R². If the test doesn't apply state so. If the curl test shows that the vector field is conservative find a potential function whose gradient gives the vector field. i) F¹ = (2xy³ – 3x²y², 3r²y² — 2r³y) ii) É = (-y², x²) iii) F = (x² + y²)i + 2xyj Y I iv) G = x² + y²¹ x² + y²
Transcribed Image Text:d) Use the curl test to determine if the following vector fields are conservative on R². If the test doesn't apply state so. If the curl test shows that the vector field is conservative find a potential function whose gradient gives the vector field. i) F¹ = (2xy³ – 3x²y², 3r²y² — 2r³y) ii) É = (-y², x²) iii) F = (x² + y²)i + 2xyj Y I iv) G = x² + y²¹ x² + y²
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