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? ? ? ? ? ? Are the following statements true or false? 1. If F. dr = 0 for one particular closed path, then F is path-independent. 2. If F = Vƒ, then I is conservative. ? 3. The circulation of any vector field F around any closed curve C is zero. + 4. √ F · dr = f(Q) – ƒ(P) whenever P and Q are the endpoints of the curve 5. If Fis path-independent and C is any closed curve, then F. dr = 0. 6. If F. dr ‡ 0 for some closed path C, then F is path dependent. ➡7. If the vector fields ₹ and ☞ have ſ F · ďř : = ? chen F = G. G. dr for a particular path C, 8. If F is path-independent, then there is a potential function for F.

? ? ? ? ? ? Are the following statements true or false? 1. If F. dr = 0 for one particular closed path, then F is path-independent. 2. If F = Vƒ, then I is conservative. ? 3. The circulation of any vector field F around any closed curve C is zero. + 4. √ F · dr = f(Q) – ƒ(P) whenever P and Q are the endpoints of the curve 5. If Fis path-independent and C is any closed curve, then F. dr = 0. 6. If F. dr ‡ 0 for some closed path C, then F is path dependent. ➡7. If the vector fields ₹ and ☞ have ſ F · ďř : = ? chen F = G. G. dr for a particular path C, 8. If F is path-independent, then there is a potential function for F.

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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? ? ? ? ? ? Are the following statements true or false? 1. If F. dr = 0 for one particular closed path, then F is path-independent. с ? Vf, then F is conservative. 3. The circulation of any vector field F around any closed curve C is zero. 4. F. dr 5. If F is path-independent and C is any closed curve, then . dr = 0. 6. If ſc F · ďř ‡ 0 for some closed path C, then I is path dependent. 7. If the vector fields F and G have ſ F · ďr = f G · ďr for a particular path C, 2. If F ? then F = G. = = ƒ(Q) – ƒ(P) whenever P and Q are the endpoints of the curve C. 8. If I is path-independent, then there is a potential function for F.
Transcribed Image Text:? ? ? ? ? ? Are the following statements true or false? 1. If F. dr = 0 for one particular closed path, then F is path-independent. с ? Vf, then F is conservative. 3. The circulation of any vector field F around any closed curve C is zero. 4. F. dr 5. If F is path-independent and C is any closed curve, then . dr = 0. 6. If ſc F · ďř ‡ 0 for some closed path C, then I is path dependent. 7. If the vector fields F and G have ſ F · ďr = f G · ďr for a particular path C, 2. If F ? then F = G. = = ƒ(Q) – ƒ(P) whenever P and Q are the endpoints of the curve C. 8. If I is path-independent, then there is a potential function for F.
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