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? ? ? ✓ 4. If F = ▼ ƒ, then F is conservative. 5. Sc F · dr = f(Q) – ƒ(P) whenever P and Q are the endpoints of the curve C. F. dr = 0. 6. If F is path-independent and C' is any closed curve, then

? ? ? ✓ 4. If F = ▼ ƒ, then F is conservative. 5. Sc F · dr = f(Q) – ƒ(P) whenever P and Q are the endpoints of the curve C. F. dr = 0. 6. If F is path-independent and C' is any closed curve, then

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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Questions 4-6 please

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