please answer **Which of the statements is true?****Check all that apply**- □ If \(\vec{F}\) is a conservative vector field in \(\mathbb{R}^3\) then there exists \(f\) such that \(\nabla f = \vec{F}\)- □ If \(\vec{F}\) is a conservative vector field then \(\int_C \vec{F} \cdot d\vec{r}\) will always yield the same value along the curve \(C\) from point \(A\) to point \(B\) *regardless of the path taken*- □ If \(\vec{F}\) is a conservative vector field in \(\mathbb{R}^3\) then \(\text{curl}(\vec{F}) = 0\)- □ Green's Theorem States: Let \(C\) be a positively oriented, piecewise-smooth, simple closed curve in the plane and let \(D\) be the region bound by \(C\). If \(P\) and \(Q\) have continuous partial derivatives on an open region that contains \(D\), then \[ \int_C P \, dx + Q \, dy = \int_D \left( \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \right) dA \]

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Which of the statements it true? Check all that apply If is a conservative vector field in R³ then there exists f such that ▼ƒ = F If is a conservative vector field then SF. dr will always yield the same value along the curve C from point A to point B regardless of the path taken 3 If is a conservative vector field in R³ then curl(F) = 0 Green's Theorem States: Let C be a positively orentied, piecewise-smooth, smple closed curve in the plane and let D be the region bound by C. If P and Q have continous partial derivatives on an open region that contains D, then Sc Pdx + Qdy = SSD(² or)dA ƏQ Ox

Which of the statements it true? Check all that apply If is a conservative vector field in R³ then there exists f such that ▼ƒ = F If is a conservative vector field then SF. dr will always yield the same value along the curve C from point A to point B regardless of the path taken 3 If is a conservative vector field in R³ then curl(F) = 0 Green's Theorem States: Let C be a positively orentied, piecewise-smooth, smple closed curve in the plane and let D be the region bound by C. If P and Q have continous partial derivatives on an open region that contains D, then Sc Pdx + Qdy = SSD(² or)dA ƏQ Ox

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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