Evaluating a Line
F(x, y, z) =
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Calculus
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- Verifying Stokes’ Theorem Confirm that Stokes’ Theorem holds forthe vector field F = ⟨z - y, x, -x⟩, where S is the hemisphere x2 + y2 + z2 = 4, for z ≥ 0, and C is the circle x2 + y2 = 4 oriented counterclockwise.arrow_forwardUsing Green's Theorem, find the outward flux of F across the closed curve C.F = xy i + x j; C is the triangle with vertices at (0, 0), (4, 0), and (0, 2)arrow_forwardFinding potential functions Determine whether the following vector fields are conservative on the specified region. If so, determine a potential function. Let R* and D* be open regions of ℝ2 and ℝ3, respectively, that do not include the origin. F = ⟨ez, ez, ez (x - y)⟩ on ℝ3arrow_forward
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