9. Let F = (0,-z, 1). Let S = {(x, y, z) | x² + y² + z² = 1, z ≥ }}. FdS using the Verify that F = curl A, where A = (0, x, xz) and evaluate 11.2. theorem of Stokes.

Q: 8. Compute the directional derivative of the following function at the given point P in the…

A:

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A: This question is about to check vector space.

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A: If vector field then from the question

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A: Here we have to find the work done using Stokes'  theorem.

Q: 49. Let f(x, y, z)=sin(x² + y² +2²). (a) Describe in words the shape of the level surfaces of f. (b)…

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Q: Let F = (y², x, z²)and S be the part of the paraboloid z = x² + y² with z < 1 and outward facing…

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Q: II. Let RVsx, Y be uniform on triangle with vertises (0, 0), (2, 2), (2, 2). Find 1. Joint pdf…

A: Note: As you've posted multiple questions, the first one will be answered as per our policy.Also,…

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Q: Find symmetric equations of the normal to the surface, r (u, v) = at a point (1, 1, 3

A: given ru,v=&lt;u2,v2,u+2v&gt; therefore ru=∂∂uu2i+∂∂uv2j+∂∂uu+2vk=2ui+0j+k…

Q: Let f(x,y, z) = a² + 2y² +z² and g(x,y,z)=z-xy. Find a unit vector u satisfying D.f (1.1,2)= 0 = D,…

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Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: A particle moves along line segments from the origin to the points (3, 0, 0), (3, 5, 1), (0, 5, 1),…

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Q: Let vector field F=(xz,-y,z) and surface, S is a cylinder x² + y² = 4 for 3≤z≤0 with the outward…

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Q: Evaluate the line integral by stokes theorem where F(vector)=[ 0, xyz ,0] , C is the boundary of a…

A: Calculate curl:  curlF=ijk∂∂x∂∂y∂∂z0xyz0         =i-xy+kyz

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A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: RAD, DIV, CURL, V², IRECTIONAL DERIVATIVE + yx, v = [y. z, 4: - x), w = [y". z, x²]. (grad f), div…

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Q: Find both ∂z/∂u and ∂z/∂v , given that F (x, y, z) = xy^2 + z^3 + sin(xyz) = 0.

A: Step 1: Step 2: Step 3: Step 4:

Q: Jika 9b+ 18a =27, dan (2a+b)c =42, nilai (c-3)^2

A: Given if 9b+ 18a =27 and (2a+b)c =42, then we have to compute (c - 3) 2 .

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Q: 12. Let A be the set of all integers = {..-3,-2,-1,0,1,2,3,...}. Define the relation R on A as…

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Q: 4- Teorema de stokes para calcular fr Fido con F(X‚J. Z) = (y² + Z² ) î + (x² + Z²) Ĵ + (x² + y²jk…

A: