3. Stokes theorem x² + y² + z² = 1, Relative to vector field -1 ≤z≤-1/2 F: = (2z, 3x, -y). counterclockwise and draw the graph

Q: Sketch the gradient vector field for the funtion f(x, y) = xy.

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Q: ey+y°.

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = tan(4x + 5y+z) . F(x, y, z) =

A: given  f(x,y,z)=tan(4x+5y+z)we know that formula of gradient field is→gradient…

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: We have to find the rate of heat flow out of a sphere of radius .

Q: Use the fact that \bF = (2xy + 3cosy) bi + (r? - 3xsiny) bj, is a gradient vector field to evaluate…

A: Given F = (2xy+3cosy)i+(x2-3x siny)j As F is a gradient vector field, it can be rewritten as F=∇f…

Q: a For the function = x²y+yz at the point (1,2,-1), find its rate of change with distance in the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let + y³)%¸ æyz 7 4 F = x² + be a vector field on U = {(x, y, z) E R° | (x, y) + (0, 0)}. Find its…

A:

Q: Given the vector field F = (In(x + 2z), xy, xyz). Calculate curl F(-1,1,1).

A: Solution:-

Q: Determine the line integral if the vector field is F(x, y) = x²yî – 2xyf On a rectilinear path that…

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Q: Compute the curl of the vector field F = sin(x) i+ cos(y) j+ 8z3 k

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Q: Consider the vector field v(x)=(y/(x^2+y^2))i − (x/(x^2+y^2)) j + 4k. Calculate ∫Cv dr, where C is…

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Q: Compute the curl of the vector field F = (r', y³, z*). curl(F(r, y, z)) = %3D What is the curl at…

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Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: the gradient vector field of f(z, y) = In(x + 4y) %3D Work

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = x²y³z¹. F(x, y, z) =

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Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: A sphere of radius 1 is x2 + y2 + z2 = 1. Parametrize the sphere as follows:Now,calculate the…

Q: A constant field vector is given by E = -5a_p + 10a_0 + 3a_z. Calculate the vector component of E at…

A: The problem is related to vector. The topic is multidimensional geometry. We find the component of…

Q: Find the gradient vector field of f(x, y, z) = ln (xy² +sin yz³ - 5x^z)

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Q: 1. Let F =i+y^2j +z^4k. Find the general flow lines for this vector field. Present the flow line…

A: Consider the provided question,

Q: Find the Curl of the vector field. F(x,y, 2) = 3e" sin(y)i+ 7e* cos(y)j+ &z k cos (y)i+ &z k. %3D…

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Q: f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?

A: To check whether it is a curve, vector or surface. f(x,y) = 2x3+4y3-3x2-120x-192y+5

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: