Find the gradient vector field of flx, y, z)=x'y+y%z4+xz6 O V flx, y,z)= (3x?y+z°, 5x³y³ + 4y*zA, 4y4z4+ 6xz°) O v flx, y,z)= (3x35+z%, 5x³y^ + 4y°zA, 4y^z3 + 6xz³) O v flx, y, z)= (3x3y³, 5x²y*, 4y^z3> O v fx,y, z)= (z6, 4y²z4, 6xz°)

Q: Calculate the gradient of h(x, y, z) = ÷ 1, Vh <-1/(x^2y)z,-1/(xy^2)z, 1/(xy):

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A: f(x, y) = x^2/(x + y)

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A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Find the total flux of the vector field F= (x^2 z)i + (y^2 z)j+(z^3)k through the closed surface of…

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Q: Find Duf at (2,−1,1) for f(x, y, z) = 3x5y²z³ in the direction given by u = (1/3, 2/3, −2/3).

A: Given function:- fx,y,z=3x5y2z3

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Q: Consider the following problem from Science: A mitochondria with velocity vector r' (t) starts out…

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