Find the divergence of the vector field F given by F(x, y, z)=sin(8x)+cos(5y)+z²k a. 8cos(x)-5sin(v) +42³ b. cos(x)+sin(y)+z³ c. 8cos(8x) + 5sin(5y) + 4z5 d. 8cos(8x)-5sin(5y)+4z³ e.cos(8x)- sin(51)+z³ a d b @

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Q: 20) For each vector field F, evaluate the circulation along the curve C consisting of the portion of…

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Q: Consider the vector field. F(x, y, z) = (4e* sin(y), 5e sin(z), 5e² sin(x)) (a) Find the curl of the…

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Q: Use the divergence of the vector field to compute F(x, y) = (tan-¹ (2x) fo tan¯¹ (2x) 4 where is the…

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Q: Find the Curl of the vector field. F(x,y, 2) = 1le sin y i+ 12e* cos(y j+3z k a. (12e* cos(y) +1le"…

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Q: a) Show that F (x, y) = (yexy + cos(x + y)) i + (xexy + cos(x + y) j is the gradient of some…

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Q: Q2. (a) Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k. (i) Determine whether if F is…

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Q: A scalar field is given by f = x2/3 + y2/3, where x and y are the Cartesian coordinates. The…

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Q: Let F(x, y, z) be the vector field (x²(1 + y²z²), Q(x, y, z), exy cos(2z)), where is a…

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Q: Find the divergence of the vector field V(x, y, z) = −4xi + (y + 7 cos(x))j + (9z + 4xy) k. (Give an…

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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: Show that the vector field F(x, y, z) = (-4y cos(4x), 4x sin(–4y), 0) is not a gradient vector field…

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Q: Given the vector field F(x, y, z) =(z cos(xz) + ze“ )î +(3y² +1)j+(xcos(xz) + xe )k 4. (a) Find the…

A: Given F→x,y,z=z cosxz+zexzi^+3y2+1j^+x cosxz+xexzk^

Q: Find the divergence of the vector field V(x, y, z) = −3xi + (y + 4 cos(x))j + (9z+ e5xy) k. (Give an…

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Q: h) Given vector field F (x, y, z) = (2x + 2y + 4z) i + (2y + 2x – 32) j + (2z – 3y + 4x) k. (a)…

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Q: PART A ] (1) Find a complex potential function g(z) of the given vector field F (x,y). (2) find the…

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Q: dr = wa x b dt r X

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Q: A conservative vector field is given as F = 6xe'i + (3x²e" –10yz')j-15y²z°k. Find the potential…

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Q: Let h be the vector field h(x, y, z) = (2xy + ²)i + (x² − 2yz)j + (2x= − y²) k. (a) Show that h is a…

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Q: 2- Calculate the divergence of the following vector functions: (a) V = (r cose) r + (r sine) 0 + (r…

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Q: (9) Determine whether or not the vector field is conservative. If it is conservative, find a…

A: F=Pi+Qj is conservative if ∂Q∂x=∂P∂yGiven F=cos x+ sin y+y sec2xy-2x+y2-2xy2i+2y+2xy-2x2y+xsec2xy+x…

Q: (a) Let F= 2xz2i+j+xy³zk and f(x, y, z) = x²y. Compute the following quantities: (i) Vf (ii) curl(F)…

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Q: Find the divergence of the vector field V(x, y, z) = −3xi + (y + 4 cos(x))j + (9z+exy) k. (Give an…

A: Given that V(x, y, z) = −3xi + (y + 4 cos(x)) j + (9z + e^(5xy)) k.