Let F(x, y, 2) = (z, 1, y). a. Find divF and curlF.

Q: Let f = zy + yx, v = [y, z, 4z - x], w Find - [vª, zª, x®]. (a) grad f and f grad f at (3, 4, 0) (b)…

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Q: Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

Q: Convert the integral  0∫2 0∫2z y∫2y dxdydz in the order a) dzdxdy b) dxdzdy

A: Given: ∫02∫02z∫y2ydxdydz

Q: Let F (r, y, z) = sin y i+r cos yj- sin z k.

A: Given,        F(x, y, z)=sinyi+xcosyj-sinzk.

Q: Find div F and curl F if F(x,y, z) = xzºi+ 5y°x²j+ 5z?yk.

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Q: Let /:R'R. S(x. y.2) = (e' tan y,x' In y). Compute D(f).

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Q: For F(x, y, z) = x²z² i+ sinx z²j+zx²y*k, find div F and curl F.

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Q: Verify if div(curl F) = o for = (x - y) i+ (x +y)j+zk.

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Q: calculate div(F) and curl(F).  F = (x, y, z}

A: Answer(a): div(F)=3

Q: Find div F and curl F if F(x,y,z) = x³i - 6j+yzk.

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Q: Suppose S is the surface where x? + y? + 3z² = 1. Let F be the vector field F = (xy, yz, z?).…

A: suppose S is the surface where x2+y2+3z2=1 let F be the vector field Fxy, yz , z2 claim- evaluate…

Q: Let f(r, y, 2) = e tan(r*z²). Compute fry: (r, y, z) . Simplify your final answer. %3D

A: We will find out the required value.

Q: Let g(r, y) = ye-, r(t) = In(t² + 1), and y(t) = vt. Find g(r(t), y(t)).

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

Q: - Find div F and curl F if F(x, y, z) = 10y¹z7i – 17xªzºj – 3xyễk. div F= curl F=

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: OW Let w = f(x, y, z) and let x =psinocos0 and y = psinosin0 and z = pcoso. Find

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Q: Let f(x,y, z) = xy – yz and v [2y, 2z, 3x]. Find Curl(fv).

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Q: Let u = (x²yz, ry z, ryz?). Compute curl i

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Q: Let f(x, y, z) = ln(x² + z) + y²e®z – cos(2yz). Find fzyn. Zyx ·

A: Given function is  f(x, y, z)=ln(x2+z)+y2exz-cos(2yz)

Q: find laplace of f(x,y,z)=2x3y2z2

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Q: Let ry w = and a = 2s + t, y = st, z = 2s - t dw dw Find ds' at

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Q: ind the curl and divergence of F(x, y, z) = (e², –2ev², 3xe").

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Q: Let f(x, y, z) = 3xyz + y?z. Find the gradient field Vf.

A: Formulae of gradient field is given below

Q: 3. Find the circulation of F 2xi + 2zj +2yk around closed contour %3D

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Q: Find Vf at the given point. f(x,y,z) = x3 + y2 – 3z2 +z In x, (1,2,4) Vil(1,2,4) =Di+j + ()k ( %3D

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Q: calculate div(F) and curl(F). F = (xy, yz, y² – x³)

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Q: Is = xjx + yjy+zźz3 an inner product on R'?

A: No it is not an inner product.  Inner product looks like a dot product.

Q: Find div F and curl F if F(x, y, z) = 4y³z'i – 11a"z°j – 4xy°k. - -

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Q: If y and z are functions of u and v, then the Jacobian of the function transforming (x, Y, z) → (x,…

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Q: Calculate div(F) and curl(F).  F =〈x^2, y^2, z^2〉

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Q: Find the defivativesof y o x with resPect Ysxě_eX

A: To find the derivative

Q: Show that the function u = p(ry) + JFÿ¢(y/x) provides the quation „Pu = 0. dy

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Q: (a) Let f(r, y) = x - 3ry + 18y, where 3r?y- y- 6x = 0. Prove that f(r, y) has extrema at the points…

A: Calculate partial derivative of f(x,y) with respect to x and y ,

Q: Find the curl and also the divergence of F(x, y, z) = (x²z, e" + zz, xyz)

A: The objective is to find the curl and divergence of Fx,y,z=⟨x2z,ey+xz,xyz⟩ Curl and divergence of…

Q: Let T(r,s,t) = (r cos(s) sin(t), r sin(s) sin(t), r cos(t)) Find the Jacobian of T at (3, π/4, π/3)

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Q: What is the largest possible magnitude of Curl(F) where F(x, y, z) = (4, a/9 – y?, 6z)? у, х

A: Given that F→x,y,z=4,x9-y2,6z

Q: Find the curl of the vectòr field F(x, y, z) = 2xyzi + 8yzj + 5zk

A: According to our guidelines we are supposed to do only one question.  Kindly repost other question…

Q: Let F(x,y,z) = (y,x²,zy) where C:R(t) = (cost,sin t , 3t) and t e [0,2]. Evaluate %3D %3D •dR

A: We have to find value of given Integral.

Q: 2. Evaluate the given line integral, (-y, x – y) · dR, where C is the line segment from (2,0) to (0,…

A: Using parametric equation, line integration is evaluated.

Q: Evaluate the fuctions at the given values of the independent variablels.   u= f (w, x, y, z)=…

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Q: 3) Evaluate curl(F F(x, y. =) = (y=+2xy, 2xy + x + =, xy + 23z) to show that is conservative.

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Q: Let i = (x²yz, ry z, zyz?). Compute curl i

A: The given vector is: u→=x2yz, xy2z, xyz2

Q: Find div F and curl F if F(x, y, z) = xz°i+ 4y°x²j+ 52?yk. 3: 62. div F= curl F=

A: A detailed solution is given below

Q: Consider p(x, y, z) = 2xyz - x²y³ v(x, y, z) = xy² + y sin(z) F(x, y, z)= F₂(x, y, z)i + F₂(x, y,…

A: Let F→=f1, f2, f3. The gradient of the scalar field: g is defined as: ∇g=∂g∂x i^+∂g∂yj^+∂g∂zk^. The…

Q: Find div F and curl F if F(x, y, z) = 9y%z®i – 4x°z1°j – 5xy°k. - -

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Q: f(z) dz where a inside r= z-a

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Q: Show that F(x, y, z) = (y² – e* sin z)i + (2xy + z)j + (y – e* cos z)k is conservative and hence…

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Q: Find div F and curl F if F(x, y, z) = 8y°z³i – 11x*z°j – 3xy°k.

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Q: let J, bessel function , if y=x J, , then dy = .a 2 J'1 dx .b 1 J 2 dx .c x J, dx X .d

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Q: Find div F and curl F of F(x, y,z) = (x z³) i + (3x²y1² )j + (3z?y) k

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Q: Find div F and curl F if F(x, y, z) = 16y°z³i – 9x°z°j – 7xy'k. - - div F= curl F=

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