Which fields in Exercises 1–6 are conservative, and which are not? 1. F = yzi + xzj + xyk 2. F = (y sin z)i + (x sin z)j + (xy cos z)k 3. F = yi + (x + z)j – yk 4. F = -yi + xj 5. F = (z + y)i + zj + (y + x)k 6. F = (e*cos y)i – (e* sin y)j + zk

Q: 11. LetF(x, y) = (ye™ – 6x))i + (xe"» + 4)j %3D (a) Show that F is a conservative vector field. (b)…

A: we need to show F conservative vector field then  potential function f=

Q: gral of the field F(x,y,z) = 7xi + 7yj + 7zk across the portion of the sphere x2 +y² +z? = a? in the…

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Q: For the vector field F(x,y,z) =  2yi +xyj + (2x-xz)k. (i) Show that  (ii) Determine whether if the…

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Q: Find the potential function f for the field F. F= (4x3y10z10, 10x4y9z10 10x4y1029) O fix, y. 2) =…

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Q: 6. Let F = (x³ sin y, a* cos y). COS (a) Is F a conservative vector field? (b) If your answer to…

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Q: Which of the following functions is a potential function for the conservative vector field F(x, y,…

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Q: Show whether or not F is a conservative field. If it is, find a potential function for it and use it…

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Q: For the vector field F(x,y,z)=ya'1+x1+2xyz k a) show that F is conservative vector field; b) find a…

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Q: 6. Consider the vector field F(ar, y) = (8a y+e")î+ (Ka4 + e")j, where K is some constant. -For…

A: Consider the vector field F(x,y)=8x3y+exi^+Kx4+eyj,^ where K is some constant. a…

Q: Find the work done between point 1 and point 2 for the conservative field F. F= (y +z)i + xj + xk;…

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Q: Let f(z) = u(x, y)+ i v(x, y) = U(r, 0) + iV (r, 0). By exploiting the relations x = r cos 0 , y = r…

A: Observe that  consider the polar transformation given in the question, for any complex number, we…

Q: Use the Divergent Theorem to find all values of b> −1 such that ∫∫SFdS = (45b/2) + (51/2), where F…

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Q: find the divergence of the field. F = (x - y + z)i + (2x + y - z)j + (3x + 2y - 2z)k

A: Given Data The field function is fx=x-y+zi+2x+y-zj+3x+2y-2zk.   The expression for the divergence of…

Q: How many of the following vector fields are NOT conservative? F= xyi + yj + zk F= - cos x cos yi +…

A: Check whether the given 4 vector fields are conservative. Since it is a three dimension, a vector F…

Q: Find the divergence of the field. F= (4x + 5y + 7z)i + (8x - 8y + 3z)j + (2x - 7y + 4z)k div F =

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Q: Determine whether the vector field F(x, y) = 5y? (yi + 2xj)is conservative. F is conservative O F is…

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Q: 1. Show that F is a conservative vector field and then find a function f such that F = Vf where F(x,…

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Q: In Exercises 7–8, find a potential function ƒ for the field F. 7. F = ey+2z(i + x j + 2x k) 8. F = (…

A: Since there are multiple question the first question is answered.Kindly re post the question if any…

Q: Find the potential function f for the field F. 2 +y F = -k 2 3 2.2 x +y +C O A. f(x.y.z) = 2 x+y O…

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Q: 6. Given F(x, y, z) = (8x° +z²,-3z, 2xz – 3y), a) Determine whether or notF is a conservative vector…

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Q: 3. Find a field F(x,y) = (M(x, y), N(x, y)) in the xy-plane with the property that at each point

A: Let f = xi + yj  Then F = ff = unit vector = xi+yjx2+y2

Q: Find a potential function for the conservative vector field. F(x, y) = xex*4Y(2yi + xj)

A: If curl f is zero then conservative field

Q: 1. Given F(x, y, 2) = (3y+z*)7+(-6y°z+3x)j+(3xz² -2y')k. a) Show that F(x, y, z) is a conservative…

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Q: Find the potential function f for the field F. 6..6. F=7x°y°z' i+ 6x y°z'j+ 7x'y°z°k O A. f(x,y.z) =…

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Q: the potential function f for the field F = 5x i + 9y j + 4z k. eral expression for the infinitely…

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Q: find the divergence of the field. 1. F = (x - y + z)i + (2x + y - z)j + (3x + 2y - 2z)k 2. F = (x ln…

A: Consider the vector field Substitute the value of vector fields then Hence, the divergence of…

Q: Find the divergence of the vector field F F(x, y, z) = In(x² + y²) i + xy j + In(y² + z²) k

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Q: 4) Determine whether or not F is a conservative vector field. If it is, find a function f such that…

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Q: Find the divergence of the vector field F(x, y, z) = ln(x² + y²)i+ ¤yj+ ln(y² + z² )k 2x 2z + x + x2…

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Q: 3. Determine if F = x*yi+ xyz j + x²y² k is a conservative vector field.

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Q: Find the potential function f for the field F. F= i- k o f(x, y, z) = - 2 + c 2x o f(x, y, z) = - 2y…

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Q: Evaluate both sides for the field- rectangular parallelepiped X = 0 and 1 Y=0 and 2 and Z=0 and 3.…

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Q: Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous…

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Q: Exercise 3 . Let R be commutative zing ao+Q;X+.-+Qg ac"e R[xJ, The derivative f and %3D ('s defined…

A: Given that R is a commutative ring with unity and f=a0+a1x+...+anxn∈Rx and…

Q: 2. Show that F is a conservative vector field and then use that fact to evaluate SF. dr along the…

A: We need to show F is conservative vector field.

Q: Find the divergence of the vector field F. F(x, y, z) = In( 7x²+ 4y² )i + 28xyj + In( 4y2 + 5z2 )k

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Q: Which fields in Exercises 1–2 are conservative, and which are not? 1. F = yz i + xz j + xy k 2. F =…

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Q: Which fields in Exercises 1–2 are conservative, and which are not? 1. F = (z + y)i + z j + (y + x)k…

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Q: Find the divergence of the vector field F(x, y, z) = In(x² + y?)i+ cyj+ ln(y² + z² )k 2x + x + 2z x2…

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Q: 6. Determine whether or not the vector field F is conservative. If so, ind a potential function f.…

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Q: Find the divergence of the field F. yj - xk F= 1/2 +: 2 OA. 3/2 2 -X O B. 3/2 2 X -y OC. 3/2 O D. 0

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Q: Evaluate the work done between point 1 and point 2 for the conservative field F. F = (y + z) i + x…

A: Given: The conservative field F, F=y+zi⏜+xj⏜+xk⏜; P10,0,0, P29,10,18 To find: Work done by force…

Q: Defn `x→- `xj diverges to minus infinity" VR>O 3N, such that Vj zN *j<-R 8;<- R Hw7 het x; = - 8j…

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Q: Find the gradient field F of the function f. f(x, y, z) = In (x 9 + y 9+ 9 F=- In ( y9 + z9ji 9 In…

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Q: Which of the following functions is a potential function for the conservative vector field F (x, y,…

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Q: Determine whether F(x, y) = (In(y) + 2xy³) i+ (3x?y? + x/y) j is a conservative vector %3D field. If…

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Q: Use Stokes's Theorem to evaluate F dr, where F(x, y, z) = x²i+z²j-xyzk and S is z = /169-x² -y² .…

A: As per our guideline we can't use any computer algebra. I calculate both line integral and surface…

Q: Consider the vector field F (x, y) = i-zj and the real-valued function = tan-(#). One has x²+y² f(x,…

A: There is no error(s). All calculations are right. Since a vector field  F¯ is conservative if and…

Q: Find the potential function p, for the conservative vector field F(x, y, z) = (2xe? – y²sin x)î +…

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