Find the divergence of the following vector field. (x.y.z) F= 2 y 4 +x + 9y The divergence of F is

Q: Make a sketch of the following vector field. F= (2y.x)

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Q: Find the divergence of the field. F = (2x+7y-8z)i + (5x +3y+6z)j + (-6x-y+2z)H div F =

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Q: If F =  P i + Q j + R k is a vector field on R  3  and aP/ax , aq/ay and  ar/az exist, hen the…

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Q: Consider the vector field F = (5x + 6y, 6x + 4y). F - dr along the curve C given by r (t) = (t², t*)…

A: ∫CF→·dr→=∫abF(r(t)) r'(t) dr

Q: What is the divergence of the vector field f=3x i+5xy j+xyz'k at the point (1, 2, 3). Select one: а.…

A: Solution:-The given vector  field is Step:-1    f=3x2i+5xy2j∧+xyz2k∧  then,  we have  to find the…

Q: Find the divergence of the vector field F. F(x, y) = 3xe*i - 9x²y²j

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Q: Q3 Given the conservative vector field, F =(x +y²)i +(2xy +5)j , evaluate the integral F•ds where C…

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Q: Q3 Given the conservative vector field, F = (x +y²)i +(2xy +5)j , evaluate the integral F•ds where C…

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Q: Q4 A) Calculate the divergence of the vector field F=y³i + xyj B) Find the Curl of F(xy.z)=3x²i +…

A: To find out the divergence of vector field.

Q: Find the divergence of the vector field F. F(x, y) = 8xe*i – 7x²y²j |

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Q: Find the divergence of the vector field F. F(x, y) = 3x2i + 5y?j %3D

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Q: Find the divergence and curl of the following vector fields. 25. F(x, y) = (3x + 4y)i + (x − 5y)j26.…

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Q: e) Find the divergence of the vector field at the given point: F (r, y, 2) = In (æyz) (i +j + k);…

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Q: (a)the curl and (b)the divergence of the vector field. F(x,y,z)= ln(2y+3z)i+ln(x+3z)j+ln(x+2y)k

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Q: 2) Find the divergence of the vector field F(r, y, z) = (re") i + (ye") j+ (ryz) k %3D

A: We have to find divergence

Q: Siven the following vector field and orientated curve C, evaluate F•Tds. (x,y) F = on the curve r(t)…

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Q: Find the divergence of the following vector field. (ху 2) F = 22 9 +x +y The divergence of F is

A: Given that: F=<x, y, z>9+x2+y2

Q: (2) For a differentiable vector field f, which of the following is (are) incorrect? (a) ▼ × (▼ × ƒ)…

A: Since we know Formula a→×(b→×c→)=(a→·c→)b→-(a→·b→)c→

Q: Given the following vector field and orientated curve C, evaluate F•Tds. (x,y) F = (x² + y²) on the…

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Q: 10. Evaluate the divergence of the following vector field at the point (0,1,2): F = (xyz, x? + y? +…

A: Given: F=xyz,x2+y2+z2, xy+yz+xz       The point 0,1,2 To find the divergence

Q: 5. Compute the Divergence and Curl of the following vector F F = e²i+ ln (xy)7 + e=v=k

A: Topic - vectors Divergence of F is dot product of F with del operator  Curl of vector is cross…

Q: (7) Find (a) the curl and (b)the divergence of the vector field. F (x, y, z) = xye' i_± yze*k

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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: b) Evaluate both sides of the divergence theorem for the vector field D = 2xyx + x²9 [C/m²] and a…

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Q: F(x.y) = (4xy, - 3y²> A V.F- 4x B VF-1 © v.F = 4x - 6y (D vi--2y

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Q: xi + yj x2 + y2' F(x, y) = k

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Q: Find the divergence and the curl of the vector field .F(x, y, z) = 1 (xi + yj + zk).

A: F(x,y,z) =xi +yj+zkx2+y2+z2 it can be written as F(x,y,z) =xi +yj+zkr   where r =x2+y2+z2 divergence…

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: Find the divergence and the curl of the vector field . F(x,y,z)=1/√(x^2+y^2+z^2 )(xi+yj+zk)

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Q: Find the divergence of the vector field F. F(x, y) = 7XEX¡ – 9x²y2j

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Q: F(x, y, z) = yj – z*k %3D (a) Find the divergence of the vector field

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Q: What is the divergence of the vector field F of F(x,y) = x² i + 2y²j?2 div F = 2x + 4y div F = 4x +…

A: Given: F→=x2i+2y2j

Q: Find the divergence of the following vector field: 00 O 2z O F = (y, -x + z², 3x)

A: We can solve this as follows:

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 山供 得 三 -5+ 5 X 三 -5+ ||| 三 5 BE 州 X x

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Q: Find the divergence of the following vector field. (x.y.z) F= 6+ 4x + 3y 2 The divergence of F is

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Q: Use the divergence of the vector field to compute F(x, y) = (tan-1 (2²)) i + (xy-2 +82²) j 4 fo…

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Q: Find the divergence of the following vector field. F = (2x?yz, - 2xy²z, - xyz²) The divergence of F…

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Q: Consider the vector field F(x, y, 2) = (–7yz, 9xz, –5xy). Find the divergence and curl of F. div(F)…

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Q: Consider the vector field F(x, y) = (x², −y). If (x, y) is in the first quadrant then the vector…

A: Part 1. (x, y) is in the first quadrant.  => x > 0 and y > 0 => x2 > 0 and - y < 0…

Q: Given the following vector field and orientated curve C, evaluate F•Tds. (x.y) F = on the curve r(t)…

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Q: Which of the following is the divergence of the vector field F=x,y,z)? none of these 3. -3

A: The correct option is 3rd option .i.e. 3 .

Q: (a) For any vector field F, the gradient of the divergence of F is always zero.

A: Since the gradient of divergence of F is given by

Q: Find the divergence of the vector field F. F(x,y,2) %3D 6хe\i + 4ye'j

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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: Which graph represents the gradient vector field of f(z,9) = Sz + y

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Q: Q5: Find the divergence of the vector field y F(x, y, z) = x² √yi + =j+zk At the point (2,4,1).

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Q: Find the divergence of the vector field V(x, y, z) = -2xi + (y + 5 cos(x))j+ (7z + e8xy) k.

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Q: Evaluate ∫C F . T ds for the vector field F = x2 i - y j along the curve x = y2 from (4, 2) to (1,…

A: Given information: The value of F=x2i+yj, x=y2 and from (4, 2) to (1, -1). Calculation: Consider…

Q: Find the curl of the vector field F. F=x*yzi + xy²zj + xyz*k curl F = Di+ Di+ (Dk

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Q: Find the divergence of the vector field F. F(x, y) = 3x?i + 4y²j

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