A new roller coaster design for Canada's Wonderland is pictured below. It's described parametrically by 7(t) = (4 cos(t) + sin(5t), 4 sin(t) – 2 cos(5t), 4 sin(2t)) , where 0

Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+e'cos (y)) j through the right…

A: Given vector field is F=  x2y + ex siny  i + x2 + ex cosy j Curve r2=cos2θ

Q: What would you call the vector field V = yī – xj Solenoidal Solid Cylindrical Symmetric Irrotational

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Q: Given vector field A = 5p sinø a, - pz cosø a, + 2p a̟. At point P(1, T, -1), the vector component…

A: A= 5ρsinϕaρ-ρzcosϕaϕ+2ρaz  at point  P(1,π,-1) =0aρ-1aϕ+2az A that is parallel to  ϕ =π is…

Q: Find the curl of the vector field F (5x sin(y), 2y cos(æ)) curl F =

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Q: Find the work done by the force field F(x, y) =(2y'+2xy, 6xy+x +1) in moving a particle over the…

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Q: The following figure shows a half-cylindrical closed surface, defined by the cylinder x² + y² = 4…

A: As per the question we have to find the total flux of the vector field V through the flat top…

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: Is the vector field F(x, y) = (In y + sin(e²“), #

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Q: 10. For a vector field F = <2xy + y³, x² + 3xy²+ 2y7 find a function f such that F = Vr.

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Q: 2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk to

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Q: If F (x, y) = x2 i + y2 j is a conservative vector field, find its potential function. With the…

A: The solution are next step is

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: A vector field v is expressed in spherical coordinates as v(r, 0, 0) = 2r sin cos o e, +r cos o cos…

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Q: Find the work done by the vector field F = (– 4z, – 3y, – 2x) in moving an object along C in the…

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Q: Find the conservative vector field for the potential function by finding its F(x, y) = x² + 5y2

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Q: Is the vector field F = y? – 2x², 2xy + 3| conserva Yes No yz Is the vector field F y? – x2 con Vy?…

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: (b) Given a vector field F = 5(x² + y²)i+ 2xyj – 3zk, evaluate JI, V· FdV for which the solid D is…

A: Here we use polar form of circle .

Q: (a) Is the vector field | F(x,y) = (xe, ye²) conservative? Justify your answer. If it is…

A: Let the vector field F = Pi + Qj.The above vector field is conservative if and only if dPdy=dQdx

Q: The circuitation of the vector field F(x, y)- (3 + xy´, 4x + xy) along the boundary of the plane…

A: The solution are next step

Q: Consider the following vector field F (x, y, z) = yz cos (xy) i+ xz cos (xy) j+ sin (xy)k (a) Use…

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Q: Is the vector field F(x, y) = (sin(x)ely=3 + 2r cos(r>)y°, -2e)y-3 + 6 sin(x³)»*) conservative?…

A: Consider the given vector field.

Q: Show that the vector field F = 2xyi + (x² – 2 y)j is conservative and evaluate the line integral…

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Q: A new roller coaster design for Canada's Wonderland is pictured below. It's described parametrically…

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Q: Given the conservative vector field, F=(x +y³)i +(2xy +5)j , evaluate th integral F•ds where C is…

A: We evaluate the given integral by using line integral. We parameterized the curve between two…

Q: Find the curl of the vector field F = (6y cos(x), 7x sin(y)) curl F =

A: If  F=f1x,y, f2x,y   thenCurl F=0,0,∂f2∂x-∂f1∂y

Q: For vector field F(x, y, z)=(1+ 9xry, 3x +e, ye' +2= (a) Carefully calculate curl F. (b) Find the…

A: We have to calculate curlF  and total work

Q: a) Determine whether or not the vector field F 8yz, – 6 cos(y) – 8xz, – 8xy + 10z > - is…

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Q: Find the curl of the vector field F = (3y cos(x), 5x sin(y))

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Q: Consider the vector field F = (r²y³, x°y?) Is this vector field conservative? Conservative If so:…

A: Given the vector field &lt;x2y3,x3y2&gt;. We need to: i) Check whether the vector field is…

Q: Find the curl of the vector field F = (3x sin(y), 7y cos(x)).

A: The solution is:

Q: 4. Show, in detail, that any vector field of the form (*,J, 2) = J (*) +8(y)/+h(z)k is irrotational,…

A: To show that the vector field is irrotational.

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: Find a potential function for the vector field F by inspection. F = (4x, 4y) Ф(х, у) 3

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Q: - xy²)i+(eº+ Please compute the work done by the vector field F(x,y) = (sin x+xy x?)j in R?, where C…

A: Given: Fx,y=sinx+xy2i+ey+x22j C is a path goes around the unit square twice. To find: Using…

Q: The vector field A is given by A = 2r cos(r* + 3y")i + 6y cos(2² + 3y*)j. a) Show that A is…

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Q: Consider the vector field F (xr, y) = (2y - 12r*y", 4ry – 9r*y?) is conservative. (a) Show that F…

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Q: The vector field F = (y², 2xy + e³2, 3ye³z + x) is conservative

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Q: The movement of air on the surface of a certain closed controlled space is studied, and every point…

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Q: Find the work done by the vector field F = (- 3z, 4y, 2x) in moving an object along C in the…

A: Work done by any vector field F is given by ∫F.dr where r is the position vector. Dot product is the…

Q: F=cos(x) î+sin(y) ĵ+cos (z) k

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Q: A path C is defined by the parametric equations z(t)=t, y(t) = 2t, 0<t<1, and a vector field is…

A: It is given that a path C is defined by the parametric equations x(t)=t, y(t)=2t, 0≤t≤1 and a vector…

Q: What is the value of a so that the vector field F(x.y)-(y eX+2xy4) i+(ax²y3+ e%)j is conservative? O…

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Q: Compute the curl of the vector field F = 2y3 i+ e j+ cos(x) k curl

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Q: find the curl for vector field F = y³i+ xyj – zk

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Q: 3. For the vector Field E = -(x² + 2y²)âx + (xy)ŷ calculate E dl around the triangular contour (V×…

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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: Consider the vector Field 7 and the curve C below. F(x,y) = (3 +4 ху?) 1 + 4x²yј, C is the arc of…

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Q: Evaluate F Î ds for the vector field F(x, y) = yì – xj counterclockwise along the circle x² + y² = 1…

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Q: Given vector field F(x, y) = (4x³y? – 2xy³,2x*y – 3x?y² +6y³) and curve C defined by C: 7(t) = (t+…

A: Here we will find out the required value.

Q: 4. Given the vector field Č = p² sin o a, + (z² cos – 1)as + (p² – z)a, Determine the x-component of…

A: Given the vector field