Suppose you need to integrate the vector fieldv – (3 cos z, ef sin y)) along the curve parameterised by r(t) = (t,tt) from the point (1, 1, 1) to the point (3, 9, 27). Which of the following integrals should give the correct ariswer? (31 sin(t) + (1 + 2t)e+ 4 sin(t di (3 cos(t) 9+2te-t+ 3P sin(t)) at (3 cos(3t)+2te-2t +3t sin(4t )) dt (3t sin(3t), 2t(1+26)e-, 2t cos(4) de

Q: 4. Find the work done by the force field F (x,y) = (x + y)î + (xy)ĵ in moving a particle along the…

A: The force field is given by F→ = x+yi^+xyj^ The end points of the straight line along which the…

Q: Consider the force field F = (2xzez — 4, cos³ z, x²eª²z – 3y cos² z sin z Find the work done by F in…

A: Given: The force field is F→=2xzex2z-4,cos3z,x2ex2z-3ycos2zsinz and the given given curve is…

Q: Find the gradient vector field for the scalar function f(x,y)=sin(2x)cos(6y).   Enter the exact…

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

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Q: Compute the curl of the following vector field. F = = (3z2 sin y, 3xz2 cos y, 6xz sin y)

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Q: Find the directional derivative of the field f(x, y, z) = In(4 x) at P = (1, –2, –5) in the…

A:

Q: If a vector field F (x, y, z) = (evz-, In (x² z), sin z), which of the following values is equal to…

A: We have to find div F(-1,0,1).

Q: Find the gradient vector field of f(x, y) = ln(5x + y)

A:

Q: 1. Find one normal vector of the tangent plane to f(x, y) = cos(x² + y²) at point P(1, 1, cos 2).

A: Please check step 2 for the solution.

Q: 10. What is the work done moving a particle from x = 0 to x = 1 m if the force acting on it is F =…

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Q: 3. The vector field F(x,y, z) = (-27x sin(rx² + z), 2ye"",– sin(rx² + 2) – 2) is conservative. Let C…

A: (3)Given:-Fx,y,z=<-2πx sinπx2+z,2yey2,-sinπx2+z-2> is conservative.To find:- ∫C F.dr  where C…

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y) =…

A: It is required to find the conservative vector field for the potential function given in the…

Q: 5. Suppose a particle is moving along a smooth path r(t) with constant speed. If a(t) + 0, show that…

A: Two vectors is perpendicular if their dot product is zero.

Q: 1. Consider the vector field F(x, y, z) = (2e2" cos(3y), –3e²" sin(3y) + Y a. Find divF(x, y, z) and…

A:

Q: then the / r(t)dt is equal to r(t) = (-2 cos (21), 3 sin (4t), In (2t)), Select one: True where C is…

A: Please see the below picture for detailed solution.

Q: Show that the field F = (cos x)i + (- y sin y)j + (z3)k is conservative and Önd a potential function…

A: F = ( Cosx )i + ( -y Siny )j + ( z3 )k  F = gradient ( - Sinx - y Siny - Cosy + z4/4 ). Thus, we can…

Q: (b) Find the derivative of g in the direction of a=2i+curl w at point (0,-1,1) where u u +2 g= In. J…

A:

Q: 2. Calculate the directional derivative of the scalar field U(x, y,z) at the point M,, along the…

A: Given that : U=xz3y-x3y=xz3y-x32y12 The gradient will be calculated as :…

Q: 2) Given the vector field F = (- Vx²+y² 2z2) write the integral to calculate the outward x²+y² flux…

A: We have to find the outward flux across the cylinder x2+y2=100.

Q: Find the conservative vector field for the potential function by finding its gradient. g (x, y, 2) =…

A: We need to find conservative vector field.

Q: Verify if the vector field F = (x° cos(4y), -x sin(4y)) is conservative and evaluate the line…

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Q: Evaluate the line integral of the vector field (3x2 + 3y + 2xy, 3y2 + 3x + x2) along the curve y = x…

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Q: Suppose you need to integrate the vector field v = (3 cos z, e"+y, sin(y²)) along the curve…

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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: The work done by the force field F(x, y) = 5y'i + (x² – 2)j in moving a particle along the arc y =…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: 1,1,0 ex 0,0,0 Show that the vector field defined under the integrals e koct and that the scaler…

A:

Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x F(x, y) = -

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Q: Consider I = ∫CF⋅dr, where (img17) is a conservative vector field and curve C is parameterized by:…

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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: Find the gradient vector field of f(x, y) = ln(4x + 2y)

A:

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

A:

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

A: The solution is:

Q: 4. Evaluate the line integral Vf-r'dt, where the curve C is given by the vector function r(1)…

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Q: Find potential 9, for the conservati ve field the vector F (x, y,a)- (2xe? - y*sinx) î * sinx) î +…

A:

Q: (2) Find the line integral of the vector field F(x, y) = (-1,3) along the path from (2, 3) to (2,…

A: The vector field F→=-1, 3To find line integral of vector field along the path 2, 3 to 2, 5

Q: Show that the vector field =(-2 x²y xy²¹ is conservative by finding all its potential functions.…

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Q: Solve by Laplace transform Utt – 9urz = 0, 0 0 %3D u(0, t) = u(r, t) = 0, %| %3D u (x, 0) = 0,…

A:

Q: The work done in moving a particle in the force field F= x- i+ 3xy j from (0,0) to (1,2) along the…

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Q: Suppose you need to integrate the vector field v = (3 cos z, e+, sin(y)) along the curve…

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Q: Express the field D = (x2 + y)-(xax + yay) in cylindrical components

A:

Q: 6. Compute ſ, F-·dr where f(x, y) = (y² cos x, 2y sin r) and C is the straight line path starting at…

A:

Q: Find the work done in moving a particle in the force field F = (2r + y)i + (3y – 2)j along the…

A: Work done in moving a particle in the force field along along the curve C is:  ∫CF→·dr→ here F→ is…

Q: Without using a potential function, find the total work performed by the force field F(x, y) = (2x…

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Q: Find the work done by the force field F(x,y) = 4yi + 2xj is moving a particle along a circle x2 + y2…

A: Application of integral: The force acting on the particle, F⃗ =4yi+2xj  Let the particle undergo a…

Q: 5) Integrate the vector field h a,y)= y2i+ (2xy-e*)J C parumetrizal by t€ £0, 5 3. over the circular…

A:

Q: The integral of the vector field F(x, y) = (cos |x|, sin y|) A = (-2,0) and final point B (0, 2),…

A: Correct answer is (B) sin(2) - cos(2) + 1 Explanation:

Q: F(x, y) = xỉ + vj and calculate the line integral of along the line segment from (5, 4) to (5, 8).…

A: The solution are next step

Q: Compute the divergence and curl of the vector field cos (22 ) sin² (z² yz) 10 yz4 – xyz2 at the…

A: We have to find divergence and curl of vector field:

Q: Find the flow of the velocity field F = b. a. Na g (2,8) : 4x (0,0) X (5y² + 1)i + (10xy)j along…

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Q: Express the vector field D = ( x2 + y2 )-1 ( xax + yay ) in cylindrical components and cylindrical…

A: