Find the work done by the force F (r, y) = yxi– (x – y) j over the straight line from (1, 1) to (2,3).

Q: Find the work done by the force F = zi + xj+ yk in moving a particle along the curve x = t y = t²…

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Q: Find the work done by the force F(x,y)=(x - y') i+xy´ j acting on a point while travelling along…

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Q: Find the workdone in moving a particle in a force field given by f=3xyi-5zj+10xk along the curve…

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Q: 1. Find the work done by the force F(x, y, z) = (xz, z² – x, y ), along C, the curve defined by x =…

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Q: Find the work done by the force field F in moving an object from A to B. F(x, y) = 4y³/2 i + 6x√y j…

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Q: 9. Find the work done by the force F(x, y, z) = e³i + ln(x)j + 3zk, in moving an object over the…

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Q: Q3) Compute the work done by the force field F(x,y,z) = (3x, xz, y) on the curve C, where C is the…

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Q: Find the gradient vector field of f(x, y, z) = 9x² + 8y* + 6z3

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Q: 1) For f(x, y,z) = x2 – (1 – y)? + z?. Find directional derivative of f at P(1, 1, 1) in the…

A: Given that  f(x,y,z)=x^2-(1-y)^2+z^2 Point P(1,1,1) Vector is a=(0,3,4)  To find the directional…

Q: Find the work done by the force F(x, y) = acting on a point along the smooth curve C, where C is the…

A: The given question is from the topic of Advanced Calculus

Q: Find a potential function for the vector field F(x, y) = (14xy + 7y- 8, 7z + 7z). f(x, y) =

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Q: Find the work done by the force field F in moving a particle along the curve C. F(x, y) = (x - y°)i+…

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Q: What is the directional derivative of the function f(x, y, z) = 2xy + z² at the point (1, –1,3) in…

A: The Directional Derivative: Let the function f(x, y) be the height of a mountain range at each point…

Q: Find the work done by the force field F on a particle that moves along the curve C. F(x, y) = (2x +…

A: Formula: The work done by the force field F that moves along the curve C is: W=∫C F·dr Suppose the…

Q: Find the directional derivative, Dvf , of (*) f(x, y, z) = 4x tan 1 at the point P = (1, 1, 1) in…

A: To find the directional derivative of f(x,y,z) at P=(1,1,1) and the Direction, v=(1,2,2).

Q: Find the work done by the force field F in moving an object from A to B. F(x, y) = 6y3/2 i + 9xyj…

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Q: For f(x,y, z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: The directional derivative of a function f  in the direction of the vector u is given by…

Q: Find the gradient vector field Vf of f. 1 f(r, y) = (y – 2)?

A: For a given vector fx, y the gradient vector denoted by ∇f is ∂ ∂ xf∂ ∂ yfSo,=∂ ∂ x12y-x2∂ ∂…

Q: Find the gradient vector field of f(x, y, z) = e3r + 8y+6z

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Q: Find the gradient vector field of f(x, y, z) 5x+ 2y+8z

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Q: 2. Find the directional derivative of the function f(x,y,z) = xy? – 4x?y + z² at (1, -1, 2) in the…

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Q: Find the work done by the force field F(x, y, z) = (x – y², y – z?, z – x2) on a particle that moves…

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Q: Evaluate the line integral faF · dr, where F(x, y, z) = -2xi – 5yj + 5zk and C is given by the…

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Q: Find the work done in moving a particle in the force field F : 3x²i + (2xz - y)j + zk along the…

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Q: Find the work done by the force field F→(x,y)=54x^2y^2i→+(36x^3y−2)j→in moving an object from the…

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Q: Given a scalar function V(x, y) =-(x² +y² ), the directional derivative of V in the direction of the…

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Q: find the work done by the force field F(x,y) =(2y+x²,x²-2x) acting on an object as it moves along…

A: Given: The force field, Fx,y=2y+x2,x2-2x.   To find: The work done by the given force field acting…

Q: Find the directional derivative of f(x, y, z) = x²y−yz³ + z at the point (1,−2, 0) in the direction…

A: Solution:f(x, y, z) = x²y−yz³ + zat the point (1,−2, 0) in the direction of the vector a = 2i +…

Q: Find the gradient vector field (F(r, Y, 2)) of f(x, y, z) = In(4x + 6y + 22) . F(7, y, 2) = (

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Q: Compute the work done by the force field F = , 0 <t<1

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Q: Find the work done by the force field F(x, y) = x sin(y)i + yj on a particle that moves along the…

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Q: Find the work done by the force F = xy i + ( y - x)j over the straight line from (1, 1) to (2, 3).

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Q: Find the work done by the force field F(x, y) = x sin y1 + y J on a particle that moves along the…

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Q: Find the work done by the force field F(x, y) = xi + 2yj on a particle moving along the path C:x =…

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Q: Ex.9 The work of the force F(x, y) = (x², xy²) along the boundary of the square [0, 1] x [0, 1]…

A: The given work force is Fx,y=x2,xy2 along the boundary of the square 0,1×0,1, counterclockwise…

Q: Find the work done by the force field F in moving an object from A to B. F(x, y) = 2y3/2 i + 3x/ỹ j…

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Q: Find the work done by the force field F in moving an object from P(-9, 7) to Q(3, 3). 2.x. F (r, y)…

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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: Let f(x,y)=y2 +sin(y+T)+x +cos(xe). At the point (TT,0) compute the unit vector in the direction of…

A: We have to find the unit vector in the direction of the maximum increase of the function f. This…

Q: For the force field F = (2xe¬Y, (2y – x²e¬y)) in some open connected region containing P(1, 0) and…

A: Given that, F=2xe-y, 2y-x2e-y If F is conservative then ∂2F∂x∂y-∂2F∂y∂x=0

Q: 1. Calculate the work done when a force F = 3xyî – y?j moves a particle in the xy-plane from (0,0)…

A: Take dot product along limit of integration and integrate

Q: (b) Find the directional derivative of the function f(x,y,z) = xy sin z at the point (1,2, %3D T2)…

A: Solution:

Q: Find the work done by the force F(x, y) =(x' – y') i+xy' j acting on a point while travelling along…

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Q: For f(x,y,z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: Since there are two questions posted, we will answer the first question posted (1). If you want the…

Q: Find the gradient vector field of f(x, y, z) = e® 5x+2y+8z

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Q: Find the work done by the force field F(z,y,2) = Ir+v,rs, y+:) on a particle that moves along the…

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Q: Find the work done by the force field F(x,y) = x²yi + y²j around the circle with radius 2.

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Q: Find the work done by the force field F in moving an object on the line segment from A to B, where…

A: Given, Fx,y=2y32 i +3xy j To find the work done by the force field F in moving an object on the line…

Q: Obtain the work done by the force field F(x, y, z)=xi - z³j+zek in moving a particle along a curve…

A: Given  Fx,y,z=xi-z3j+zeyk               =x,-z,zeyr(t)=sin ti+2etk                  0≤t≤π

Q: Find the gradient vector field of f(x, y, z) = e9z+6y+7z V

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