ind the work done by the force F=xyi + (y – x)j over the straight line from (- 1,2) to (1, - 2). he amount of work done is ype an integer or a simnlified fraction)

Q: L is the straight line in the xy plane from (0,0) to (2, 2). Evaluate T, F.dr for each of the…

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Q: Use Green's Theorem to evaluate the line integral. cx2 - y?) dx + 5y? dy C: x² + y² = 9 (x² .

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Q: Let f (x, y) = g(u), where u = x² + y² and g(u) is differentiable. Prove that () = 4u du + ax 2.

A: Given, f(x,y)=g(u)=x2+y2 To prove that, ∂f∂x2+∂f∂y2=4udgdu2

Q: Find the work done by a force F = 4i + 9j (in N) in moving an object in a straight line from point…

A: Given:           F=4i+9j

Q: Find the work done by the force F (r, y) = yxi– (x – y) j over the straight line from (1, 1) to…

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Q: Find the work done by a force F = 5i (mag-nitude 5 N) in moving an object along the line from the…

A: Given,

Q: KB is ∀xy F(x, y). Prove using resolution-refutation that ∀xy F(y, x).

A: Solution: First, we convert clauses to CNF : (1) ∀xy Fx,y from KB (2) ∀x Fx,Ax (3) Fx,Ax CNF

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 curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

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Q: Determine la derivada direccional de f (x, y) = y In z en el punto P (1, 4) en la dirección de v = i…

A: Topic:- calculus

Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,-3) to (3,-9).

A: Given force is F→=xyi^+y-xj^ and straight line coordinates are 1,-3 and 3,-9

Q: Use Green's Theorem to find the work done by F(x,y)=x(3x+y)i+xy^2j in moving a particle from the…

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Q: Find the work done by the force F in mving an object from P to Q. F = 2i – 4j; P(0, 0), Q(3, 6)

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Q: السؤال 6 The electro static force given by (ke^2)/r^2, where k=1/ (4nE) 0 صواب İhi

A: False

Q: Calculate the work done by the force F(x, y) = x3yi+ (x - y)j along the parabola y= x2 from (-2, 4)…

A: To find the workdone

Q: c) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x…

A: Stoke's law is given as ∫cF→.dr→=∫s∫∇×F.n→ds F=x2+y2i^-2xyj^ dr→=(dxi^+dyj^) So F.dr=x2+y2dx-2xydy…

Q: Show that(i × j) × j = i × (j × j)Conclude that the Associative Law does not hold for cross…

A: Using the cross products of the unit vectors i,j, k, we obtain

Q: a) Evaluate the line integral TM UTM in terms of 7 where F = cos yi+ rj + ye*k and C is the line F…

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Q: Q1 show thot the force F-ljz-6xz+2xy2) ij+(3xyz-6x²z)is cors.ervotive, hence find the Potenial fum…

A: According to our guidelines, we can answer only the first question or first three subparts of a…

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

A: The given problem is to evaluate the integral using stokes theorem, we have to convert the line…

Q: 21 Work Find the work done by the force F = xyi + (y – x)j over the straight line from (1, 1) to (2,…

A:

Q: An object is moving along the x-axis from x = 1 (Point a) to x = %3D 2 (Point b) according to the…

A: As per guidelines we are solving one question .Please re-post other question.   Given:…

Q: Assume that a spring does not follow Hooke’s Law. Instead, the force required to stretch the spring…

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Q: 222 Compute the work done for a force F=12/x N from x=1 to x=2 m.

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Q: nto v. t of u orthogonal to v.

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Q: What force is required so that a particle of mass m has the position function r(t) = ti + 3t²j +°k?…

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Q: Find the work done by the force F = xyI+ (y– x)j over the straight line from 3) to (1,0). ..... The…

A: Given; F=xyi +(y-x)j.

Q: F/ prove JhaT cosh(z1+2=)=Coshz.coshaa + Sinh2,Snhze

A: Note: You have not mentioned which question to be solved. Here we are providing answer for 1…

Q: Compute the work done by the force along the curve (use defini- tion): 1 F = [3r – y + y] curve is…

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Q: Find div F and curl F if F(x, y, z) = 4y³z'i – 11a"z°j – 4xy°k. - -

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Q: A force F(x) = 10−2x N applied in the positive x-direction moves an object 3m from x = 2to x = 5.…

A: Given that , Fx=10-2x N Work (W)=?

Q: Find the work done by the force F = xyi + (y-x)j over the straight line from (0,0) to (1, - 3). The…

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Q: The work done by the force F = in the displacement along the path C: r(t)=from the point (1,0,0) to…

A: To find the work done by a force

Q: Find the work done for a force F = N from x =2 to x =3 m. x2

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Q: Find the work done by the force F = 7i − 9j in moving an object from the point  (8, 8)  to the…

A: Work done= Force X Displacement

Q: Find the work done by the force F= 6i – 2j in moving an object from the point (1, 7) to the point…

A: Work done by force F→ in moving object from point P to point Q is given by F→.PQ→ , where PQ→ = OQ→…

Q: Find the work done when a constant force F=16l bs moves a chair from x =2.4 to x =3.1 ft. along the…

A: Solve the following

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 F in moving an object from P to Q. F = 200i + 45j; P(-1, 1), Q(300,…

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Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, Yo: 20) is given by the…

A: This is the question from vectors.

Q: 44. Let f(x, y) = g(u), where u = x² + y² and g(u) is differentiable. Prove that 2 4u (dg Әх du

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Q: Find the work done by the force F = eyi + (ln x)j + 3z k, where force is measured in newtons, in…

A: Given information:

Q: Find div F and curl F if F(x, y, z) = 9y%z®i – 4x°z1°j – 5xy°k. - -

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Q: If f(z) = sin(z 2) = U(x, y) + iV (x, y), determine U and V . Verify that the C-R conditions are met…

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Q: Find the work done by the force F in moving an object from P to Q. F = 2i – 4j; P(0, 0), Q(3, 6)

A: First you will calculate the displacement which is equal to final position minus initial position.…

Q: a) Evaluate the line integral S. (2x - y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

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Q: Find the work done for a force F 36 N from x =2 to x =6 m. %3D

A: Here we have to find the work done by the given force on the given interval. Here we use integration…

Q: How much work is required to move an object from x = 1 to x = 3 (measured in meters) in the presence…

A: The function f(x)=2x2. N moves an object from x = 1 to x = 3. We have to find work required to move…