Question 5. Consider the vector field F= 2° + y* + 2*)} (z, v, 2). Using the component test, verify that F is conservative. (b) Find a potential function for F. (c) Let S be the quadric surface defined by (r- 1)2 + (y+1)2 + 2z2 = 18. Find the points q on S where the integral %3D F. dr (0,0,0) attain its maximal and minimal values.

Q: Confirm that the force field F(, y) = 2xy°i+ 3x²y² j is conservative in some open connected region…

A: Solution:- The given function is  F(x,y)=2xy3i+3x2y2jpoint P(-9,8) and Q(6,7)we have to find the…

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Q: Consider the conservative vector field 8 4 F(x, y, z) = - 2xz, - 3y²cos(3nz), 3ny sin(3nz) – x² ) 2х…

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Q: Confirm that the force field F = xy²i + x²yj is conservative in some open connected region…

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

A: Given the vector field F→x,y=2xsiny+y2ex,x2cosy+2yex. The particle moves along the curve x=sinπy2…

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A: Given:

Q: 3. A flow is represented by the velocity field (y² + z²)i + xzj + 2x²y²k, check if: a) A possible…

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Q: QUESTION 1 a) Evaluate the line integral F. dr in terms of a where F = cos yi + rj+ ye*k and C is…

A: Work done by the force is the line integral from initial point to terminal point. A force field will…

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A: We will use the Divergence Theorem in 2D to solve the given flux integral.

Q: F(1, y, 2) = (2c" cos(3y), –3e²" sin(3y) + VV:). a. Find divF(x, Y, 2) and curlF(x, y, z). b. Based…

A: This is a problem of multi-variable calculus.

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Q: Find a potential function for the vector field F by inspection. F = (4x, 4y) P(x, y) =

A: Given:

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.

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A: Step2

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A: We have to show that F is conservative. When F is given as F=cosx+2yi+2cosx+2yj For the conservative…

Q: 23. Find the outward flux of the field i + (e + tan'y)j 1 + y², F 3xy %3D across the cardioid r =…

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Q: The flow of a gas with a density of d = 0.001 kg/m2 over the closed curve r(t) = (-sin t)i + (cos…

A: Given information:

Q: 2: Consider the vector field F = (y cos z – z sin y, x cos z – xz cos y, –xy sin z x sin y + 2e22).…

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Q: Question 3 (4-u (2y+z -5y over surface S: f(u, v) =2+v ), (u, v) E [-1,1] x Cive surface integral of…

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Q: Question 2 Find the flux of the vector field F across the surface S in the indicated direction. F =…

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Q: 2. Given F(x, y) = (4x³y² - 2xy³)i + (2x¹y − 3x²y² + 4y³)j is a - conservative vector field. a. Find…

A: To find the potential function for the given conservative vector field :-

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A: Given

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Q: (iv) Find the work done by the force field F(x, y) = x²i+ yeªj on a particle that moves along the…

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Q: I Need help for this question

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Q: Question 3 (2y +z z2 Give line integral of vector field v(x,y,z) = along curve y: ř(t) = | -t),t E…

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Q: Compute the flux

A: Compute the flux

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

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Q: (a) Show that the vector field F(x, y, z) = (1 + 3x²y)i + x³j is conservative and find the potential…

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Q: If F = (4xy – z³) î + 2x² ĵ – 3xz² k is a conservative force field, then scalar potential of F is…

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Q: (iv) Find the work done by the force field F(x, y) = x²i+ye¹j on a particle that moves along the…

A: We have to find the work done by the force using line integral

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…

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Q: he temperature in a temperature-controlled chamber is given by a 3D scalar field Tlx, y, 2) = Ax®yz…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

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

A:

Q: Confirm that the force field F = xy'i+ x²yj is conservative in some open connected region containing…

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Q: Consider the conservative vector field 4 8 F(x, y, z) = – 3y²cos (3nz),37y sin (3tz) – x2). 2xz, %3D…

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Q: d the work done by the force field F in moving a particle along the curve C. F = xyi + 3j + 9xk; C:x…

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Q: he line integral of the vector field F= over the curve C which is the quarter of the rcle from…

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Q: F(x, y, 2) = (y² cos r + 2*)i+ (2y sin æ – 4)j+ (3xz² + 2)k Cos z

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

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Q: 43 Find the work done by the force field F(x, y) = (x² ln(y + 5), -) on a particle 3(y + 5) that…

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Q: 2. Find the circulation and flux of the field F(r.y) = (-y,r) along and across the curve 7(1) =…

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

Q: Consider the vector of electric field Е(х, у.2) %3 (sinh x)1 - (сosh y)) — хуг k a. Compute the…

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Q: - Here is a graph of the vector field F(r, y) = r²i+ y°j. 2 (a) Calculate div F. (b) For which…

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Q: 10. Find the work done by the force F=vx +2y y - 7 for a particle that moves between points (-1,0,1)…

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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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