Use a potential function to evaluate the line integral of the vector field F along the curve C. y? çi+2yarctan(x)j 1 + x2 F(x,y) = C:r(t) = t?i + 3tj, Ostsl а. 81/3 b. 18 п/3 С. 9π/4 d. 9π/3 е. 18 п/5 a b.

Q: In words, describe the curve r(t) = (2 sint,e',2 cost) for 0<= t <=6 . Be sure to a -- give enough…

A: To Explain: The parametric curve is r(t)=(2sint,et,2cost) for 0≤t≤6π , so that its graph can be…

Q: For the vector field G = (yey + 3 cos (3x + y))i + (xeªy + cos(3x + y)), find the line integral of G…

A: We find the required integrtion using fundamental theorem of line Integral.

Q: (1) Is the vector field F(x, y) = (2æ*y^ + æ) î + (2a*y³ + y) Î conservative? Support your answer…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: x-y, z + y + 3,z²) and the net is decribed by the equation y = 1- x² - z on

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Q: Find the mass of a wire that lies along the curve r(t)= (t² – 8) j+2tk, 0≤t≤2, if the 3 density is…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Use the equation giving the flux of the vector field across the curve to calculate the flux of F(x,…

A: The given function across C the segment  along the y-axis oriented upwards Now, r= dr=

Q: Suppose a particle, whose initial position is (1, 0, 0), moves with velocity given by v(t) = (-1,…

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Q: 5.- Determine the tangential and normal components of the acceleration for the vector function:…

A: Step 1:Step 2:

Q: What is the work done by a force field F (x, y) := 2x to move a particle in a straight line from (0,…

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Q: Sketch a direction field for the equation y'= 2y(1-y) by hand. Then use that and sketch a few…

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Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: Since the surface is whole sphere, that is S is closed so we can apply Gauss Divergence Theorem.

Q: Find the work done by F over the curve in the direction of increasing t. F = 4zi + 4xj + 4yk, r(t) =…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: A Particle moves 2 X half way around the circle y² = 4 oriented in the counter-clockwise direction…

A: Given force field: and the path of the particle moving half way around the circle  in the…

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Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: We have to find the heat flow out of the sphere of radius

Q: Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then 0…

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Q: 2. Letr =√x² + y² + z². (a) For n ≥ 1 and r> 0, express V(r-n) in terms of r and the radial vector…

A: Given  solution(a): Radial vector field  solution(b):

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: A sphere of radius 1 is x2 + y2 + z2 = 1. Parametrize the sphere as follows:Now,Now,calculate the…

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Q: 2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find…

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