Use the Divergence Theorem to find the outward flux of F = (4x³ + 3xy²) i+ (3y³ + eˇsin z) j + (4z³ + eº cos z) k across the boundary of the region D: the solid region between the spheres x² + y² + z² = 1 and x² + y² + z² = 2.

Q: Use Stokes' theorem to evaluate the surface integral I of the two-form w = dŋ, with n = (xz+ yz²) dæ…

A: η=(xz+yz2)dx+(sin(y)+z+5x)dy+xyz dzz=13-x2-y2,   z≥9 F→=xz+yz2i+(sin(y)+z+5x)j+xyzk z=9⇒9=13-x2-y2…

Q: Use the Divergency Theorem to evaluate F. Nds and find the outward flux of F through the surface of…

A: F(x,y)=(xy2+cosz)i+(x2y+sinz)j+ezkS:z=12x2+y2,z=2. By using Divergence theorem to evaluate the…

Q: Let F(x,y,z) = ztan(y2) i + z³In(x² + 4)j+z k. Find the flux of F across the part of the paraboloid…

A: Given that, F(x,y,z)=ztan-1(y2)i+z3ln(x2+4)+zk To find flux of F: Divergence theorem:…

Q: Use the Divergence Theorem to evaluate [/F F. N ds and find the outward flux of F through the…

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Q: Let E be the solid bounded by the xy-plane and paraboloid z = 4 - x2 - y2 so that S is the surface…

A: According to question, Paraboloid z =4-x2-y2,Fx, y, z = xz sinyz + x3 i + cosyz j + 3zy2-ex2 +y2 k

Q: Use Gauss' Divergent Theorem to calculate F. dS, where F = (2x + sen (e+1)) i+ 3yj+ cos(z?)k and S…

A: Given

Q: Use the Divergence Theorem to evaluate [/F. F.N dS and find the outward flux of F through the…

A:

Q: (5) Find the area of surface of -3. (a) The part of the paraboloid z = 1 - ² - y² that lies above…

A: The given problem is to find the surface area for the given surfaces over the given region. a) Part…

Q: 5.PT. PLN has $140000 to invest. The alternative investments and the corresponding annual returns…

A: According tot he given information it is required to form an linear programming problem for the…

Q: Evaluate . F dr where F(x,y,z) = (cos x, -2x, y + sin(z³)) and C is the boundary of the triangle…

A: This is a problem of surface integral.

Q: Tell whether each of the following questions is biased or fair. Why? a. What type of music do you…

A: Part(a) The correct option is option A. Because in option A has the  question does not make an…

Q: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

Q: Evaluate the flux integral F-ds where Pis the part of the paraboloid -= 4-x -y above the xy plane…

A: Any integral which is to be evaluated at the surface is called the surface integral. Divergence…

Q: Let S be the solid obtained by rotating the region bounded by C1: y = x2 − 6x + 9 = (x − 3)2 and C2:…

A: The given curves are y=x-32, and y=x+3. To Sketch: The region bounded by the above curves and which…

Q: Use Stokes' Theorem to evaluate fF.dr if F(x,y,z) =( z-y)i +(x+z)]- (x +y)K and C is the curve of…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = 3x°i+ 3.x²yj+ 33xyk across the surface…

A: According to the given information, it is required to use the divergence theorem to find the flux.

Q: 2) Find the outward flux of F across the region D where F(x, y, z) = (In(x² + y²), –tan'(), zVx² +…

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Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(x, y, z) = x²i+ %3D Pj+ z°k.

A: Given: x+32+5y-22=16 Fx,y,z=x2+y2+z2

Q: Use the Divergence Theorem to find the flux of F(x, y, z) = 3x³i + 3x²yj + 24xyk across the surface…

A: Flux of a vector field over a closed surface is equal to the divergence of the field in the volume…

Q: Use Gauss’ theorem to evaluate F.ndS for the given F and o. (b) F(x, y, z) = x³ i+x?yj+xy k, o : the…

A: We will use gauss divergence theorem to find value of given surface integral  If E is a  simple…

Q: The complex potential of a line vortex of strength k centred on the origin is W=iklnz. Determine the…

A: The objective of this question is to find the complex potential of two line vortices of the same…

Q: Integrate VX F, F = (3y, -xz, -yz) over the portion of the surface 2z = x² + y² below the plane z =…

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