(5 2ryz the surface x + y° + z? = 1 where z > 0 and the surface is oriented away from the origin. Let v = re cos y, y z, e cos y) be the velocity field of a fluid. Compute the flux of v across Hint: Use the Divergence Theorem.

Q: Find the divergence and curl of the vector function V(x, y, z) = x cos z î + xyz j – sin z k.

A:

Q: Which of the following is the directional derivative of f(z, y) = at the point (0,0) in the…

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A: on solving this we get the

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A: Accleration is given by  a→ =DV→Dt= ∂V→∂t+(V.→∇)V→Here, V→ =2xy i^+xz j^+yz k^Hence, ∂V→∂t= ∂2xy…

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A: Given, wz=iz5cosnt-isinnt=iz5cosnt+z5sinntThen,u=z5sinntv=z5cosnt

Q: Q2: A. For the surface f derivative at (1,1 derivative and the line to the surface

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Q: O Using part (a), compute the directional derivative of f in the following case: 12 3 4 f(x, y, z) =…

A: I am solving  only part (b) as you mentioned.

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

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A: According to bartlrby guidelines we have to answer only first three subparts please upload the…

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A:

Q: tz = g(x, y) = f(3 cos(xy), y + e#") provided that f(3, 7) = 4, f1(3, 7) = 2, (3, 7) = 3. %3D Find…

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Q: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 6) = 7, fi(3, 6) = 2, f2(3,6) = 3. i) Find…

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Q: Q5: For the velocity field vz =xỉ x2 , V2 =2 x² x3 V3 =3 x1X2 X3 determine the rate of stretching…

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A: a)

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Q: 5. Test the Stokes' theorem for the function: V 3xy'x-zcos (2x)ÿ + xy°ż .Do it for the plane surface…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.