Stokes's theorem is a special case of the theorem of Green.

Q: What is meant by Laplace operator?

A: What is meant by Laplace operator?

Q: State the theorem for Vector Surface Integral.

A: More precisely, the divergence theorem states that the surface integral of a vector field over a…

Q: Se) Define moments, skewness, and kurtosis. Mention their applications.

A: Moments are to statistical data/distribution what physical features are for human beings. In…

Q: Integral of Vector A= 2p sin(4)ap +0.5z2cos(4)az along L3 L2 LI L3 180° 30° -5 12.5 20 -12.5 O o o o

A: integral of vector A = line integral (A.dl). First we will calculate A.dl along L3 and than we will…

Q: Find equations of the tangent plane and normal line to the surface z + 19 = xe cos z at the point…

A: We have to find tangent plane equation and normal line.

Q: Calculate directional derivatives and gradients in three dimensions. Find an equation for the…

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Q: Find the unit tangent vector at the point with the given value of the parameter t.

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Q: What is basically purose or used of stokes and greens thoeom? Exapain it details with application

A: Stroke's theorem is basically the Generalization of green's theorem. Green's theorem is circulation…

Q: Define Vector Line Integral.

A: A line integral is the integral of some function along a curve. One can integrate a scalar-valued…

Q: PART 2 - MOMENT OF INERTIA 1. Determine the radius of gyration of the shaded area with respect to…

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Q: laplace of a2u2(a)

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Q: 1. A particle moves a distance of 150ft along a straight line. As it moves, it is acted upon by a…

A: As per our honor code, we are answering only the first question. The distance traveled by the…

Q: Write the importance of stokes theorem. Also write statement and proof of Stokes theorem.

A: Importance of Stoke's Theorem:-  This theorem gives the relationship between the surface integral…

Q: Q4 (a) Define Gauss's theorem and Stokes' theorem.

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Q: Use Stokes' theorem to calculate c

A: Given,        F=xzi^+2zj^-xyk^ and C is the intersection of the plane y=z+2 with cylinder…

Q: find the equation of the plane tangent line anch normal r= Cost cos (et) Cost Simlz) } + Sint Ŕ

A: Given that, r=costcos2ti→+costsin2tj→+sintk→

Q: laplace of a2u4(a)

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Q: Can Stokes' Theorem be used to find the flux of F through S? Clearly answer yes or no, and then…

A: Given, F→=-9z,xexz-2xex2,12 and S is the portion of the plane 2x+3z=6 that lies in the first octant…

Q: What is the difference between homogeneous and non-homogeneous equations? What makes homoge- neous…

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Q: Laplace equation is called a harmonic function. Let the functions u = u(x, y) and v = v(x, y) be of…

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Q: What is a di¡erentiable curve’s unit tangent vector? Give an example.

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Q: Write an equation in general form of the tangent plane to the surface x^2+siny + z^3 = −4 at the…

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Q: What is the relationship between Green’s Theorem and Stokes’ Theorem?

A: Recall the statement of Stokes theorem. The Stokes theorem gives the relationship between the…

Q: Find the moment of inertia: y = x³; x = 1; y = 0 about x = -1.

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Q: What formulas are available for writing a moving object’s acceleration as a sum of its tangential…

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Q: State ONE (1) application of Stokes’ theorem in the field of engineering.   PLEASE CLEAR

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Q: Use Stokes' Theorem to evaluate curlF · dS, where

A: Let, F→=xyz , xy , x2yz. Stokes theorem states that ," Where C is the boundary of surface oriented…

Q: What is the relationship between Stokes’ Theorem and the Fundamental Theorem of Calculus?

A: Solution: Stokes Theorem: Stoke's theorem states that ''the surface integral of the curl of a…

Q: Green's Theorem (8x – f,) dA = f dx + g dy %3D (Circulation form)

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Q: What are intermolecular forces? How do they differ from intramolecularforces? What are dipole-dipole…

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Q: Explain the meaning of Stokes’ Theorem.

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Q: Explain carefully why Green's Theorem is a special case of Stokes' Theorem.

A: According to the question, we have to explain why Green;s theorem is a special case of Stokes's…

Q: Evaluate each side of Stokes theorem for a portion of sphere : r=2m , Θ = π/3, 0 < ɸ < π H= 2r cosΘ…

A: This question is about application of stkoes theorem

Q: Problem 2. Using line integral of vector filed, show that the vector filed F = (2ryz,r²z-r,r²y-r) is…

A: If a vector field F is conservative, then it's curl will be zero. If it is not conservative The its…

Q: Can you prove that: the right side = the lift side, please? cosh(x-y)=cosh x cosh y-sinh x sinh y

A: To prove: The identity coshx-y=coshx·coshy-sinhx·sinhy. Formula used: Hyperbolic function:…

Q: Give deep concept about steam line and path line with their mathematical form and all respects? This…

A: The objective is to define the terms streamlines and path lines along with their mathematical forms.

Q: What is Stokes stream function ? Derive and explain its mathematical relationship.

A: The stream function at a point has been defined as the quantity of fluid moving across some…

Q: The Stokes' theorem states that: Ir = || (v-V)-n do True False o

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Q: What does the differential equation = Orepresent in polar plane? A family of parallel straight lines…

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Q: the max and min directional derivative and their directions; (4) the parametric equation of the…

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Q: ■ Use Stokes’ Theorem to evaluate curl F dS

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Q: Describe the particle's acceleration

A: Given s(t) = t (2t - 1)2 and t = 2s The velocity v(t) = s'(t) = 12t2 + 1 - 8t The acceleration a(t)…

Q: Sketch the velocity field V= in the first quadrant.

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Q: Find a vector normal to the surface x2 + y2 − z = 0 at the point (3, 4, 25). Find the equations of…

A: Given: The equation of the surface x2+y2-z=0 at the point (3,4,25)

Q: Define Gauss's theorem and Stokes theorem.

A: We will define first the Gauss's theorem then we will define the stokes theorem.

Q: Solve for an equation of tangent plane and parametric and equations of normal line to the given…

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Q: Stokes stream fuction defination

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Q: find inverse laplace of frs)= los-3 25-S %3D

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