Use Stokes' theorem to evaluate // V x 7.1 ds where 7 = (9y²z, 3xz, 6x²y²) and S is the paraboloid z = x² + y² inside the cylinder x² + y² = 1, oriented upward.

Q: A particle is under the influence of the force F= (-cosh (4x4) + xy)i + (e-y + x)j. The corner…

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Q: Use Green's Theorem to compute y dx+(x³+3xy²) dy where C is the closed curve around the triangle…

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Q: Find the moving tri hedral of f R CE) = t, 2E> at %3D

A: This is a problem of differential Geometry.

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: The number of antelope in a national park is modeled by the function dA A that satisfies the…

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

Q: Use Stokes' theorem to evaluate Ĝ - dĩ, vhere Ĝ(1, Y, 2) = (2r, y,0) and D is any closed curve.

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Q: 1 (x+y')* dy dx -J3X 2

A: Double integration of function gives the area under the function curve. Double integration can be…

Q: At what point on the paraboloid y = x² + z² is the tangent plane parallel to the plane 3x + 2y + 3z…

A: Introduction: Let z=f(x, y) be the equation of a surface S in R3, and let P=(a, b, c) be a point on…

Q: 5. Find u-dr for a unit square in the first quadrant with vertex at the origin by Stokes's C theorem…

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Q: Use Stokes' Theorem to caleulate ſ. F - dř, where F = zyi+3=3+5zk, and C is the closed path around a…

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Q: Use Stokes' Theorem to compute 1 z? dx + (ry) dy + 2020 dz, where C is the triangle with vertices at…

A: Given I=∮C12x2+xydy+2020dz where C is the triangle with vertices at 1,0,0 , 0,2,0 , 0,0,2 traversed…

Q: A =-4i +3j +k B =-3i +2j – 5k AB AC C =-6i – 2j +k Y 中 are Vertices of this triangle? B BC C nluoto…

A: Note: since you posted multiple question. As per our guidelines we are supposed to solve one for…

Q: Prdlem 6.36 Pert B)

A: It is double Integral

Q: ntegrate ze²² dz where C from 1 along the axes to i C

A: (.)   Given integral is,    where  along to the axes to .(.) If a function is analytic then integral…

Q: (b). Use Green's Theorem to evaluate SF. dr. F(x, y) = (e³x², 2xy), where C is the triangle from…

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Q: 2 w2 In(w) dw

A: To evaluate the integral ∫12w2lnwdw

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: H=pz coup ap te'sing a4 tp'ar At point (1, ,0)

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Q: Let F = < 4x + y², 5y + z, 9z + x So F. dī, Use Stokes' Theorem to evaluate C where C is the…

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Q: Let Q be the rectangle formed by (0, 0, 0), (1, 0, 0), (0, 1, 1) and (1, 1, 1) oriented CCW as x² dx…

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Q: Describe all extensions of the identity map of ℚ to an isomorphism mapping ℚ(3rd root of 2) onto a…

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Q: the value of $[(3x + 4y) dx + (2x + 3y2) dy] around the circle x² + y² = 4. Find the line integral…

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Q: a. Find the normal vector to the tangent plane b. Find an equation of the tangent plane to the given…

A: What is Parametric Surface: The concept of parameterized curves is extended to vector-valued…

Q: By changing to spherical coordinate, evaluate (a) z' Vx² + y² +z² dz dy dx (b) " ST* E x² + y° +z?…

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Q: At what point on the paraboloid y = x + (x, y, z)=( is the tangent plane parallel to the plane 3x +…

A: The given parabola is y=x2+z2 .Let f(x,y,z)=x2+z2-y. Also the given plane  is 3x+4y+3z=2.

Q: Use Stokes' Theorem to find m # 0 satisfying F · dr = -5, whereF(r,y, z) = (3yx² + z³, y², 4yx²) e C…

A: Given:

Q: Find the tangent plane to the elliptic paraboloid z = x² – 2y at the point (1,1,1). - O A. z = 2x –…

A: Given that: z=x2-2y2      and point is:   (1, 1, 1)