Verify Stoke's Theorem for F(x, y, z) = (3y, 4z, −6z) and S is the part of the paraboloid z = 9x² - y² that lies above the xy - plane with outward facing normal.

Q: ermine the point(s) on the surface z = 30x - 28y - 5x² - 7y² at which the tangent plane is parallel…

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Q: Let F= (0,0, z) and S be the part of the paraboloid z = x² + y² between the plan z = 1 and 2 = 4,…

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Q: Find the surface area of the part of the plane z = 4 + 3x + 7y that lies above the rectangle [0, 6]…

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Q: Verify Stokes' theorem where A = (x-z)i + (x³ +zy)j - 3x y²k and S is the surface of z=2-√√x² + y²…

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Q: Find the surface area of the portion of the part of the paraboloid z = 7 - 2x² – 2y² that lies above…

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Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

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Q: Find a parametrization of the portion of the plane x + y + z = 7 that is contained inside the…

A: According to the given data, find a parametrization of the portion of the plane

Q: Find the regions of the (x, y)-plane where the equation (1+ x) + 2xy; Əxðy + 2y? 2 + x xy? + (1 –…

A: Given equation is, 1+x∂2u∂x2+2xy∂2u∂x∂y+2y2∂2u∂y2+x2∂u∂x-xy2∂u∂y+(1-y)u=0 The equation…

Q: effF.d5 where F-dS Calculate F = (4x³z, 4y³z, 32¹) and S is the surface of the solid bounded by the…

A: The given problem is to evaluate the given surface integral of the given vector field over the given…

Q: Let S be the portion of the plane 2x + 3y + z = 2 lying between the points (-1, 1, 1), (2, 1, −5),…

A: S is the portion of the plane 2x+3y+z=2 lying between the points (-1, 1, 1), (2, 1,-5), (2, 3,-11)…

Q: sin(7y), 8x2+7x°cos(7y)). vative servative n of the parabola y=x2-16 from (4,0) to (-4,0). Which of…

A: We have to choose the option

Q: F = (x² – y²,x, 2yz); C is the boundary of the plane z = 6 – 2x – y in the first octant.

A: Given, F=x2-y2,x,2yz Find the line integral ∮CF·dr in the following. Here C is the boundary of the…

Q: The points on the surface x2−2y2−3z2 = 33 at which the tangent plane is parallel to the 8x+4y+6z=5…

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Q: Find a vector parametric equation for the ellipse that lies on the plane 4x - 4y + z = -7 and is…

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Q: Consider the ellipsoid 4x2 + 2y2 + z² = 27. Find all the points where the tangent plane to is…

A: We have to find the points.

Q: Find the points on the surface 1x² + 1y² + 3x² = 1 at which the tangent plane is parallel to the…

A: We know that two planes are parallel if their normal vector are parallel. That is their, gradient…

Q: Determine the intersection of the hyperbolic paraboloid z = (y2/b2) − (x2/a2) with the plane bx + ay…

A: Given The hyperbolic paraboloid equation is z=y2b2-x2a2 and the plane bx + ay − z = 0 .

Q: Use Stokes' Theorem to evaluate of intersection of the plane x + 3y +z = 12 with the coordinate…

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Q: True or False: The vector (10, 2, –4) is normal to the surface x2 + y? – 22 = 22 at the point P =…

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Q: • SS,F. F = (4x³z, 4y³z, 3z¹) Calculate F.ds where and S is the surface of the solid bounded by the…

A: Given,                           F→=4x3z, 4y3z, 3z4, and S is the surface of the solid bounded by…

Q: Evaluate ff F.n ds where F(x, y, z) = 12xi +24j+24x²k and is that portion of the paraboloid z = x² +…

A: We will find normal vector n and region of integral on xy plane to find value of integral .

Q: Calculate |E F.dr, where F(aа, у) — (2? —Зу)і+(ye®)j and the сurve and curve ' is the parabola х %3D…

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