IF F= 3yI - Xy I+ 9ZK and s is the Surface of the Pasabolied 2X =x2 fy Bounded By Evaluate %3D I=2 ff(VXF). ds ising stoks theorem,

Q: Assume S is the surface x1000 + y8000 + z1000 = 1,000,000 and F = [9 + ee^(xyz), x8yz, 3x - 5y -…

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Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Evaluate exp{}dA where R is the region in the ry-plane bounded by the trapezoid with vertices (0,…

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Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: Find the area of the cap cut from the paraboloid y^2+z^2=2x by the plane x=2

A: To Find: Area of the cap cut from the paraboloid y2+z2=2x by the plane x=2.

Q: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

Q: Suppose F 2.xz + 3y²) ay + (4yz²) az. (a) Calculate fLL F dS, where S is the shaded surface in…

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Q: Sketch the surface x = 2y2 +3z2

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Q: Calculate SS dxdy D (x+y)² in Surface D limited to curve y=x² and the lines 2 Y=x+2 and x = 1.

A: Given:  integral ∫∫Ddxdy(x+y)2  in the surface D limited to curve y=x2 , y=x+2, x=1  To Find : value…

Q: Find the area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x =…

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Q: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3

Q: d(fv) = df ^ ¢v + fdý %3D

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Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: Sketch the surface 1<z</9-x² - y² and x²+y² <1

A: To sketch the given surfaces.

Q: Evaluate | F-dS, where F(x, y, z) = (3y, –2x, –), %3D and S is the surface that is composed of the…

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Q: Graph the surface 1 = y2 + z2 –- by first sketching at least three cross sections in each of the xy…

A: We have to sketch the graph of the following surface in the 3D space: . First we have to sketch the…