a) Let G be the wedge in the first octant that is cut from the cylindrical solid y² + z? < 4 by the planes y = 2x and x = 0. Evaluate S S S xyz dV.

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

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

Q: 2. Sketch the cylinder y = x² +1.

A: complete graph provided below with python code Explanation:  code behind above :  import numpy as…

Q: A point moves along the intersection of the elliptic paraboloid z = a2 + 3y? and the plane y = 1. At…

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Q: Find the area of the vertical wall whose base is the semicircle {(x, y) | x² + y² = 1 and y>0} and…

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Q: Which graph shows the intersection curve, in the first octant, between a cylinder of equation: (x −…

A: In this question, we need to find the curve which describes the intersection of the surfaces.…

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 +y? + 2? = 1 is T =…

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Q: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

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Q: FIND THE DIVERGENCE AND CURL OF U = i (x 2+ yz)+j Cy?+Zx) t K (z?+xy] %3D

A: Given :u=i x2+yz+jy2+zx+kz2+xy.We need to find the divergence and curl of u.

Q: Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x…

A: In the given question we have to find the double integral of paraboloid z=x2-y2 ovet the triangle…

Q: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: Draw the part that is in the first octant of the cylinder whose equation is 4y² + 9z² = 36 in R³.

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Q: If the two spheres (x-4)^2+(y-1)^2+z^2=27 and (x-13)^2+(y-10)^2+(z+9)^2=a are externally tangent to…

A: Consider the given two spheres x-42+y-12+z2=27 and x-132+y-102+z+92=a are externally tangent to each…

Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

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Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3