Consider D to be the region below the paraboloid z = 3+x² + y² , inside the cylinder x + y² =1 and above the plane z = 1. (a)

Q: Evaluate ff, (F n) dS in the following cases: (a) F = (2y+z, x+z, y − x) and S is the portion of the…

A: (a)

Q: REE - Oct. 1996 13. Find the equation of the plane passing thru the points P(2, -3, 1), P'(5, -3,…

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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: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

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Q: B- Find the area of the ellipse resulting from the intersection of the plane x+y+z=6 with the…

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Q: Let C be the positively oriented square with vertices (0, 0), (2, 0), (2, 2), (0, 2). Use Green's…

A: Introduction: According to Green's Theorem, a line integral of a vector over a closed curve C…

Q: I3D Find the coordinates of the point (x, y, z) on the plane z = 2 x + 2y + 2 whi X = y =

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Q: Sketch the cylinder given by x = 4- Z*2（z square）in three-dimensional space.

A: Given: The equation is x=4-z2. To sketch: The given equation in three-dimensional space.

Q: (c) Find the flux of F through S. Show your work, and circle your final answer. (Note: This exercise…

A: c) Given the field equation, F=-9zi+xexz-2xex2j+12k The surface S is the portion of the plane…

Q: The volume of the solid bounded by the plane 3x+6y-2z=12 and the coordinate planes is O A. 2-2y+4 1…

A: We need to find the volume of the solid bounded by the plane 3x+6y-2z=12. Now,…

Q: (C) (D) 6 32. Let AABC - ADEF and their areas be, respectively 64 cm? and 121, cm2. If EE = 15.4 cm,…

A: Here a given set of questions. The solution to each of the given problem is as follows.

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: 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: 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 the area of the surface. The part of the plane z = 5 + 5x + 2y that lies above the rectangle…

A: given  z = 5 + 5x + 2y               ⇒  ∂z∂x = 5   and  ∂z∂y = 2                  ds =…

Q: Let F(x, y, z) = -3y² + 4z + 6æk and C is the curve of the intersection of the plane x + y + z = 2…

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Q: Use the transformation u = x2 –- y²,v = x² + y² to find ff, xydA where R is the region in the first…

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Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Theorem to…

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Q: Evaluate F.ndS for the given F and o. (b) F(x, y, z) = (x² + y) i+ xyj– (2xz + y) k, o: the surface…

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Q: Find the envelope of the plane y Z + u X a + u + + b+uc = 1.

A: Given Data: Let us consider the given data, xa+u+yb+u+zc+u=1 To Find: The envelope of the plane.

Q: The sphere, x + y² + z? – 4y + 2z – 20 = 0, has a center at which point? (0,-2,-1) (0,2,-1) (2,1,1)…

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Q: Let E be the region in the plane between the two ellipses 4x² +9y? = 1 and 4x2 + 9y2 = 4. Evaluate…

A: Given that two ellipse 4x2+9y2=1 and 4x2+9y2=4 Ans given E be the region in the plane between these…

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A: Surface integral

Q: Find the coordinates of the point (x, y, z) on the plane z = 4 x + 1 y + 2 which is closest to the…

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