· ƒ [‚²³ · F . S F = (4x³z, 4y³z, 3z¹) Calculate dS where and S is the surface of the solid bounded by the hemispheres z = √√25 – x² - y², z = √√√9 — x² - y² and the plano7-0

Q: If a parametric surface given by r₁(u, v) = f(u, v)i + g(u, v)j + h(u, v)k and −4 <u≤ 4,-2 ≤v < 2,…

A: The surface is  and The surface area of the parametric surface given by r1(u,v) =

Q: (1) Let T be the triangle in the xy-plane with vertices at (0,0), (0,2) og (2,2). Calculate the…

A: Let T be the triangle in the xy-plane with vertices at (0,0), (0,2) og (2,2). Calculate the double…

Q: The equation of the tangent plane to the surface 32 = x² + y² +1 at (-1,1,2) is O A.-2x-2y+3z = 2 O…

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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: Which of the following quadratic surfaces describe an elliptic paraboloid shape ? OA. z = 2? – y² +…

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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: 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: Describe and sketch the surface given by the function.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 2 The values of a and b such that the surfaces ax - byz = (a + 2)x and 4x2y + z3 = 4 cut…

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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: 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: / (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: The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid

A: Solution Given The intersection gives z2=1-x2+y2we need to find the centroid

Q: Find the flux of F = z²k upward through the part of the sphere æ² + y² + z² = a² in the first octant…

A: Given vector field is  F=z2k to find the flux through sphere x2+y2+z2=a2 in the first octant.

Q: Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1,…

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Q: Find the center and the radius of the sphere that has the given x2 + y2 + z2 + 10x – 7y + 2z + 26 =…

A: Given a equation of the sphere , x2+y2+z2+10x-7y+2z+26=0 To fin the center and the radius of the…

Q: Find an equation for the sphere centered at (2, 2, –2) and passing through (2, 2, 3). 1. x² + y + z²…

A: Given center is (2,2,-2) and the point is (2,2,3)We know the equation of sphere is…

Q: A region R consists of a square bounded by the lines x = -5, x = 5, y = 0, and y = -10 and a half…

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Q: Use hyperbolic functions to parametrize the intersection of the surfaces x² - y² = 4 and z = 5xy.…

A: Use hyperbolic functions to parametrize the intersection of the surfaces  and (Use symbolic notation…

Q: The cosine of the angle between the planes 2x - y +2z - 3 = 0 and 3x + 2y – 6z – 11 = 0 is (a)를 (b)를…

A: We'll answer the first question since the exact one wasn't specified. 13. For two planes given by…

Q: Find both parametric and rectangular representations for the plane tangent to r(u, v) = u’i + u…

A: Answer is mentioned below

Q: Find the surface area of the portion of the cone x² + y² = z² above the region inside the…

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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…