Which of the following best describes the surface with parameterization r(u, v) = (4 cos (v), 4 sin (v), u²), over the parameter domain D = {(u, v) | 0 ≤ u ≤ 7, 0 ≤ v ≤ 2n}? Select the correct answer below: O Circular cone O Circular cylinder O Circular paraboloid Elliptic cone O Elliptic cylinder O Elliptic paraboloid

Q: [10] (1) GIVEN: The surface : xy + 2xz+z z² + y2 + 2, and the point P₁ = (1,– 1,1). Note that P. €…

A: Given surface: xy+2xz+z=z2+yz+2 i.e., xy+2xz+z-z2-yz=2 Let f(x,y,z)=xy+2xz+z-z2-yz Here ∇f=i…

Q: Sketch and describe, in your own words, the surface S parametrized as follows: r(u, v) = (3 cos v,…

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Q: 2. Consider the surface defined by 1² + 2xy + y² + 2²-25 Let F(x, y, z)-1² + 2xy + y² + 2². (a)…

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Q: Given the surface 2x² + y² = 3+z², (a) find the points on the surface where the tangent plane is…

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Q: B Suppose we want to find all the points on the surface gx, y) x+ 4y - 4 where the tangent plane is…

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Q: Let S be the parametric surface, parameterized by r(u, v) = e" cos vi + e" sin vj + uk, (u,v) E D =…

A: given S be the parametric surface, parametrized by  ru,v=eu cosv i^+eu sinv j^+u k^  here…

Q: Let S be the surface with defining equation x + 12y + 12z + 8yz = 16. Find all points P = (a, b, c)…

A: The function of the surface is given by:  fx,y,z=x2+12y2+12z2+8yz-16=0

Q: If f(x)=14-x^(2) and g(x)=\sqrt(x+31), compute g(f(3)). Simplify your answer as much as possible.

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

A: We need to find points of intersection.

Q: 6. Find the surface area of the surface defined parametrically as r(u,v) = (v cosu, cosu,sinu), for…

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Q: 2. -) Consider the surface x² + y²-2xy-x+3y-z=-4 at the point Po(2, -3, 18). Determine the…

A: Let's find equation of tangent plane and parametric equations of normal line.

Q: The parametric representation of the surface y2 - 4y + z2 = 0,0 < x < 3 is a) 7(u, v) = (v, 2 + 2…

A: solution:y2-4y+z2=0 , 0≤x≤3considery2-4y+z2=0∴y2-4y+4+z2=4∴y-22+z2=22

Q: Match the parametrizations to the surfaces shown in the figures. Þ(u, v) = v 4² u cos(v) (u, U) = |…

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Q: Evaluate F dS, S where 4 F(x, y, z) = (3y, -2x, -), and S is the surface that is composed of the…

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Q: The parametric representation of the surface x² – 6x + z² = 0,0 < y < 2 %3D is a) (u, v) = (3 cos u…

A: The general form of the parametric equation of the surface in three-dimensional space is given by…

Q: 9. Justify why the surfaces below are not pairwise locally isometric (a) Sphere S1 = {(x, y, 2) e R…

A: This is a problem of Differential Geometry.

Q: In each of the following cases, draw each solid Q bounded by the surfaces whose equations are given…

A: To graph the below surface that is in the first octant. x2=−z−3z=2y+z=3

Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: Determine whether the statement is true or false. Assume the space is R3 The plane x+y+2z=4 does…

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Q: 28 Describe the surface withe cylindrical equabion p?+z?=9. [ Oraw it and Solve it] .

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Q: Describe the surface with parameterization r(u, v) = (3 cos u, 3 sin u, v) 0 < u s 0svS3. Select the…

A: Given surface with parameterization r(u,v)= &lt;3 cos u, 3 sin u, v&gt;

Q: 7. Consider the parametric surface S given by r(u, v) = 3u cos vi+ 3u sin vj + u? k, for 0 <u < 2,…

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