Which of the following best describes the surface with the vector equation r(u, v) = (cos u)i + (sin u)j + vk? %3D O A plane passing through the origin A cylinder whose axis is the z-axis O A sphere of radius 1 centered at the origin O A right circular cone whose vertex is the origin

Q: Let S be the surface of revolution of the curve C: z? + (y+ 5)² = 4. (a) Find a parametrization of…

A: Consider the given information: Let the surface is given by, z2+(y+52)=4

Q: Find the rectangular equation for the surface by eliminating the parameters from the vector-valued…

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Q: Identify the surface with the given vector equation. 5. r(s,t) = < s cos t, s sin t, s>

A: The given vector equation is r(s,t)=s cos t , s sin t, s

Q: a) Find a vector parametric equation for the ellipse that lies on the plane y – 4x + z = -8 and…

A: (a) Given y-4x+z=−8 and x2+y2=4 Let x=ucosv and y=usinv Then z=−8+4x−y ⇒z=−8+4ucosv−usinv Hence,…

Q: Q3 Evaluate Curlv-n, where v=2xyi +(x -2y)j+xzk and ñ is a unit vector normal to the surface shown…

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Q: 1. Evaluate the surface integral fs (r + y + z)dS, S is the parallelogram with parametric equations…

A: We are entitled to solve only one question at a time. As the question number is not mentioned, So we…

Q: Consider the surface given by x²z+ 2yz2 = 3æy?. %3D (a) Find and (b) Find the tangent plane to the…

A: Surface given, x2z+2yz2=3xy2 ....(i) a)we have to find ∂z∂x  and ∂z∂y  Take equation (i) and…

Q: The equation of the tangent plane to the parametric surface x = u, y = v², z = uv at the point where…

A: This question can be solved using the concept of finding the tangent plane when the parametric…

Q: Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u,…

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Q: and v ∈ [1, 3], which describes the surface S represented in the following graph: image1 A normal…

A: Consider the parametrization r (u, v) = (v, 2 cos u, 4 sin u), with u ∈ [ 0 , π/2]and v ∈ [1, 3],…

Q: Describe the surface with the parametrization x(u, v) = cos(u), y(u, v) = sin(u), z(u, v) = for 0…

A: The parametrization, x(u, v) = cos (u), y(u, v) = sin (u), z(u, v) = v, Interval : 0≤u≤2π, v ∈ ℝ

Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the…

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,v)…

A: Please see the explanation below

Q: Consider surface S of the cone S : z = 2/a2+ y² at the point P(1, , V5). (a) Determine the vector…

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Q: Q3 Evaluate Curlv-ñ , where v=2xyi +(x -2y)j+xzk and ñ is a unit vector normal to the surface shown…

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Q: A) N = (0,4 cos u, 2 sin u) %3D B) N = (0, –4 cos u, –2 sin u) C) N = (1,0,0) D) N = (0, –2 sin u, 4…

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Q: Match the parametrizations to the surfaces shown in the figures. Answer Bank u cos (v) Ф (и, v) —D|…

A: (a) ∅(u,v)=(21+u2)cosv, 21+u2sinv,u) Consider x=21+u2cosv, y=21+u2 sinv and z=u…

Q: Q3 Evaluate Curlv•n , where i = 2xyi + (x – 2y)j+xzk and i is a unit vector normal to the surface…

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Q: Let S be the surface pictured below. S has two boundary components: Cj is the unit circle contained…

A: To Determine: let S be the surface pictured below .S has two boundary components  a) which of the…

Q: Evaluate ⌠⌠(x+y)ds, where S is the cone whose parametric equations are x=ucosv, y=usinv, z=2u,…

A: Given  cone whose parametric equations are x=ucosv, y=usinv, z=2u, 0≤u≤3, 0≤v≤π/2 we find the given…

Q: 1. Consider the ellipsoid (a) Parametrize the surface S = r(u,v) by z = a sin(u) sin(v), y = bcos(u)…

A: Using the parameters on the equation of ellipsoid:…

Q: Identify the type of parametric surface produced by the parametric vector function r(u, v) = (2 sin…

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Q: - 2 and Evaluate || curl(F)·dS where S is the portion of the top half of the sphere x +y +z? = 4…

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Q: The ancient Japanese hand fan pictured below is described parametrically by *(u, v) = (v² cos(u), v²…

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Q: Find the area of the surface. The helicoid (or spiral ramp) with vector equation r(u, v) = u cos(v)…

A: Follow step 2nd .

Q: Consider the following surface parametrization. x = 3 cos(0) sin(4), y = 2 sin(0) sin(4), cos(4)…

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Q: 1. Consider the ellipsoid a?a? + B*y? +v°z? = 7? (a) Parametrize the surface S = r(u, v) by x = and…

A: Given  α=1, β=6, γ=13The ellipsoid α2x2+β2y2+γ2z2=γ2and parametrize the surface S=ru,v…

Q: 2) Given vector Á = r?cos²Øâ, + zsinøâg, and function f = r?cosØ + z, find the followings: a) Div.…

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Q: Find

A: We find surface area of given region.

Q: Verify Stokes' theorem for A = (p a, + cos o a, + a:) on the upper half-surface of the sphere x + y?…

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Q: Consider the surface S, where S is the part of the paraboloid  z = x2 + y2  that lies between the…

A: Consider the surface S, where S is the part of the paraboloid  z=x2+y2 that lies between that planes…

Q: Three coplanar forces are given as follows: A = 5 N at 180°, B 13 N at 75°, and C = 9N at 105° .…

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Q: Find a parametrization of the circle of radius 5 in the zy-plane, ce riented clockwise. The point…

A: Given problem:- Find a parametrization of the circle of radius 5 in the xy-plane, centered at the…

Q: Select the correct parametrization of the following curve: The intersection of the plane y = 2 with…

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Q: 1. Identify the parametric surface S given by: r(u, v) = 3 cos ui+ vj + 3 sinu k where 0 <u < 2n and…

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Q: The surface S is parameterized by r(u, v) = (u, 2 cos(v), 2 sin(v)), 1 ≤ u ≤ 3,0 ≤ v≤n. 1. Identify…

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Q: Identify the surface with the given vector equation. r(0,0) = 2sinocosei +2sinosinej +2/1+sin?ok a.…

A: The minimum number of parameters needed to represent a surface is two. Therefore, in general, the…

Q: Find two parametric representations for the part of the ellipsoid 2x + y° + 22- 17 thất lieš tő thé…

A: Given:2x2+y2+2z2=17

Q: Consider the spherical surface E with center at C= ( 4, 3, 2 ) and radius 4 . Let π be the tangent…

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Q: Evaluate the surface integral.     Sy dS,  S is the helicoid with vector equation  r(u, v) =   u…

A: Given, r(u,v)=ucosv,usinv,v Now differentiate above with respect to u partially. We get,…

Q: Which of the following sets of parametric equations is for the surface obtained by rotating the…

A: For a fixed value of z, that is surface cut by a plane z=k it is a Circle, of radius 1/(10+k^2).

Q: Q3 Evaluate Curlvoñ, where v = 2.xyi +(x² – 2 y)j + xzk and i is a unit vector normal to the surface…

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Q: #2. Find an equation of the tangent plane to the given parametric surface at the given point (a) x =…

A: The posted question has multiple questions but according to guidelines we will solve the first…

Q: 12. Find the distance from the point P(0,0,0) to the plane given by x + y +z= 6.

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Q: Use the polar coordinates to evaluate volumes : 1 2) Below z = 1– x² – y² inside x? + y2 above the…

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Q: 1) Calculate the curvature of the position vector 7(t) = sin tax + %3D 2cos tay + V3 sin tāz is a…

A: In this question we have to find curvature and radius of curvature.

Q: (2) Write parametrizations 7(u, v) for the following surfaces (a) a sphere with radius 5 (b) a cone…

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Q: The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but…

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