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
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- Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.Sketch the solid that results when the given circle of radius length 1 unit is revolved about the horizontal line that lies 1 unit below the center of that circle.
- Find the surface area of the parametric surface 7(u, v) = (2 cos(2u) + v cos(u), 2 sin(2u) + v cos(u), v sin(u)) where -T < uDescribe the surface with parameterization r(u, v) = (2 cos u, 2 sin u, v) , 0Q4) given the surface: cos nx – x²y + exz + 2yz = 2 Find the equation of the tangent plane and normal line at (1,1,2).Let f(x,y) = sin(xy-x-3y+3) a) Find the domain and range of f b) Factor the argument on the sin function. Does this factored form give any hints about the appearance of the surface z = f(x,y) c) Find a relationship for the x cross-sections by letting x = k, k & R. Then, tabulate the relationships for k = 0, 1, 6 and sketch the relationships for k = 3, 4, 5, 6 on E ... the interval y € [1-π, 1+ π] and with respect to the cross-sections for k = 4, describe the cross-sections for k = 0, 1,2 d) Find a relationship for the level curves/contours by letting z = m, me R. By 5,6, recognising the periodic nature of f and ensure that the relationship accounts for it. e) Sketch the contours m = O on the interval x € [-1,7], y € [-3,5]Find the area of the surface generated by revolving the curve x = 3 ,0sys2, about the y-axis. The area of the surface generated by revolving the curve x = ,02 Sketch the parametric surface x = Vu“ +v , y = u, z = v. luFind the points on the surface y² = 16 + xz that are closest to the origin. smaller y-value (x, y, z) = larger y-value (x, y, z) =Let Sbe the surface of the sphere of radius 6 centered at the origin, and let F(x, Y, z) = x°zi+ (3yz3 + 2²)j+ (y² + sin z) k. Find F- dS. Select one: а. 18т b. бл O c. O O d. \(24\pi\) O e. \(12\pi\)ii) Find the area of the surface obtained by rotating the curve y = e- -1Recommended textbooks for youTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,