Sets in cylindrical coordinates Identify and sketch the following sets in cylindrical coordinates.
11.
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Calculus: Early Transcendentals (2nd Edition)
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
Precalculus (10th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
- (4) Express the surface of the conez=2*sqrt(x^2+y^2)using equations (or inequalities) in...(a) cylindrical coordinates.(b) spherical coordinates.arrow_forwardfind a parametrization of the surface. 1.The upper portion cut from the sphere x2 + y2 + z2 = 8 by the plane z =-2 2. Parabolic cylinder between planes The surface cut from the parabolic cylinder z = 4 - y2 by the planes x = 0, x = 2, and z = 0arrow_forwardWhat symmetry will you find in a surface that has an equation of the form r = ƒ(z) in cylindrical coordinates? Give reasons for your answer.arrow_forward
- Change from rectangular to cylindrical coordinates. (a) (0, −1, 2) (r, ?, z) =arrow_forwardA circular helix in xyz-space has the following parametric equations, where θ ∈ R. x(θ) = 4cosθ y(θ) = 4sinθ z(θ) = 3θ Let L(θ) be the arclength of the helix from the point P (θ) = (x(θ), y(θ), z(θ)) to the point P (0) = (4, 0, 0), and let D(θ) be the distance between P (θ) and the origin (0, 0, 0). Let L(θ) = 10. Which statements do hold? a) θ = 4 b) θ = 2 c) To calculate the value of D for a given θ, x(θ) and y(θ) have to be evaluated explicitely. d)D(θ)= 52arrow_forwardA lamina occupies the part of the disk x2 + y2 ≤ 49 in the first quadrant. Find the center of mass of the lamina if the density at any point is proportional to the square of its distance from the origin. Hint: use polar coordinatesarrow_forward
- a parametric position vector is defined as pictured - the final condition makes sure of a positive radius plots show space curves for the pos. vector alpha = 3, beta = 1, k = 2, h = 4, and w = 1. cylindrical vector definitions x = p cos(phi), y = psin(phi), z = z , p = sqrt(x^2+y^2), phi = arctan(y/x) a) find when the velocity vector r'(t) is perpendicular to the position vector (pictured) b) simplify the answer to a) for the parameter values used to construct the space curve in thefigure. Is the result consistent with the space curve?arrow_forwardDescribe the set in cylindrical coordinates. x^2 + y^2 + z^2 ≤ 1arrow_forwardThe disc S is the intersection of the massive sphere x2+ y2+ z2≤2 and the planex = y.(a) Use spherical coordinates to find a parametrization of the surface S.(b) Calculate ∫∫xy dσS.arrow_forward
- Let S be the surface given by the section of the unit sphere that lies above the cone z = Sqrt(x^2 + y^2).For the standard parametrization of the sphere, give the appropriate intervals of theta and phi to plot S. part 2. Let the orientation of S be such that the normal vectors point away from the origin. What is the normal vector r(small phi) x r(small theta) at the coordinates (0.5,0,sqrt(3)/2)?arrow_forwardA lamina occupies the part of the disk x^2+y^2<16 in the first quadrant. find the center of mass of the lamina if the density at any point is proportional to the square of its distabce from the orgin. Use polar coordinates (x,y)=arrow_forwardChange from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ θ ≤ 2π.) a) (4,-3,9)arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,