Find a parametrization for each of the following surfaces. [Note: There are many correct answers!] Show...
4. Using spherical coordinates, evaluate the triple integral: ry: dl, where E lies between the spheres r2+94:2-4 and r2+92+ะ2-16 and above the cone V+v) or Recommend separating! 5. Using spherical coordinates, find the volume of the solid that lies within the sphere r2+y2+2 9, above the ry-plane, and below the cone ะ-V/r2 + y2 Reconnnend separating! 6. Using spherical coordinates, evaluate the triple integral: 2 + dV where E is the portion of the solid ball 2+2+2 s 4 that...
Solve c and d Please. Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the first octant. b) The part of the cone zVy that lies between the plane y z and the cylinder y-x c) The surface with vector equation r(u, u) = (u . cos(v), u . sin(v), u) , where 0 u 1, 0 v S T. d) The portion of the unit sphere that...
Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b) (Circular cylinder band) The portion of the cylinder y+z+5)2 25 between the planes x--2 and x-2. Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b)...
Could you do number 4 please. Thanks 1-8 Evaluate the surface integral s. f(x, y, z) ds Vx2ty2 -vr+) 1. f(x, y, z) Z2; ơ is the portion of the cone z between the planes z 1 and z 2 1 2. f(x, y, z) xy; ơ is the portion of the plane x + y + z lying in the first octant. 3. f(x, y, z) x2y; a is the portion of the cylinder x2z2 1 between the planes...
Sketch the described surfaces. Give a parametrization of each. (Be sure to include bounds of parameters as necessary): (a) A cone with its point at (1, 3, 4) and its base a circle of radius 6 on the plane z = 7, centered at (1, 3, 7) (b) A cylinder of radius 3/2 centered at the y-axis, with a base on the plane y = 0 and height going on to y = +. (c) The plane 2x+3y+z=10 restricted to...
(a) Let R be the solid in the first octant which is bounded above by the sphere 22 + y2+2 2 and bounded below by the cone z- r2+ y2. Sketch a diagram of intersection of the solid with the rz plane (that is, the plane y 0). / 10. (b) Set up three triple integrals for the volume of the solid in part (a): one each using rectangular, cylindrical and spherical coordinates. (c) Use one of the three integrals...
11. Evaluate S. 'S*(1 + 3x2 + 2y?) dx dy. 12. Find the volume in the first octant of the solid bounded by the cylinder y2 + z2 = 4 and the plane x = 2y. Graph for Problem 12 13. Find the volume under the paraboloid z = 4 - x2 - y2 and above the xy-plane. N Consider the solid region bounded above by the sphere x + y + z = 8 and bounded below by the...
The region is a cone, z == ? + ytopped by a sphere of radius 4. Find the limits of integration on the triple integral for the volume of the snowcone using Cartesian, cylindrical, and spherical coordinates and the function to be integrated. For your answers 0 = theta, o =phi, and p = rho. Cartesian V= "SC"}, "plz,y,z2) dz dydz where A B = .D= and p(x, y, z) = E= F= Cylindrical v=L" S "*P10,0,2)dz dr do where...
Cale3 Final Take Home (19S) NAME ID Dac Monday (May 6> (Show sact valuc and Show all your work by using both Cyl coordinates for hoth part I and part 2) Cylindrical & Spherical 1. Find the volume of the solid E between +y') fa cone and-xta semi-sphere) by evaluanting the triple insegral V-ldrby any coondinates 2. will he the denominuo i 2 Fins the centroithEbre, Illis an the -axi) he er f formula for the centroid)y Cale3 Final Take...
Let M be the outward oriented capped cylindrical surface which is the union of two surfaces, a cylinder given by x2 + y2 = 25, 0 <z < 1, and a hemispherical cap defined by x2 + y2 + (z – 1)2 = 25, z > 1. For the vector field F = (zx + z2 y + 3y, z’yx + 5x, z4 x2), compute M (V x F). dS in any way you like. DM (V x F). dS...