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4. Let S be the part of upper cone == (2x +2y)" lies below 2 =1+2....
13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S. 13. (1 point) Let S be the part of the paraboloid 1 222y that lies above...
13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S.
13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S.
Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the f...
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...
Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane. (2) Determine the...
Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane. (2) Determine the parametric equation of the tangent line to C at (1,1.0) (3) Find the plane that carries the tangent line found above and the vector (4) Set up but not solve, a formula that will determine the length of C for 1StS2
Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane....
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone ...
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find the surface area of the part of the plane 2a 4y+z 1 that lies inside the cylinder 2y21. Surface Area2pi
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area
(1 point) Find...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first oc...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first oct...
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and ...
please help with Q1 and 3
1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and below the cone z -Vx2 + y2 (a) Sketch the region V (b) Calculate the volume of V by using spherical coordinates. (c) Find the surface area of the part of V that lies on the sphere z2 y 24, by calculatinga surface integral. (d) Verify your solution to (c) by calculating the surface integral...
The equation z - x ^ 2- 2y ^ 2 + 2x - 4y - 2...
The equation z - x ^ 2- 2y ^ 2 + 2x - 4y - 2 = 0 is given. Surface: a) Explore the type of the intersection curve with the z = 0 plane and draw it. b) Find the tangent plane and normal line at point (0,0,2).
Check that the point (1,-1,2) lies on the given surface. Then, viewing the surface as a level surface for a function f(...
Check that the point (1,-1,2) lies on the given surface. Then, viewing the surface as a level surface for a function f(x,y,z), find a vector normal to the surface and an equation for the tangent plane to the surface at (1,-1,2). 2x^2-3y^2+z^2=3. Vector normal? and tangent plane?
1 3. (10 points) Let S be the quadratic surface given by 22-2-y (a) Classify S...
1 3. (10 points) Let S be the quadratic surface given by 22-2-y (a) Classify S (B) S is a hyperboloid of one sheet (E) S is an (A) S is an (D) S is an (b) Find the equation of the tangent plane to S at the point (1,1, v3) (C) S is a hyperboloid of two sheets ellipsoid elliptic cone elliptic paraboloid point P(ro.Mo, 20) on S where the tangent plane to S at the point P contains...
13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S.
13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S.
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...
Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane. (2) Determine the parametric equation of the tangent line to C at (1,1.0) (3) Find the plane that carries the tangent line found above and the vector (4) Set up but not solve, a formula that will determine the length of C for 1StS2
Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane....
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find the surface area of the part of the plane 2a 4y+z 1 that lies inside the cylinder 2y21. Surface Area2pi
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area
(1 point) Find...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
please help with Q1 and 3
1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and below the cone z -Vx2 + y2 (a) Sketch the region V (b) Calculate the volume of V by using spherical coordinates. (c) Find the surface area of the part of V that lies on the sphere z2 y 24, by calculatinga surface integral. (d) Verify your solution to (c) by calculating the surface integral...
1 3. (10 points) Let S be the quadratic surface given by 22-2-y (a) Classify S (B) S is a hyperboloid of one sheet (E) S is an (A) S is an (D) S is an (b) Find the equation of the tangent plane to S at the point (1,1, v3) (C) S is a hyperboloid of two sheets ellipsoid elliptic cone elliptic paraboloid point P(ro.Mo, 20) on S where the tangent plane to S at the point P contains...
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