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(b) The surface of the quarter sphere 2+y2+z2=4, y >0, z 2 0, is made of...
2. Consider the conical surface S={(x,y,z)∈R3 : x2 + y2 = z2, 0 ≤ z ≤...
2. Consider the conical surface
S={(x,y,z)∈R3 : x2 + y2 =
z2, 0 ≤ z ≤ 1},
and the vector field
(a) Carefully sketch S, and identify its boundary ∂S.
(b) By parametrising S appropriately, directly compute the flux
integral
S (∇ × f) · dS.
(c) By computing whatever other integral is necessary (and
please be careful about explaining any orien- tation/direction
choices you make), verify Stokes’ theorem for this case.
Let S be the part of the sphere x^2 + y^2 + z^2 = 4 that lies between the cones z = √x^2 + y^2 an...
Let S be the part of the sphere x^2 + y^2 + z^2 = 4 that lies
between the cones z = √x^2 + y^2 and z = √3x^2 + 3y^2.
(1) Let S be the part of the sphere x2 + y2 + Z2-4 that lies between the cones X +y and z a) Find a differentiable parametrization of S b) Find the area of S c) Find 22 dS.
(1) Let S be the part of the sphere...
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)...
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...
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2. 2. (20 pts) Find the surface area of that part of the sphere x2 + y2 +...
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
Let F(x, y,z) = < x + y2,y + z2,z + x2 >, let S be a surface with boundary C. C is the triangle with vertices...
Let F(x, y,z) = < x + y2,y + z2,z + x2 >, let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
Let F(x, y,z) = , let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the pa...
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2. Hints: * Complete the square for ×2 + y2 + Z2-42+ (it is a sphere with center (0, 0,) Find the intersection to determine the region of integration
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2....
ASAP please 1) Compute the surface area of the surface S, which is the part of the sphere x2 + y2 + Z2-4, and that lies between the planes z 0 and z 1. Extra Credit: Does anything strike you as od...
ASAP please
1) Compute the surface area of the surface S, which is the part of the sphere x2 + y2 + Z2-4, and that lies between the planes z 0 and z 1. Extra Credit: Does anything strike you as odd about this answer?]
1) Compute the surface area of the surface S, which is the part of the sphere x2 + y2 + Z2-4, and that lies between the planes z 0 and z 1. Extra Credit: Does...
Evaluate the surface integralG(x, y, z) ds G(x, y, z) (x2 +y')z; S that portion of...
Evaluate the surface integralG(x, y, z) ds G(x, y, z) (x2 +y')z; S that portion of the sphere x2 + y2 + z2-16 in the first octant eBook
Compute in two ways the flux integral ‹ S F~ · N dS ~ for F= <2y, y, z2> and S the closed surface formed by the paraboloid z = x2 + y2 and the disk x2 + y2 ≤ 4 at z = 4. Use divergence theorem...
Compute in two ways the flux integral ‹ S F~ · N dS ~ for F=
<2y, y, z2> and S the closed surface
formed by the paraboloid z = x2 + y2 and the
disk x2 + y2 ≤ 4 at z = 4. Use divergence
theorem to solve one way, and use SSs F * N ds to solve the other
way. (This is a Calculus 3 problem.)
* 36.3. Compute in two ways the fux integral ф...
Evaluatef(x, y, z) dS. f(x, y, z) = x2 + y2 +z2
Evaluatef(x, y, z) dS. f(x, y, z) = x2 + y2 +z2
Evaluatef(x, y, z) dS. f(x, y, z) = x2 + y2 +z2
2. Consider the conical surface
S={(x,y,z)∈R3 : x2 + y2 =
z2, 0 ≤ z ≤ 1},
and the vector field
(a) Carefully sketch S, and identify its boundary ∂S.
(b) By parametrising S appropriately, directly compute the flux
integral
S (∇ × f) · dS.
(c) By computing whatever other integral is necessary (and
please be careful about explaining any orien- tation/direction
choices you make), verify Stokes’ theorem for this case.
Let S be the part of the sphere x^2 + y^2 + z^2 = 4 that lies
between the cones z = √x^2 + y^2 and z = √3x^2 + 3y^2.
(1) Let S be the part of the sphere x2 + y2 + Z2-4 that lies between the cones X +y and z a) Find a differentiable parametrization of S b) Find the area of S c) Find 22 dS.
(1) Let S be the part of the sphere...
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...
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
Let F(x, y,z) = < x + y2,y + z2,z + x2 >, let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
Let F(x, y,z) = , let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2. Hints: * Complete the square for ×2 + y2 + Z2-42+ (it is a sphere with center (0, 0,) Find the intersection to determine the region of integration
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2....
ASAP please
1) Compute the surface area of the surface S, which is the part of the sphere x2 + y2 + Z2-4, and that lies between the planes z 0 and z 1. Extra Credit: Does anything strike you as odd about this answer?]
1) Compute the surface area of the surface S, which is the part of the sphere x2 + y2 + Z2-4, and that lies between the planes z 0 and z 1. Extra Credit: Does...
Evaluate the surface integralG(x, y, z) ds G(x, y, z) (x2 +y')z; S that portion of the sphere x2 + y2 + z2-16 in the first octant eBook
Compute in two ways the flux integral ‹ S F~ · N dS ~ for F=
<2y, y, z2> and S the closed surface
formed by the paraboloid z = x2 + y2 and the
disk x2 + y2 ≤ 4 at z = 4. Use divergence
theorem to solve one way, and use SSs F * N ds to solve the other
way. (This is a Calculus 3 problem.)
* 36.3. Compute in two ways the fux integral ф...
Evaluatef(x, y, z) dS. f(x, y, z) = x2 + y2 +z2
Evaluatef(x, y, z) dS. f(x, y, z) = x2 + y2 +z2
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