Suppose F(z, y, z) = (z, y, 5z). Let W be the solid bounded by the paraboloid z = x2 + y2 and the plane z = 16.
Suppose F(z, y, z) = (z, y, 5z). Let W be the solid bounded by the paraboloid z = x2 + y2 and the plane z = 16. Let S be the closed boundary of
W oriented outward.
(a) Use the divergence theorem to find the mux of F through S.
(b) Find the flux of F out the bottom of S (the truncated paraboloid) and the top of S (the disk).
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Suppose F(z, y, z) = (z, y, 5z). Let W be the solid bounded by the paraboloid z = x2 + y2 and the plane z = 16.
(1 point) Suppose F(x, y, z) = (x, y, 4z). Let W be the solid bounded...
(1 point) Suppose F(x, y, z) = (x, y, 4z). Let W be the solid bounded by the paraboloid z = x2 + y2 and the plane z = 4. Let S be the closed boundary of W oriented outward. (a) Use the divergence theorem to find the flux of F through S. ſ FdA = 48pi S (b) Find the flux of F out the bottom of S (the truncated paraboloid) and the top of S (the disk). Flux...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly,...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
7. Assume (x, y,x)(2xy, y',5z - y). Let E be the solid upright cylinder between the planes z 0 and z-3 with base the disc x2 + y2 < 9, and let S be the outwardly oriented boundary surface...
7. Assume (x, y,x)(2xy, y',5z - y). Let E be the solid upright cylinder between the planes z 0 and z-3 with base the disc x2 + y2 < 9, and let S be the outwardly oriented boundary surface of E. Note that S consists of three smooth surfaces; the surface Si of the cylinder, plus the top disc Di and the bottom disc D2. Follow the steps to verify the Divergence Theorem. (a) [12 pts.] Evaluate dS directly
7....
Answer all 3 and I will positively rate your answer 1. F(x, y, z) = (x,y2,...
Answer all 3 and I will positively rate your answer
1. F(x, y, z) = (x,y2, z3), S is a surface bounded by the cylinder x2 + y2 = 4,2 = 0 and z = 1. Evaluate the outward flux Sf. Nds using the Divergence Theorem. S 2. F(x, y, z) = (2x3, 2y3, 3z2), S is a surface bounded by the cylinder x2 + y2 = 4, z = 0 and z = 1. Evaluate the outward flux Sf....
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...
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane...
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane. Use the Divergence Theorem to evaluate F.N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results F(x, y, z) =xyì + 7yj +xzk...
Evaluate ∫∫ (x2i+ xyj+ zk) ∙ ndA over the closed surface bounded by the paraboloid S: z = 4 − x2−...
Evaluate ∫∫ (x2i+ xyj+ zk) ∙ ndA over the closed surface bounded by the paraboloid S: z = 4 − x2−y2, on sides, and the bottom plane z = 0 (a) directly, (b) by the divergence theorem.
5. Let E be the solid bounded by the paraboloid y = x2 + z2 ,...
5.
Let E be the solid bounded by the paraboloid y
= x2 + z2 , the cylinder x2 +
z2 = 1, and the plane y = 2. Let S be
the surface of E with outward orientation.
(b) Evaluate the volume integral
FX,Y,Z) = yj + zk We were unable to transcribe this image
Let F(x,y,z) =( x3z)I+(y3z-yz3)j+z4k use the divergence theorem to calculate ∫∫cF•ds, that is , calculate flux of F across S, where S is the surface of the solid bounded by the hemisphere z = √ 2 - x2...
Let F(x,y,z) =( x3z)I+(y3z-yz3)j+z4k use the divergence theorem to calculate ∫∫cF•ds, that is , calculate flux of F across S, where S is the surface of the solid bounded by the hemisphere z = √ 2 - x2 - y2 and the xy - plane .
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in the xy plane.
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
(1 point) Suppose F(x, y, z) = (x, y, 4z). Let W be the solid bounded by the paraboloid z = x2 + y2 and the plane z = 4. Let S be the closed boundary of W oriented outward. (a) Use the divergence theorem to find the flux of F through S. ſ FdA = 48pi S (b) Find the flux of F out the bottom of S (the truncated paraboloid) and the top of S (the disk). Flux...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
7. Assume (x, y,x)(2xy, y',5z - y). Let E be the solid upright cylinder between the planes z 0 and z-3 with base the disc x2 + y2 < 9, and let S be the outwardly oriented boundary surface of E. Note that S consists of three smooth surfaces; the surface Si of the cylinder, plus the top disc Di and the bottom disc D2. Follow the steps to verify the Divergence Theorem. (a) [12 pts.] Evaluate dS directly
7....
Answer all 3 and I will positively rate your answer
1. F(x, y, z) = (x,y2, z3), S is a surface bounded by the cylinder x2 + y2 = 4,2 = 0 and z = 1. Evaluate the outward flux Sf. Nds using the Divergence Theorem. S 2. F(x, y, z) = (2x3, 2y3, 3z2), S is a surface bounded by the cylinder x2 + y2 = 4, z = 0 and z = 1. Evaluate the outward flux Sf....
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...
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane. Use the Divergence Theorem to evaluate F.N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results F(x, y, z) =xyì + 7yj +xzk...
5.
Let E be the solid bounded by the paraboloid y
= x2 + z2 , the cylinder x2 +
z2 = 1, and the plane y = 2. Let S be
the surface of E with outward orientation.
(b) Evaluate the volume integral
FX,Y,Z) = yj + zk We were unable to transcribe this image
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in the xy plane.
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
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