I believe i have the div correct here but it is complex and so I think there would be ample room for error.. just wanting to double check a and b
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I believe i have the div correct here but it is complex and so I
think...
a) A vector field F is called incompressible if div F = 0. Show that a vector field of the form F = <f(y,z),g(x,z),h(x,y)> is incompressible. b) Suppose that S is a closed surface (a boundary o...
a) A vector field F is called incompressible if div F = 0. Show
that a vector field of the form F = <f(y,z),g(x,z),h(x,y)> is
incompressible.
b) Suppose that S is a closed surface (a boundary of a solid in
three dimensional space) and that F is an incompressible vector
field. Show that the flux of F through S is 0.
c)Show that if f and g are defined on R3 and C is a closed curve
in R3 then...
Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl...
Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl F Show steps (1 point) Let F (8y2)i(7xz)j+(6y) k Compute the following: A div F В. curl F- i+ k C, div curt F= Note: Your answers should be expressions of x, y and/or z; e.g. "3xy" or "z" or 5 (1 polnt) Consider the vector field F(r,y, ) = ( 9y , 0, -3ry) Find the divergence and curl of F div(F) VF=...
I got the correct answer, but how does the r|r|^2 formula work? My work is shown...
I got the correct answer, but how does the r|r|^2 formula work?
My work is shown in the second picture.
Calculate the divergence of the following radial field. Express the result in terms of the position vector r and its length r. F= (x,y,z) (x2 + y2 + z2) =r|r12 Choose the correct answer below. A. The divergence of F is 51114. OB. The divergence of Fis 0. OC. The divergence of F is OD. The divergence of Fis Il...
Consider the vector field. F(x, y, z) = (3ex sin(y), 3ey sin(z), 5e7 sin(x)) (a) Find...
Consider the vector field. F(x, y, z) = (3ex sin(y), 3ey sin(z), 5e7 sin(x)) (a) Find the curl of the vector field. curl F = (-3d"cos(z))i – (36*cos(x)); – (5e+cos(y) )* * (b) Find the divergence of the vector field. div F = 3e'sin(y) + 3e'sin(z) + 5e+ sin(x)
Tutorial Exercise Use the Divergence Theorem to calculate the surface integral ss F. ds; that is,...
Tutorial Exercise Use the Divergence Theorem to calculate the surface integral ss F. ds; that is, calculate the flux of F across F(x,y,z) 3xy2 i xe7j + z3 k S is the surface of the solid bounded by the cylinder y2 + z2-4 and the planes x4 and x -4. Part 1 of 3 If the surface S has positive orientation and bounds the simple solid E, then the Divergence Theorem tells us that div F dV. For F(x, y,...
(1)Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j (2)...
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this...
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this vector field b) Determine the divergence of this vector field c) If this vector field shows a flow field, explain if the flow is rotational or irrotational. Also, explain if the flow is compressible or incompressible. d) Compute the rate of change of Q(x, y, z) at Po in the direction of r, where P(x, y,z)=2xy + xe”; Po = (-2,1, 6) and r=-2i+j+6k
this is calculus 4 and i need work shown Consider the following region R and the...
this is calculus 4 and i need work shown
Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate the double integral in the flux form of Green's Theorem. F = (-x-Y); R=(x,y): x² +y? 59 a. div F- b. Set up and evaluate the integral over the region. Write the integral using polar coordinates, with r as the radius and as the angle. U rdrdo
(1 point) Verify that the Divergence Theorem is true for the vector field F = 3x´i...
(1 point) Verify that the Divergence Theorem is true for the vector field F = 3x´i + 3xyj + 2zk and the region E the solid bounded by the paraboloid z = 9 - x2 - y2 and the xy-plane. To verify the Divergence Theorem we will compute the expression on each side. First compute div F dV JE div F= Waive av = f II Σ dz dy dx where zi = MM y1 = y2 = MM мм...
It is divergence free and an open surface so I think you have to think of...
It is divergence free and an open surface so I think you have
to think of it as a closed surface and subtract the flux of the
unit circle. Thank you!
6 7. (4 pts) Without using a calculator, find the flux of the vector field } = (1 + 21+2) 7 + ze +17+ (x² + y2) through S: the portion of the open surface x2 + y2 = 1 – 24 (as shown) above the ty-plane, oriented downward.
a) A vector field F is called incompressible if div F = 0. Show
that a vector field of the form F = <f(y,z),g(x,z),h(x,y)> is
incompressible.
b) Suppose that S is a closed surface (a boundary of a solid in
three dimensional space) and that F is an incompressible vector
field. Show that the flux of F through S is 0.
c)Show that if f and g are defined on R3 and C is a closed curve
in R3 then...
Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl F Show steps (1 point) Let F (8y2)i(7xz)j+(6y) k Compute the following: A div F В. curl F- i+ k C, div curt F= Note: Your answers should be expressions of x, y and/or z; e.g. "3xy" or "z" or 5 (1 polnt) Consider the vector field F(r,y, ) = ( 9y , 0, -3ry) Find the divergence and curl of F div(F) VF=...
I got the correct answer, but how does the r|r|^2 formula work?
My work is shown in the second picture.
Calculate the divergence of the following radial field. Express the result in terms of the position vector r and its length r. F= (x,y,z) (x2 + y2 + z2) =r|r12 Choose the correct answer below. A. The divergence of F is 51114. OB. The divergence of Fis 0. OC. The divergence of F is OD. The divergence of Fis Il...
Consider the vector field. F(x, y, z) = (3ex sin(y), 3ey sin(z), 5e7 sin(x)) (a) Find the curl of the vector field. curl F = (-3d"cos(z))i – (36*cos(x)); – (5e+cos(y) )* * (b) Find the divergence of the vector field. div F = 3e'sin(y) + 3e'sin(z) + 5e+ sin(x)
Tutorial Exercise Use the Divergence Theorem to calculate the surface integral ss F. ds; that is, calculate the flux of F across F(x,y,z) 3xy2 i xe7j + z3 k S is the surface of the solid bounded by the cylinder y2 + z2-4 and the planes x4 and x -4. Part 1 of 3 If the surface S has positive orientation and bounds the simple solid E, then the Divergence Theorem tells us that div F dV. For F(x, y,...
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this vector field b) Determine the divergence of this vector field c) If this vector field shows a flow field, explain if the flow is rotational or irrotational. Also, explain if the flow is compressible or incompressible. d) Compute the rate of change of Q(x, y, z) at Po in the direction of r, where P(x, y,z)=2xy + xe”; Po = (-2,1, 6) and r=-2i+j+6k
this is calculus 4 and i need work shown
Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate the double integral in the flux form of Green's Theorem. F = (-x-Y); R=(x,y): x² +y? 59 a. div F- b. Set up and evaluate the integral over the region. Write the integral using polar coordinates, with r as the radius and as the angle. U rdrdo
(1 point) Verify that the Divergence Theorem is true for the vector field F = 3x´i + 3xyj + 2zk and the region E the solid bounded by the paraboloid z = 9 - x2 - y2 and the xy-plane. To verify the Divergence Theorem we will compute the expression on each side. First compute div F dV JE div F= Waive av = f II Σ dz dy dx where zi = MM y1 = y2 = MM мм...
It is divergence free and an open surface so I think you have
to think of it as a closed surface and subtract the flux of the
unit circle. Thank you!
6 7. (4 pts) Without using a calculator, find the flux of the vector field } = (1 + 21+2) 7 + ze +17+ (x² + y2) through S: the portion of the open surface x2 + y2 = 1 – 24 (as shown) above the ty-plane, oriented downward.
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