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In R3 minus the z-axis, consider the vector field 2(e) = (n Typ me i my2...
2. Consider the vector field F = (z v)a I zy (z + a)2. Consider also...
2. Consider the vector field F = (z v)a I zy (z + a)2. Consider also a frustum of cone defined as: (see figure). Let us call V the volume of this solid. Alio, let S be the closed surface enclosing the volume: S -S1 U S2 U S3, where Si is the flat bottom (z = 1), S2 is the curved surface and Ss is the flat top (z 4). (a) calculate the flux Ф-ISF ds, using the appropriate...
Question 11 (2 marks) Attempt 7 S is the half cylinder 2+y2=9, y>0, 0<z<2 Given the vector field: E=(12+7yz)i+...
Question 11 (2 marks) Attempt 7 S is the half cylinder 2+y2=9, y>0, 0<z<2 Given the vector field: E=(12+7yz)i+(622+72)j+(1322-823)k, Calculate the outward flux (away from the z-axis) of E through surface S. That is find J- 1-48 S Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3*Pi+5/7 J =
Question 11 (2 marks) Attempt 7 S is the half cylinder 2+y2=9,...
Let F be the vector field on R3 given by F(x,y,z)=(2xz,-x,y^2) evalute the volume integral below....
Let F be the vector field on R3 given by F(x,y,z)=(2xz,-x,y^2)
evalute the volume integral below. cheers
19. Let F be the vector field on R given by F(r,y,z) = (2xz, -x, y2) Evaluate 2xzdV, FdV xdV where V is the region bounded by the surfaces 0, y = 6, z = x2 and z = 4. 0, y
Question 11 (2 marks) Attempt 1 s is the half cylinder 2+y2 16, y20, 0Sz1 Given the vector field z-223), Calculate the...
Question 11 (2 marks) Attempt 1 s is the half cylinder 2+y2 16, y20, 0Sz1 Given the vector field z-223), Calculate the outward flux (away from the z-axis) of E through surface S. That is find Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3 Pi+5/7
Question 11 (2 marks) Attempt 1 s is the half cylinder 2+y2 16, y20, 0Sz1...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisph...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisphere of radius 3). (a) Compute the flux of the curl of F across the surface (with upward pointing unit normal vector N). That is, compute actually do the surface integral here. V x F dS. Note: I want you to b) Use Stokes' theorem to compute the integral from part (a) as a circulation integral (c) Use Green's theorem (ie...
3. Consider the vector field A = (x – z)i + (x3 + yz)j – 3xyềk....
3. Consider the vector field A = (x – z)i + (x3 + yz)j – 3xyềk. Use Stokes' theorem to calculate S/CD x A) . nds where S is the surface of the cone z = 2 - V x2 + y2 above the zy plane. You may use the formula n cos" u du = – cos”- u sin u + 2 -1 [ cos”-2 u du.
Q4 only: Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketc...
Q4 only:
Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketch of V. (Hint: You could consider the cross-section of S2 with y-0, and then use the circular symmetry. (b) Express V in cylindrical coordinates. (c) Calculate the volume of V, working in cylindrical...
(a3, y3,4z3). Let Si be the disk in the 12. Consider the vector field in space...
(a3, y3,4z3). Let Si be the disk in the 12. Consider the vector field in space given by F(x, y, z) xy-plan described by x2 + y2 < 4, z = 0; and let S2 be the upper half of the paraboloid given by z 4 y2, z 2 0. Both Si and S2 are oriented upwards. Let E be the solid region enclosed by S1 and S2 (a) Evaluate the flux integral FdS (b) Calculate div F div F...
S is the quarter cylinder 2+y2=4, x>0, y >0, 0< z<1 Given the vector field: E (10-2y)i+(1222+10y)+(14yz-4z4...
S is the quarter cylinder 2+y2=4, x>0, y >0, 0< z<1 Given the vector field: E (10-2y)i+(1222+10y)+(14yz-4z4)k, Calculate the outward flux (away from the z-axis) of E through surface S. That is find Sp.H Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3*Pi+5/7 J =
S is the quarter cylinder 2+y2=4, x>0, y >0, 0
EXERCISE 2 [2.5/10] Given the following vector subspaces: W, Ξ {(x, y, z) E R3 / 0) x + y a) [1.0/10] Calculate base...
EXERCISE 2 [2.5/10] Given the following vector subspaces: W, Ξ {(x, y, z) E R3 / 0) x + y a) [1.0/10] Calculate bases of Wi and W2. b) [1.0/10] Calculate a basis of W1 n W2 c) [0.5/10] Calculate a basis of W1 + W2
EXERCISE 2 [2.5/10] Given the following vector subspaces: W, Ξ {(x, y, z) E R3 / 0) x + y a) [1.0/10] Calculate bases of Wi and W2. b) [1.0/10] Calculate a basis of...
2. Consider the vector field F = (z v)a I zy (z + a)2. Consider also a frustum of cone defined as: (see figure). Let us call V the volume of this solid. Alio, let S be the closed surface enclosing the volume: S -S1 U S2 U S3, where Si is the flat bottom (z = 1), S2 is the curved surface and Ss is the flat top (z 4). (a) calculate the flux Ф-ISF ds, using the appropriate...
Question 11 (2 marks) Attempt 7 S is the half cylinder 2+y2=9, y>0, 0<z<2 Given the vector field: E=(12+7yz)i+(622+72)j+(1322-823)k, Calculate the outward flux (away from the z-axis) of E through surface S. That is find J- 1-48 S Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3*Pi+5/7 J =
Question 11 (2 marks) Attempt 7 S is the half cylinder 2+y2=9,...
Let F be the vector field on R3 given by F(x,y,z)=(2xz,-x,y^2)
evalute the volume integral below. cheers
19. Let F be the vector field on R given by F(r,y,z) = (2xz, -x, y2) Evaluate 2xzdV, FdV xdV where V is the region bounded by the surfaces 0, y = 6, z = x2 and z = 4. 0, y
Question 11 (2 marks) Attempt 1 s is the half cylinder 2+y2 16, y20, 0Sz1 Given the vector field z-223), Calculate the outward flux (away from the z-axis) of E through surface S. That is find Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3 Pi+5/7
Question 11 (2 marks) Attempt 1 s is the half cylinder 2+y2 16, y20, 0Sz1...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisphere of radius 3). (a) Compute the flux of the curl of F across the surface (with upward pointing unit normal vector N). That is, compute actually do the surface integral here. V x F dS. Note: I want you to b) Use Stokes' theorem to compute the integral from part (a) as a circulation integral (c) Use Green's theorem (ie...
3. Consider the vector field A = (x – z)i + (x3 + yz)j – 3xyềk. Use Stokes' theorem to calculate S/CD x A) . nds where S is the surface of the cone z = 2 - V x2 + y2 above the zy plane. You may use the formula n cos" u du = – cos”- u sin u + 2 -1 [ cos”-2 u du.
Q4 only:
Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketch of V. (Hint: You could consider the cross-section of S2 with y-0, and then use the circular symmetry. (b) Express V in cylindrical coordinates. (c) Calculate the volume of V, working in cylindrical...
(a3, y3,4z3). Let Si be the disk in the 12. Consider the vector field in space given by F(x, y, z) xy-plan described by x2 + y2 < 4, z = 0; and let S2 be the upper half of the paraboloid given by z 4 y2, z 2 0. Both Si and S2 are oriented upwards. Let E be the solid region enclosed by S1 and S2 (a) Evaluate the flux integral FdS (b) Calculate div F div F...
S is the quarter cylinder 2+y2=4, x>0, y >0, 0< z<1 Given the vector field: E (10-2y)i+(1222+10y)+(14yz-4z4)k, Calculate the outward flux (away from the z-axis) of E through surface S. That is find Sp.H Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3*Pi+5/7 J =
S is the quarter cylinder 2+y2=4, x>0, y >0, 0
EXERCISE 2 [2.5/10] Given the following vector subspaces: W, Ξ {(x, y, z) E R3 / 0) x + y a) [1.0/10] Calculate bases of Wi and W2. b) [1.0/10] Calculate a basis of W1 n W2 c) [0.5/10] Calculate a basis of W1 + W2
EXERCISE 2 [2.5/10] Given the following vector subspaces: W, Ξ {(x, y, z) E R3 / 0) x + y a) [1.0/10] Calculate bases of Wi and W2. b) [1.0/10] Calculate a basis of...
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