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3. Consider the field F =< y - 2,2-3, 2-y >. Consider the curve C defined...
a) Draw a surface whose boundary in the curve C b) Use Stoke's Theorem to set...
a) Draw a surface whose boundary in the curve C b) Use Stoke's Theorem to set up the alternative integral to Fodr Let C be the curve of intersection of the plane. X+2=6 and the cyclinder x² + y2 = 9. Where F(x, y, z)=<xy, 32, 7y) and C is the Curve of intersection of the plane X+Z²6 and the Cylinder x² + y2 =9 view as clockwise as above
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 F(x,y) = (27x D = {(1,y): 0 < rº + y2...
3. Consider the vector field F(x,y) = (27x D = {(1,y): 0 < rº + y2 <2}. +ya) defined on the region D where a) Directly compute SF. Tds using the definition of the line integral, where C is the unit circle oriented counterclockwise. b). Use Theorem 3.3 (Test for Conservative Vector Fields) from the text to determine if F is conservative. Is your answer consistent with part a)? If not, what is the source of the discrepancy?
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(...
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(x) from (0,0) to (π, 0) and the line segment from (π,0) to (0,0). 4 3 3. (2 points) Evaluate F di where F.y,(ry, 2:,3) and C is the curve of intersection of 5 and y29. going...
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that li...
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be...
10) Given F(x, y, z) = 4xzi + yſ + 4xyk And a surface S: z...
10) Given F(x, y, z) = 4xzi + yſ + 4xyk And a surface S: z = 9 - x2 - y2, z 20 a) Find Curl(F). Show all support work. 24 b) Use Stoke's theorem to evaluate the circulation flux 8c F. dr where C is the boundary of the surface S as shown in the picture above. Show all support work. GO
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in...
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 27) F 3xi2xj + 7zk; C: the cap cut from the upper hemisphere x2 + y2 + z2 = 16 (z z 0) by the cylinder x2+ y2 =4 27)
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 27) F 3xi2xj + 7zk; C: the cap cut from the upper...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 2yzi...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 2yzi + 3yj + xk and the surface S the part of the paraboloid Z-5-x2-y2 that lies above the plane z 1, oriented upwards. / curl F diS To verify Stokes' Theorem we will compute the expression on each side. First compute curl F <0.3+2%-22> curl F - ds - where y1 curl F ds- Now compute /F dr The boundary curve C...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 3yd-...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 3yd-2ǐ + 2xk and the surface S the part of the paraboloid z = 20-x2-y2 that lies above the plane z = 4, oriented upwards. To verify Stokes' Theorem we will compute the expression on each side. First computel curl F dS curl F- curl F. dS- EEdy di where curl F dS- Now compute F dr The boundary curve C of the...
a) Draw a surface whose boundary in the curve C b) Use Stoke's Theorem to set up the alternative integral to Fodr Let C be the curve of intersection of the plane. X+2=6 and the cyclinder x² + y2 = 9. Where F(x, y, z)=<xy, 32, 7y) and C is the Curve of intersection of the plane X+Z²6 and the Cylinder x² + y2 =9 view as clockwise as above
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 F(x,y) = (27x D = {(1,y): 0 < rº + y2 <2}. +ya) defined on the region D where a) Directly compute SF. Tds using the definition of the line integral, where C is the unit circle oriented counterclockwise. b). Use Theorem 3.3 (Test for Conservative Vector Fields) from the text to determine if F is conservative. Is your answer consistent with part a)? If not, what is the source of the discrepancy?
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(x) from (0,0) to (π, 0) and the line segment from (π,0) to (0,0). 4 3 3. (2 points) Evaluate F di where F.y,(ry, 2:,3) and C is the curve of intersection of 5 and y29. going...
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be...
10) Given F(x, y, z) = 4xzi + yſ + 4xyk And a surface S: z = 9 - x2 - y2, z 20 a) Find Curl(F). Show all support work. 24 b) Use Stoke's theorem to evaluate the circulation flux 8c F. dr where C is the boundary of the surface S as shown in the picture above. Show all support work. GO
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 27) F 3xi2xj + 7zk; C: the cap cut from the upper hemisphere x2 + y2 + z2 = 16 (z z 0) by the cylinder x2+ y2 =4 27)
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 27) F 3xi2xj + 7zk; C: the cap cut from the upper...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 2yzi + 3yj + xk and the surface S the part of the paraboloid Z-5-x2-y2 that lies above the plane z 1, oriented upwards. / curl F diS To verify Stokes' Theorem we will compute the expression on each side. First compute curl F <0.3+2%-22> curl F - ds - where y1 curl F ds- Now compute /F dr The boundary curve C...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = 3yd-2ǐ + 2xk and the surface S the part of the paraboloid z = 20-x2-y2 that lies above the plane z = 4, oriented upwards. To verify Stokes' Theorem we will compute the expression on each side. First computel curl F dS curl F- curl F. dS- EEdy di where curl F dS- Now compute F dr The boundary curve C of the...
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