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13. (6 pts) FTLIs, Green's, and Divergence Theorems (a) Complete the table below. Theorem Need to check: FTLIs The vector field Il curve Il surface IS: Green's Theorem | The vector field II c...
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S h...
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S has a consistentorientation F = 〈y,-x, 11), s is the upper half of the sphere x2 + y2 +22-1 and C is the circle x2 + y2-1 in the xy-plane Construct the line integral of Stokes' Theorem using the parameterization r(t)= 〈cost, sint, O. for 0 sts2r...
Table 14.4 Fundamental Theoremsdtb)-a) or Calculus Fundamental Theorem f.dr-un-nA) of Line Integr...
need help with #4. need to identify best theorem to use and find
solution.
Table 14.4 Fundamental Theoremsdtb)-a) or Calculus Fundamental Theorem f.dr-un-nA) of Line Integrals Green's Theorem Circulation form) Stokes' Theorem F-nds Divergence Theorem Evaluate the line integral for the following problems over the given regions: 1. F (2xy,x2 C:r(t) (9-2.),0sts3 3X3dy-3y3dz; C is the circle of radius 4 centered at the origin with clockwise orientation. 2. 3. ye""ds; C is the path r(t) (t,3t,-6t), for Ost s In8...
Consider the following region and the vector field F. a. Compute the two-dimensional divergence of the...
Consider the following region and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency F= (2x-2y); R=(x,y): x2 + y²59 a. The two-dimensional divergence is (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates with r as the radius and O as the angle SO rdr d0 (Type exact answers.) 0 o Set up the line...
Computing dS: A student is asked to compute the downward pointing vector surface element ds for the cone z x2 y2 in Cartesian coordinates, parameterized by the vector function: Their work is shown be...
Computing dS: A student is asked to compute the downward pointing vector surface element ds for the cone z x2 y2 in Cartesian coordinates, parameterized by the vector function: Their work is shown below. There are mistakes in each of the four lines of their work! Correct the mistakes as they occur (Only correct the mistake in the first line it occurs in; ignore it in the following work. This is how I assign partial credit -take off points for...
(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...
Computing dS: A student is asked to compute the downward pointing vector surface element ds for...
Computing dS: A student is asked to compute the downward pointing vector surface element ds for the cone z x2 y2 in Cartesian coordinates, parameterized by the vector function: Their work is shown below. There are mistakes in each of the four lines of their work! Correct the mistakes as they occur (Only correct the mistake in the first line it occurs in; ignore it in the following work. This is how I assign partial credit -take off points for...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
I lost in this I need help please thank you 6) [8] с Use Green's Theorem...
I lost in this I need help please thank you
6) [8] с Use Green's Theorem to rewrite the integral [F.dr for the given vector field over the path C. F(x,y)=(x? In y, log; y+x’ tan-' x) and C is the boundary of the region D, bounded by the parabola x = y² and the line y=x-2. Assume positive orientation. SET UP the integral using Green's Theorem and include all bounds and variables of integration but DO NOT evaluate the...
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...
2. [5 POINTS] Use the divergence theorem to calculate the flux of the vector field F(x,...
2. [5 POINTS] Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = y z' i + 2yzj + 4z2k across the surface of the solid E enclosed by the paraboloid z = x2 + y2 and the plane z = 9. V
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S has a consistentorientation F = 〈y,-x, 11), s is the upper half of the sphere x2 + y2 +22-1 and C is the circle x2 + y2-1 in the xy-plane Construct the line integral of Stokes' Theorem using the parameterization r(t)= 〈cost, sint, O. for 0 sts2r...
need help with #4. need to identify best theorem to use and find
solution.
Table 14.4 Fundamental Theoremsdtb)-a) or Calculus Fundamental Theorem f.dr-un-nA) of Line Integrals Green's Theorem Circulation form) Stokes' Theorem F-nds Divergence Theorem Evaluate the line integral for the following problems over the given regions: 1. F (2xy,x2 C:r(t) (9-2.),0sts3 3X3dy-3y3dz; C is the circle of radius 4 centered at the origin with clockwise orientation. 2. 3. ye""ds; C is the path r(t) (t,3t,-6t), for Ost s In8...
Consider the following region and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency F= (2x-2y); R=(x,y): x2 + y²59 a. The two-dimensional divergence is (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates with r as the radius and O as the angle SO rdr d0 (Type exact answers.) 0 o Set up the line...
Computing dS: A student is asked to compute the downward pointing vector surface element ds for the cone z x2 y2 in Cartesian coordinates, parameterized by the vector function: Their work is shown below. There are mistakes in each of the four lines of their work! Correct the mistakes as they occur (Only correct the mistake in the first line it occurs in; ignore it in the following work. This is how I assign partial credit -take off points for...
(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...
Computing dS: A student is asked to compute the downward pointing vector surface element ds for the cone z x2 y2 in Cartesian coordinates, parameterized by the vector function: Their work is shown below. There are mistakes in each of the four lines of their work! Correct the mistakes as they occur (Only correct the mistake in the first line it occurs in; ignore it in the following work. This is how I assign partial credit -take off points for...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
I lost in this I need help please thank you
6) [8] с Use Green's Theorem to rewrite the integral [F.dr for the given vector field over the path C. F(x,y)=(x? In y, log; y+x’ tan-' x) and C is the boundary of the region D, bounded by the parabola x = y² and the line y=x-2. Assume positive orientation. SET UP the integral using Green's Theorem and include all bounds and variables of integration but DO NOT evaluate the...
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...
2. [5 POINTS] Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = y z' i + 2yzj + 4z2k across the surface of the solid E enclosed by the paraboloid z = x2 + y2 and the plane z = 9. V
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