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Help Entering Answers (1 point) Write down the given line integral in terms of t Ay...
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...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = yzi - yj + xk and the surface S the part of the paraboloid z= 4 a2 ythat lies above the plane z = 3, oriented upwards. curl FdS To verify Stokes' Theorem we will compute the expression on each side. First compute S curl F = Σ <0,y-1,-z> curl F.dS Σ dy dπ (y-1)-2y)+z where 3 -sqrt(9-x^2) Σ 3 sqrt(9-x^2) curl F...
Help Entering Answers (1 point) Use Stokes' Theorem to evaluate ll curl F. dS where F(x,...
Help Entering Answers (1 point) Use Stokes' Theorem to evaluate ll curl F. dS where F(x, y, z) = xyzi + 3xyj + 2x2yzk and S consists of the top and the four sides (but not the bottom) of the cube with vertices (+2, +2, +2), oriented outward. Since the box is oriented outwards the boundary curve must be transversed when viewed from the top. A parametrization for the boundary curve C seen below from above can be given by:...
(1 point) Evaluate the surface integral || (3x yi – 3yzj + zxk) · dS. JJ...
(1 point) Evaluate the surface integral || (3x yi – 3yzj + zxk) · dS. JJ s . Where S is the part of the paraboloid z = 9 – x2 - y2 that lies above the square 0 < x < 2, 0 < y < 1, and has upward orientation. X2 / 2 (3xyi – 3yzj + zxk) · dS = JJS 9-x^2-y^2 Σ dy dx J xi Jyi where M M O-ON x1 = M M Evaluate...
MM M MM Help Entering Answers (1 point) Express the volume encloded by the torus p...
MM M MM Help Entering Answers (1 point) Express the volume encloded by the torus p = 3 sin i as a triple integral. NOTE: When typing your answers use "rh" for p, "ph" for , and "th for 0 Volume E dp dp do P JJ3 P= P2= 02 M Evaluate the integral Volume Σ If you don't get this in 3 tries, you can see a similar example (online). However, try to use this as a last resort...
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...
Help Entering Answers (1 point) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, ...
Help Entering Answers (1 point) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, y + 2 tan(2), X22-1 and S is the top half of the sphere x2 +y2 25 Hint: S is not a closed surface. First compute integrals over S and S2, where Si is the disk x2 +y s 25, z 0 oriented downward and s,-sus, F-ds, = 滋 dy dx F.dS2 = S2 where X1 = 리= Z2 = IE F-ds, =...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F -yi+ z...
Verify that Stokes' Theorem is true for the vector field
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F -yi+ zj + xkand the surface S the hemisphere x2 + y2 + z2-25, y > 0oriented in the direction of the positive y- axis To verify Stokes' Theorem we will compute the expression on each side. First compute curl F dS curl F The surface S can be parametrized by S(s, t) -...
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...
(1 point)G Get help entering answers See a similar example (.PDF) Use the given conditions to...
(1 point)G Get help entering answers See a similar example (.PDF) Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. When entering the point-slope form, keep terms with y on the left and keep terms with on the right. Simplify any fractions as much as possible and do not use decimals. x-intercept and y-intercept 3 The point-slope form is y-3 The slope-intercept form is y =
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...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = yzi - yj + xk and the surface S the part of the paraboloid z= 4 a2 ythat lies above the plane z = 3, oriented upwards. curl FdS To verify Stokes' Theorem we will compute the expression on each side. First compute S curl F = Σ <0,y-1,-z> curl F.dS Σ dy dπ (y-1)-2y)+z where 3 -sqrt(9-x^2) Σ 3 sqrt(9-x^2) curl F...
Help Entering Answers (1 point) Use Stokes' Theorem to evaluate ll curl F. dS where F(x, y, z) = xyzi + 3xyj + 2x2yzk and S consists of the top and the four sides (but not the bottom) of the cube with vertices (+2, +2, +2), oriented outward. Since the box is oriented outwards the boundary curve must be transversed when viewed from the top. A parametrization for the boundary curve C seen below from above can be given by:...
(1 point) Evaluate the surface integral || (3x yi – 3yzj + zxk) · dS. JJ s . Where S is the part of the paraboloid z = 9 – x2 - y2 that lies above the square 0 < x < 2, 0 < y < 1, and has upward orientation. X2 / 2 (3xyi – 3yzj + zxk) · dS = JJS 9-x^2-y^2 Σ dy dx J xi Jyi where M M O-ON x1 = M M Evaluate...
MM M MM Help Entering Answers (1 point) Express the volume encloded by the torus p = 3 sin i as a triple integral. NOTE: When typing your answers use "rh" for p, "ph" for , and "th for 0 Volume E dp dp do P JJ3 P= P2= 02 M Evaluate the integral Volume Σ If you don't get this in 3 tries, you can see a similar example (online). However, try to use this as a last resort...
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...
Help Entering Answers (1 point) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, y + 2 tan(2), X22-1 and S is the top half of the sphere x2 +y2 25 Hint: S is not a closed surface. First compute integrals over S and S2, where Si is the disk x2 +y s 25, z 0 oriented downward and s,-sus, F-ds, = 滋 dy dx F.dS2 = S2 where X1 = 리= Z2 = IE F-ds, =...
Verify that Stokes' Theorem is true for the vector field
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F -yi+ zj + xkand the surface S the hemisphere x2 + y2 + z2-25, y > 0oriented in the direction of the positive y- axis To verify Stokes' Theorem we will compute the expression on each side. First compute curl F dS curl F The surface S can be parametrized by S(s, t) -...
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...
(1 point)G Get help entering answers See a similar example (.PDF) Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. When entering the point-slope form, keep terms with y on the left and keep terms with on the right. Simplify any fractions as much as possible and do not use decimals. x-intercept and y-intercept 3 The point-slope form is y-3 The slope-intercept form is y =
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