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(14 points) Let F be the radial vector field Ft(z, y, z) =zi+w+sk And S be the surface of the cone shown at right parameterized by G(r,)-(rcos(0),r sin(0),6-3r) Write the integral F dS using an outwa...
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...
(2) Let F zi + xj+yk and consider the integral vx Fi n dS where S is the surface of the paraboloid z = 1-x2-y2 corr...
(2) Let F zi + xj+yk and consider the integral vx Fi n dS where S is the surface of the paraboloid z = 1-x2-y2 corresponding to 0, and n is a unit normal vector to S in the positive z-direction. (a) Apply Stokes' theorem to evaluate the integral. b) Evaluate the integral directly over the surface S. (c) Evaluate the integral directly over the new surface S which is given by the disk
(2) Let F zi + xj+yk...
4. Let K be the cone with equation z = 4Vr2 + уг, for 0 Compute 4, and let F be the vector field F = <-y,za). z F dS...
4. Let K be the cone with equation z = 4Vr2 + уг, for 0 Compute 4, and let F be the vector field F = <-y,za). z F dS
4. Let K be the cone with equation z = 4Vr2 + уг, for 0 Compute 4, and let F be the vector field F =
Evaluate the integral Ms (x, y, z) ds over the surface o represented by the vector-valued...
Evaluate the integral Ms (x, y, z) ds over the surface o represented by the vector-valued function r (u, v). -; r(u, v) = 7 u cos vi+7 u sin vj + 7 u’ k (0 sus sin v, 0 SV ST) 9 f (x, y, z) = 49 + 4x2 + 4y2 Enter the exact answer. 144 f (x, y, z) dS = ? Edit 0 action Attornten of 1
Use Stokes' Theorem to evaluate S (double integral) curl F · dS. F(x, y, z) = x^2*y^3*z i + sin(xyz) j + xyz k, S is the part of the cone y^2 = x^2 + z^2 that lies between the planes y = 0 and y =...
Use Stokes' Theorem to evaluate S (double integral) curl F · dS. F(x, y, z) = x^2*y^3*z i + sin(xyz) j + xyz k, S is the part of the cone y^2 = x^2 + z^2 that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis.
Use the fact that the vector field -e' i + (ze +2) j F(z, y) is conservative to evaluate the line integral IF ds along a smooth curve C from (0, 1) to (e, 2). 1. I2e3 +1 2. I2e - 1 4. Ie -4 5...
Use the fact that the vector field -e' i + (ze +2) j F(z, y) is conservative to evaluate the line integral IF ds along a smooth curve C from (0, 1) to (e, 2). 1. I2e3 +1 2. I2e - 1 4. Ie -4 5. Ie + 2
Use the fact that the vector field -e' i + (ze +2) j F(z, y) is conservative to evaluate the line integral IF ds along a smooth curve C from (0,...
all questions are related and need help answering! rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B)...
all questions are related and need help answering!
rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B) 2n/3 (C) π (D) 4T/3 (E) 2π Use Stokes, Theorem to evaluateⅡcurl F.dS, where F(x, y, z)-(x2 sin Theorem to evaluate Jceun F'.asS , where Fl.e)(', ») and 5. (5pts.) F,y, sin z, y', xy) and s is the part of the paraboloid : -...
NO.25 in 16.7 and NO.12 in 16.9 please. For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs...
NO.25 in 16.7 and NO.12 in
16.9 please.
For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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...
(2) Let F zi + xj+yk and consider the integral vx Fi n dS where S is the surface of the paraboloid z = 1-x2-y2 corresponding to 0, and n is a unit normal vector to S in the positive z-direction. (a) Apply Stokes' theorem to evaluate the integral. b) Evaluate the integral directly over the surface S. (c) Evaluate the integral directly over the new surface S which is given by the disk
(2) Let F zi + xj+yk...
4. Let K be the cone with equation z = 4Vr2 + уг, for 0 Compute 4, and let F be the vector field F = <-y,za). z F dS
4. Let K be the cone with equation z = 4Vr2 + уг, for 0 Compute 4, and let F be the vector field F =
Evaluate the integral Ms (x, y, z) ds over the surface o represented by the vector-valued function r (u, v). -; r(u, v) = 7 u cos vi+7 u sin vj + 7 u’ k (0 sus sin v, 0 SV ST) 9 f (x, y, z) = 49 + 4x2 + 4y2 Enter the exact answer. 144 f (x, y, z) dS = ? Edit 0 action Attornten of 1
Use the fact that the vector field -e' i + (ze +2) j F(z, y) is conservative to evaluate the line integral IF ds along a smooth curve C from (0, 1) to (e, 2). 1. I2e3 +1 2. I2e - 1 4. Ie -4 5. Ie + 2
Use the fact that the vector field -e' i + (ze +2) j F(z, y) is conservative to evaluate the line integral IF ds along a smooth curve C from (0,...
all questions are related and need help answering!
rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B) 2n/3 (C) π (D) 4T/3 (E) 2π Use Stokes, Theorem to evaluateⅡcurl F.dS, where F(x, y, z)-(x2 sin Theorem to evaluate Jceun F'.asS , where Fl.e)(', ») and 5. (5pts.) F,y, sin z, y', xy) and s is the part of the paraboloid : -...
NO.25 in 16.7 and NO.12 in
16.9 please.
For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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