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3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ &l...
7T Find the surface of revolution if the curve (t) 3 cos(t), y(t) = 3 sin(t),...
7T Find the surface of revolution if the curve (t) 3 cos(t), y(t) = 3 sin(t), for telo, is revolved around the z-axis. a) O 9V3 2 ग b) (36 - 18/3) c) O (18 - 9/3) d) Ол 7 e) 2
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evalu...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
solve the given de or ivp 3. [2xy cos (x²y) - sin x) dx + rcos...
solve the given de or ivp
3. [2xy cos (x²y) - sin x) dx + rcos (2²y) dy = 0.
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by y = p sin d, p cos integer, find expressions...
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by y = p sin d, p cos integer, find expressions for the following quantities in where p 0,0 < 0 < 2t. If n is an terms of p, ф, z and p, ф, 2. (а) Vф; (b) Vр"3; (c) V2(p2 cos ); (d) V :(pp + pфф + z2); (F) V. (p*-1 sin(nф)р + pr-1 cos(nф)ф). (e) V x
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by...
4. Let C be the closed curve defined by r(t) = costi + sin tj +...
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. (b) [20 pts] By using Stokes’ Theorem, evaluate the line integral| vi F. dr where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
4. Let C be the closed curve defined by r(t) = costi + sin tj +...
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) [5 pts) Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts) By using Stokes' Theorem, evaluate the line integral F. dr с where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0<t<2m. Marks 4 3. Find...
Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0<t<2m.
Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0
3. If z = f(x,y), where x = r cos, y=r sin 0 show that 222...
3. If z = f(x,y), where x = r cos, y=r sin 0 show that 222 222 1 222 1.az + + +) ar2 ду? ar2 a02 rar
4. Let C be the closed curve defined by r(t) = costi + sin tj +...
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. F. dr (b) (20 pts] By using Stokes' Theorem, evaluate the line integral| " where F(t,y,z) = (y2 + cos z)i + (sin y+z)j + tk
Let C be the closed curve defined by r(t) = costi + sin tj + sin...
Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) (5 pts] Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts] By using Stokes' Theorem, evaluate the line integral F. dr C where F(x, y, z) = (y2 + cos x)i + (sin y +22)j + xk
7T Find the surface of revolution if the curve (t) 3 cos(t), y(t) = 3 sin(t), for telo, is revolved around the z-axis. a) O 9V3 2 ग b) (36 - 18/3) c) O (18 - 9/3) d) Ол 7 e) 2
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
solve the given de or ivp
3. [2xy cos (x²y) - sin x) dx + rcos (2²y) dy = 0.
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by y = p sin d, p cos integer, find expressions for the following quantities in where p 0,0 < 0 < 2t. If n is an terms of p, ф, z and p, ф, 2. (а) Vф; (b) Vр"3; (c) V2(p2 cos ); (d) V :(pp + pфф + z2); (F) V. (p*-1 sin(nф)р + pr-1 cos(nф)ф). (e) V x
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by...
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. (b) [20 pts] By using Stokes’ Theorem, evaluate the line integral| vi F. dr where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) [5 pts) Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts) By using Stokes' Theorem, evaluate the line integral F. dr с where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0<t<2m.
Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0
3. If z = f(x,y), where x = r cos, y=r sin 0 show that 222 222 1 222 1.az + + +) ar2 ду? ar2 a02 rar
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. F. dr (b) (20 pts] By using Stokes' Theorem, evaluate the line integral| " where F(t,y,z) = (y2 + cos z)i + (sin y+z)j + tk
Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) (5 pts] Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts] By using Stokes' Theorem, evaluate the line integral F. dr C where F(x, y, z) = (y2 + cos x)i + (sin y +22)j + xk
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