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4. Let F(x, y, z)=(уг cosz, 2y sinx + e2z,Zye2z). Find JeF . Tds, where C is the straight line going from (0,1, 1) to (...
What is the value of ScF. Tds, where F(x, y, z) = y² i + 2xzj...
What is the value of ScF. Tds, where F(x, y, z) = y² i + 2xzj + 6xk and C is the straight-line segment r(t) = ti + tj + tk, 0 <t<1 from (0,0,0) to (1,1,1)?
9. (10pts) Answer true or false: (a) The domain of f(x,y) = In(1-z?-уг) + Vi-z?-уг is the unit ball {(z, y): x2 + y2 1} . (b) The direction of the maximum rate of increase of g(x, y, 2yz at the point...
9. (10pts) Answer true or false: (a) The domain of f(x,y) = In(1-z?-уг) + Vi-z?-уг is the unit ball {(z, y): x2 + y2 1} . (b) The direction of the maximum rate of increase of g(x, y, 2yz at the point (1,1,1) is 2,1,1 (c) For F2y,2r3y1>, F-dr is independent of path in the plane. (d) × (▽ . F) makes sense. (e) ▽f.dr =4 where f(x, y, z) = zyz and C is the line segment starting at...
(3 + 2ry,12-3уг), 5. Find JeF . Tds, (et sin t, et cost),0 t where F(x,y) and C is given by r(t) - T. (3 + 2ry,12-...
(3 + 2ry,12-3уг), 5. Find JeF . Tds, (et sin t, et cost),0 t where F(x,y) and C is given by r(t) - T.
(3 + 2ry,12-3уг), 5. Find JeF . Tds, (et sin t, et cost),0 t where F(x,y) and C is given by r(t) - T.
5. Let F-(2x3y4 + 22, 2r4y3 + y). Given that f(x,y) rV + 2 2 + уг is a potential function of F. Find scVf dF, where C i...
5. Let F-(2x3y4 + 22, 2r4y3 + y). Given that f(x,y) rV + 2 2 + уг is a potential function of F. Find scVf dF, where C is a curve defined by() ,y int/2),0 st2.
5. Let F-(2x3y4 + 22, 2r4y3 + y). Given that f(x,y) rV + 2 2 + уг is a potential function of F. Find scVf dF, where C is a curve defined by() ,y int/2),0 st2.
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 =
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/...
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z.
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z.
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 point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be ...
(I point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be x =- (a) Find a point P-(zo, 30, zo) where F is parallel to 1. Find a point Q (which F and I are perpendicular. Q= and l are perpendicular Give an equation for the set of all points at which F and l are perpendicular. equation:
(I point) Let F=21+(z...
5 Use the Divergence theorem to find the outward flux. a. F(a, y,z)-(6x2+ + 2xy, 2y + xz, 4x2y); ...
5 Use the Divergence theorem to find the outward flux. a. F(a, y,z)-(6x2+ + 2xy, 2y + xz, 4x2y); G: The solid cut from the first octant by the cylinder x2+y - 4 and the plane 3. (In(x2+Уг),-2z arctan(y/x), z (x2 +y2); G:The solid between the b. F(r, y, z) Vx + y*); G: The solid between the cylinders x2 + y.2 1 and x2+ y2 2, -1szs4. c Fxy)-(2xy', 2x'y, -): G: The solid bounded by the cylinder x?1...
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal...
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal tangent 1. Find all points (a,b,c) where the graph z = plane (parallel to the xy-plane). 0 has a horizontal 2. Find all points (a,b) where the level curve f(x,y) tangent line (parallel to the z-axis).
What is the value of ScF. Tds, where F(x, y, z) = y² i + 2xzj + 6xk and C is the straight-line segment r(t) = ti + tj + tk, 0 <t<1 from (0,0,0) to (1,1,1)?
9. (10pts) Answer true or false: (a) The domain of f(x,y) = In(1-z?-уг) + Vi-z?-уг is the unit ball {(z, y): x2 + y2 1} . (b) The direction of the maximum rate of increase of g(x, y, 2yz at the point (1,1,1) is 2,1,1 (c) For F2y,2r3y1>, F-dr is independent of path in the plane. (d) × (▽ . F) makes sense. (e) ▽f.dr =4 where f(x, y, z) = zyz and C is the line segment starting at...
(3 + 2ry,12-3уг), 5. Find JeF . Tds, (et sin t, et cost),0 t where F(x,y) and C is given by r(t) - T.
(3 + 2ry,12-3уг), 5. Find JeF . Tds, (et sin t, et cost),0 t where F(x,y) and C is given by r(t) - T.
5. Let F-(2x3y4 + 22, 2r4y3 + y). Given that f(x,y) rV + 2 2 + уг is a potential function of F. Find scVf dF, where C is a curve defined by() ,y int/2),0 st2.
5. Let F-(2x3y4 + 22, 2r4y3 + y). Given that f(x,y) rV + 2 2 + уг is a potential function of F. Find scVf dF, where C is a curve defined by() ,y int/2),0 st2.
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 =
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z.
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z.
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 point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be x =- (a) Find a point P-(zo, 30, zo) where F is parallel to 1. Find a point Q (which F and I are perpendicular. Q= and l are perpendicular Give an equation for the set of all points at which F and l are perpendicular. equation:
(I point) Let F=21+(z...
5 Use the Divergence theorem to find the outward flux. a. F(a, y,z)-(6x2+ + 2xy, 2y + xz, 4x2y); G: The solid cut from the first octant by the cylinder x2+y - 4 and the plane 3. (In(x2+Уг),-2z arctan(y/x), z (x2 +y2); G:The solid between the b. F(r, y, z) Vx + y*); G: The solid between the cylinders x2 + y.2 1 and x2+ y2 2, -1szs4. c Fxy)-(2xy', 2x'y, -): G: The solid bounded by the cylinder x?1...
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal tangent 1. Find all points (a,b,c) where the graph z = plane (parallel to the xy-plane). 0 has a horizontal 2. Find all points (a,b) where the level curve f(x,y) tangent line (parallel to the z-axis).
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