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![-1 ( 1 2 (2-5)nton, it] ㄧ丨/1 Hence 2 6.514 The total charge on S is 6.514 units,](http://img.homeworklib.com/images/de043fd5-16ac-491f-9b2e-0960cf522158.png?x-oss-process=image/resize,w_560)
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please write the word clearly. 1. Let S be the cylinder with parametric equation for 0 < u < 1 and 0 < u <...
Let f(0, -2) = 4 and 0f (0, -2) = 6,23). a. Write the parametric equations...
Let f(0, -2) = 4 and 0f (0, -2) = 6,23). a. Write the parametric equations of the line in the xy-plane that is perpendicular to the contour f(x,y) = 4 at ( 0-2). b. Write an equation for the tangent plane to the surface z = f(x,y) at (0, -2,4).
(1 point) Let S be the surface defined by ř(u, u)-< ucosu, u sinu, u > for (u,t) in D-((mu) : 0 < u < 3,0 &...
(1 point) Let S be the surface defined by ř(u, u)-< ucosu, u sinu, u > for (u,t) in D-((mu) : 0 < u < 3,0 < u < π} Evaluate the surface integral of F-<,z,y>upward across S. F-dS =
(1 point) Let S be the surface defined by ř(u, u)- for (u,t) in D-((mu) : 0
Please solve all parts of this question clearly and neatly 1. Let S be part of the paraboloid z = 5-22-уг, z--3. Assume that the charge density of s is (x,y,2-7x +5 -z Coulombs per unit of surface ar...
Please solve all parts of this question clearly and neatly
1. Let S be part of the paraboloid z = 5-22-уг, z--3. Assume that the charge density of s is (x,y,2-7x +5 -z Coulombs per unit of surface area. (a) Sketch S (b) Using a parametrisation based on cylindrical coordinates, determine a normal vector to S c) Using part (b), determine the total charge on S
1. Let S be part of the paraboloid z = 5-22-уг, z--3. Assume that...
QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the par...
QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the parametric representation r(z,0) for the cylinder x2 +y2 4 in term of z (a) and 0 (2 marks) Based on (a), find the magnitude of llr, x rell for the given cylinder (b) (6 marks) 1 1+ (e) Evaluate z dS for the given S (8 marks) Hence, use the divergence theorem to evaluate f,...
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F d...
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F dS, the flux of F across S
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be...
F-dS where S is the cylinder x? +-2, 0 s y < 2 oriented by the unit normal 5- Let F(x,y,z)= (-6x,0,-62). Evaluat...
F-dS where S is the cylinder x? +-2, 0 s y < 2 oriented by the unit normal 5- Let F(x,y,z)= (-6x,0,-62). Evaluate pointing out of the cylinder. 6-Let F(x, y,2)- yi- xj +zx°y?k. Evaluate (Vx F) . dS where S is the surface x2+y+32 - 1, z <0 oriented by the upward- pointing unit normal.
F-dS where S is the cylinder x? +-2, 0 s y
Help would be greatly appreciated!! 1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped...
Help would be greatly appreciated!!
1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
Question 1 1 pts Let F= (2,0, y) and let S be the oriented surface parameterized...
Question 1 1 pts Let F= (2,0, y) and let S be the oriented surface parameterized by G(u, v) = (u? – v, u, v2) for 0 <u < 12, -1 <u< 4. Calculate | [F. ds. (enter an integer) Question 2 1 pts Calculate (F.ds for the oriented surface F=(y,z,«), plane 6x – 7y+z=1,0 < x <1,0 Sysi, with an upward pointing normal. (enter an integer) Question 3 1 pts Calc F. ds for the oriented surface F =...
Evaluate the surface integrat S «..z) ds using a parametric description of the surface S f(x,y.z)...
Evaluate the surface integrat S «..z) ds using a parametric description of the surface S f(x,y.z) = x2 +y? where S is the hemisphere x² + y² + z = 4, for z 20 Write a parametric description of the given hemisphere using u = p and v=0. rſu v)=000 where O susandsvs (Type exact answers.) The value of the surface integral is (Type an exact answer.)
Help with question 2 1. what is the electric field at the centre (r = 0)...
Help with question 2
1. what is the electric field at the centre (r = 0) of a hemisphere bounded by r = a, 0 < θ < π/2 and 0 < φ < 2m, that carries a uniform volumetric charge density P3(The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) Consider some charges that are lined up in a straight line. This line of charge carries a uniform linear charge density....
Let f(0, -2) = 4 and 0f (0, -2) = 6,23). a. Write the parametric equations of the line in the xy-plane that is perpendicular to the contour f(x,y) = 4 at ( 0-2). b. Write an equation for the tangent plane to the surface z = f(x,y) at (0, -2,4).
(1 point) Let S be the surface defined by ř(u, u)-< ucosu, u sinu, u > for (u,t) in D-((mu) : 0 < u < 3,0 < u < π} Evaluate the surface integral of F-<,z,y>upward across S. F-dS =
(1 point) Let S be the surface defined by ř(u, u)- for (u,t) in D-((mu) : 0
Please solve all parts of this question clearly and neatly
1. Let S be part of the paraboloid z = 5-22-уг, z--3. Assume that the charge density of s is (x,y,2-7x +5 -z Coulombs per unit of surface area. (a) Sketch S (b) Using a parametrisation based on cylindrical coordinates, determine a normal vector to S c) Using part (b), determine the total charge on S
1. Let S be part of the paraboloid z = 5-22-уг, z--3. Assume that...
QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the parametric representation r(z,0) for the cylinder x2 +y2 4 in term of z (a) and 0 (2 marks) Based on (a), find the magnitude of llr, x rell for the given cylinder (b) (6 marks) 1 1+ (e) Evaluate z dS for the given S (8 marks) Hence, use the divergence theorem to evaluate f,...
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F dS, the flux of F across S
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be...
F-dS where S is the cylinder x? +-2, 0 s y < 2 oriented by the unit normal 5- Let F(x,y,z)= (-6x,0,-62). Evaluate pointing out of the cylinder. 6-Let F(x, y,2)- yi- xj +zx°y?k. Evaluate (Vx F) . dS where S is the surface x2+y+32 - 1, z <0 oriented by the upward- pointing unit normal.
F-dS where S is the cylinder x? +-2, 0 s y
Help would be greatly appreciated!!
1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
Question 1 1 pts Let F= (2,0, y) and let S be the oriented surface parameterized by G(u, v) = (u? – v, u, v2) for 0 <u < 12, -1 <u< 4. Calculate | [F. ds. (enter an integer) Question 2 1 pts Calculate (F.ds for the oriented surface F=(y,z,«), plane 6x – 7y+z=1,0 < x <1,0 Sysi, with an upward pointing normal. (enter an integer) Question 3 1 pts Calc F. ds for the oriented surface F =...
Evaluate the surface integrat S «..z) ds using a parametric description of the surface S f(x,y.z) = x2 +y? where S is the hemisphere x² + y² + z = 4, for z 20 Write a parametric description of the given hemisphere using u = p and v=0. rſu v)=000 where O susandsvs (Type exact answers.) The value of the surface integral is (Type an exact answer.)
Help with question 2
1. what is the electric field at the centre (r = 0) of a hemisphere bounded by r = a, 0 < θ < π/2 and 0 < φ < 2m, that carries a uniform volumetric charge density P3(The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) Consider some charges that are lined up in a straight line. This line of charge carries a uniform linear charge density....
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