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![21 - 1/3 s coso.de - [sino] et = -f(oinatt- sino] = 0 Ħado - - O Now 17.0 (xydx +4 xy dx + y 2 dy C c. cix² + y² = x = roso,](http://img.homeworklib.com/questions/fda891e0-e8ae-11ea-a24b-937e8504f2a4.png?x-oss-process=image/resize,w_560)
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7.) (12 pts.) Verify Green's Theroem 2 for the Vector Field F(x, y) = (xy)i +...
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the...
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized by (u,v)-(ucos v, u sin v, hu) x2+y2 a at height h above the xy-plane Z = a V 0<vsa, OSvs 2n, and as is the curve parametrized by ē(f) =(acost,asint, h), 0sis27 as x2+ a
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized...
13. (6 pts) FTLIs, Green's, and Divergence Theorems (a) Complete the table below. Theorem Need to check: FTLIs The vector field Il curve Il surface IS: Green's Theorem | The vector field II c...
13. (6 pts) FTLIs, Green's, and Divergence Theorems (a) Complete the table below. Theorem Need to check: FTLIs The vector field Il curve Il surface IS: Green's Theorem | The vector field II curve ll surface is: and: Divergence Theorem The vector field |l curve l surface is: (b) For each of the following, choose all correct answers from the list below that can be used to evaluate the given integral. List items may be used more than once. i....
I Verify Green, Theorem for the field F(x, y) = (x - y) + + x...
I Verify Green, Theorem for the field F(x, y) = (x - y) + + x 7 and the region R bounded by the unit circle x² + y² = 1. b) Use the Green's theorem to evoluate the line integral 3 y dx + 2xdy where C is the boundary of the region Os x a , Os y < siax orciented counter clockwise. (Answer : -2)
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vec...
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vector field F(x.y)-(r-yi+r+y)j and the circle C: r y-9. Verify Green's Theorem by calculating the outward flux of F across C (12 points) Find the absolute extreme values of the function .-2-4--3 on the closed triangular region in the xy-plane bounded by the lines x...
y? +1 e a vector field 12) Let F(x,y) = (10 + 15y3 + cos (In(xe*)))i...
y? +1 e a vector field 12) Let F(x,y) = (10 + 15y3 + cos (In(xe*)))i + (-6- 15x3 – sin" (ev? V In on R2. Use Green's Theorem to compute (F. dr Where C is the negatively oriented boundary of the region bounded by x2 + y2 = 4 and x2 + y2 = 9, in the first quadrant only.
3.) (12 pts.) Find the Flux of the velocity vector field F(x, y) = (yº)i +...
3.) (12 pts.) Find the Flux of the velocity vector field F(x, y) = (yº)i + (y)} along path C given by x2 + y2 = 4.
D Question 11 12 pts to Consider the vector field F (x, y, z) =< 2x...
D Question 11 12 pts to Consider the vector field F (x, y, z) =< 2x – yz, 2y – az,2z – xy>. a) (3) Is this vector field conservative? Justify your answer. b) (9) Find the amount of work done by this vector field in moving a particle along the curve (t) =< 3cost, cos’t, cos” (2t) > from t = 0 tot = 1
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where...
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where Surface S is that portion of the paraboloid z = 6 - 22 - y2, which lies above the plane z = 2.
8.) (16 pts.) Verify Stoke's Theorem for the Vector Field F (, y, z) = (-y)i...
8.) (16 pts.) Verify Stoke's Theorem for the Vector Field F (, y, z) = (-y)i + (-2)5+(z)k, where Surface S is that portion of the paraboloid z= 6 – 12 – yº, which lies above the plane z = 2.
Consider the vector field: f (x, y)= «M(x, y), N(x, y)= v promet Let C be...
Consider the vector field: f (x, y)= «M(x, y), N(x, y)= v promet Let C be any simple, positively oriented, closed curve that encloses the origin. Show that: F. do 21. We will solve this problem by completing the following steps: STEP 1 Let C be a positively oriented circle of radius r with the center at the origin. Letr be so small that the circle Člies within the region enclosed by the curve C(see figure below) Compute the integral...
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized by (u,v)-(ucos v, u sin v, hu) x2+y2 a at height h above the xy-plane Z = a V 0<vsa, OSvs 2n, and as is the curve parametrized by ē(f) =(acost,asint, h), 0sis27 as x2+ a
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized...
13. (6 pts) FTLIs, Green's, and Divergence Theorems (a) Complete the table below. Theorem Need to check: FTLIs The vector field Il curve Il surface IS: Green's Theorem | The vector field II curve ll surface is: and: Divergence Theorem The vector field |l curve l surface is: (b) For each of the following, choose all correct answers from the list below that can be used to evaluate the given integral. List items may be used more than once. i....
I Verify Green, Theorem for the field F(x, y) = (x - y) + + x 7 and the region R bounded by the unit circle x² + y² = 1. b) Use the Green's theorem to evoluate the line integral 3 y dx + 2xdy where C is the boundary of the region Os x a , Os y < siax orciented counter clockwise. (Answer : -2)
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vector field F(x.y)-(r-yi+r+y)j and the circle C: r y-9. Verify Green's Theorem by calculating the outward flux of F across C (12 points) Find the absolute extreme values of the function .-2-4--3 on the closed triangular region in the xy-plane bounded by the lines x...
y? +1 e a vector field 12) Let F(x,y) = (10 + 15y3 + cos (In(xe*)))i + (-6- 15x3 – sin" (ev? V In on R2. Use Green's Theorem to compute (F. dr Where C is the negatively oriented boundary of the region bounded by x2 + y2 = 4 and x2 + y2 = 9, in the first quadrant only.
3.) (12 pts.) Find the Flux of the velocity vector field F(x, y) = (yº)i + (y)} along path C given by x2 + y2 = 4.
D Question 11 12 pts to Consider the vector field F (x, y, z) =< 2x – yz, 2y – az,2z – xy>. a) (3) Is this vector field conservative? Justify your answer. b) (9) Find the amount of work done by this vector field in moving a particle along the curve (t) =< 3cost, cos’t, cos” (2t) > from t = 0 tot = 1
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where Surface S is that portion of the paraboloid z = 6 - 22 - y2, which lies above the plane z = 2.
8.) (16 pts.) Verify Stoke's Theorem for the Vector Field F (, y, z) = (-y)i + (-2)5+(z)k, where Surface S is that portion of the paraboloid z= 6 – 12 – yº, which lies above the plane z = 2.
Consider the vector field: f (x, y)= «M(x, y), N(x, y)= v promet Let C be any simple, positively oriented, closed curve that encloses the origin. Show that: F. do 21. We will solve this problem by completing the following steps: STEP 1 Let C be a positively oriented circle of radius r with the center at the origin. Letr be so small that the circle Člies within the region enclosed by the curve C(see figure below) Compute the integral...
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