Homework Answers
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z...
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z cos y, xz sin y, x cos y). a) Determine which vector field above is conservative. Justify. Foly = fjol so, <ea sin(J2), 20% cos(82), y acos (92)) Conservative. b) For the vector field that is conservative, find a function f such that F - Vf. Lxelsing2, zetos yea, yet cosy 2 c) Use the Fundamental Theorem of Line Integrals to find the work...
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,...
Problem 5 (10 points) Calculate the work done by a force field F, given by F(x,...
Problem 5 (10 points) Calculate the work done by a force field F, given by F(x, y) = (x + y, x - y) when an object moves from (0,0) to (1,1) along the path x = y2.
Find the work done by the force field F on a particle that moves along the...
Find the work done by the force field F on a particle that moves along the curve rve C. F(x,y) = 2xy i+ 3x j C: x=y from (0,0) to (1,1) Enter the exact answer as an improper fraction, if necessary. 1 W= Edit 2
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-< ye", e + z,y >...
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-< ye", e + z,y >
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-
help pleasee ignore the first photo, i need help with number 2 4. Let F(x, y,...
help pleasee
ignore the first photo, i need help with number
2
4. Let F(x, y, z) = (e" cos(y) + yz, xz - e" sin(y),ry+z). Compute 5.F-ds , where c: [0, 1] → R is given by c(t) = (tet, arcsin(t),t +1) 4. Let F(x, y, z) = (e" cos(y) + yz, xz - e" sin(y),ry+z). Compute 5.F-ds , where c: [0, 1] → R is given by c(t) = (tet, arcsin(t),t +1)
Find the work done by the force field F(x, y, z) = (x – y, x...
Find the work done by the force field F(x, y, z) = (x – y, x + z, y + z) in moving a particle along the line segment from (0,0,1) to (2, 1, 0).
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector...
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
3. [10 Marks] Find the work done by the force F(z, y)-(e 2019y 233 cos(sin(4y )) 2 + + 1)y,-r + e...
3. [10 Marks] Find the work done by the force F(z, y)-(e 2019y 233 cos(sin(4y )) 2 + + 1)y,-r + e 2019r 233 sin χ -(2 along the cardioid r 3+3 sin 0, 0 (0, 2m
3. [10 Marks] Find the work done by the force F(z, y)-(e 2019y 233 cos(sin(4y )) 2 + + 1)y,-r + e 2019r 233 sin χ -(2 along the cardioid r 3+3 sin 0, 0 (0, 2m
Find the work done by the vector field F(x, y) = {xy i + áraj (the...
Find the work done by the vector field F(x, y) = {xy i + áraj (the vector field from Question 1) on a particle that moves from (0,0) to (0, 1) (moving in a straight line up and along the y axis) and then from (0, 1) to (3, 2) along the curvey= Vx+1. Thus the path is given by along the curve y=x+1 (0,0) up the y-axis + (0,1) (3,2) 1 F. dr 2 F. dr = 0 18...
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z cos y, xz sin y, x cos y). a) Determine which vector field above is conservative. Justify. Foly = fjol so, <ea sin(J2), 20% cos(82), y acos (92)) Conservative. b) For the vector field that is conservative, find a function f such that F - Vf. Lxelsing2, zetos yea, yet cosy 2 c) Use the Fundamental Theorem of Line Integrals to find the work...
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,...
Problem 5 (10 points) Calculate the work done by a force field F, given by F(x, y) = (x + y, x - y) when an object moves from (0,0) to (1,1) along the path x = y2.
Find the work done by the force field F on a particle that moves along the curve rve C. F(x,y) = 2xy i+ 3x j C: x=y from (0,0) to (1,1) Enter the exact answer as an improper fraction, if necessary. 1 W= Edit 2
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-< ye", e + z,y >
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-
help pleasee
ignore the first photo, i need help with number
2
4. Let F(x, y, z) = (e" cos(y) + yz, xz - e" sin(y),ry+z). Compute 5.F-ds , where c: [0, 1] → R is given by c(t) = (tet, arcsin(t),t +1) 4. Let F(x, y, z) = (e" cos(y) + yz, xz - e" sin(y),ry+z). Compute 5.F-ds , where c: [0, 1] → R is given by c(t) = (tet, arcsin(t),t +1)
Find the work done by the force field F(x, y, z) = (x – y, x + z, y + z) in moving a particle along the line segment from (0,0,1) to (2, 1, 0).
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
3. [10 Marks] Find the work done by the force F(z, y)-(e 2019y 233 cos(sin(4y )) 2 + + 1)y,-r + e 2019r 233 sin χ -(2 along the cardioid r 3+3 sin 0, 0 (0, 2m
3. [10 Marks] Find the work done by the force F(z, y)-(e 2019y 233 cos(sin(4y )) 2 + + 1)y,-r + e 2019r 233 sin χ -(2 along the cardioid r 3+3 sin 0, 0 (0, 2m
Find the work done by the vector field F(x, y) = {xy i + áraj (the vector field from Question 1) on a particle that moves from (0,0) to (0, 1) (moving in a straight line up and along the y axis) and then from (0, 1) to (3, 2) along the curvey= Vx+1. Thus the path is given by along the curve y=x+1 (0,0) up the y-axis + (0,1) (3,2) 1 F. dr 2 F. dr = 0 18...
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