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2. Consider the vector field F = (yz - eyiz sinx)i + (x2 + eyiz cosz)j...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = yzi - yj + xk and the surface S the part of the paraboloid z= 4 a2 ythat lies above the plane z = 3, oriented upwards. curl FdS To verify Stokes' Theorem we will compute the expression on each side. First compute S curl F = Σ <0,y-1,-z> curl F.dS Σ dy dπ (y-1)-2y)+z where 3 -sqrt(9-x^2) Σ 3 sqrt(9-x^2) curl F...
Question 6 6 pts Suppose that f(x, y, z) is a scalar-valued function and F(x, y,...
Question 6 6 pts Suppose that f(x, y, z) is a scalar-valued function and F(x, y, z) = (P(x, y, z), Q(2,y,z), R(x, y, z)) is a vector field. If P, Q, R, and f all have continuous partial derivatives, then which of the following equations is invalid? O curl (aF) N21 = a curl F for any positive integer Q. REC o div (fF) = fdiv F+FVF Odiv curl F = 0 O grad div f = div grad...
(2 pts) Calculate the circulation, rF dr, in two ways, directly and using Stokes' Theorem. The vector field F (...
(2 pts) Calculate the circulation, rF dr, in two ways, directly and using Stokes' Theorem. The vector field F (8x-8y+62)(i + j) and C is the triangle with vertices (0,0,0), (8, 0, 0), (8,2,0), traversed in that order. Calculating directly, we break C into three paths. For each, give a parameterization r (t) that traverses the path from start to end for 0sts 1 On Ci from (0,0, 0) to (8,0,0), r(t) = <8t,0,0> On C2 from (8, 0, 0)...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F -yi+ z...
Verify that Stokes' Theorem is true for the vector field
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F -yi+ zj + xkand the surface S the hemisphere x2 + y2 + z2-25, y > 0oriented in the direction of the positive y- axis To verify Stokes' Theorem we will compute the expression on each side. First compute curl F dS curl F The surface S can be parametrized by S(s, t) -...
Consider the vector field F(x, y) = (ey – ysin x + 2x, xey + cos...
Consider the vector field F(x, y) = (ey – ysin x + 2x, xey + cos x) (a) (4pts) Compute curl F. (b) (2pts) Is F conservative? Clearly indicate yes or no. (c) (8pts) Suppose C is the curve parameterized by r(t) = (t3 + 1, t– 2t) 0<t< 2 Compute ( F. dr.
(1)Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j (2)...
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
(1 point) Determine whether the vector field is conservative and, if so, find the general potential...
(1 point) Determine whether the vector field is conservative and, if so, find the general potential function. F = (cos z, 2y!}, -x sin z) Q= +c Note: if the vector field is not conservative, write "DNE". (1 point) Show F(x, y) = (8xy + 4)i + (12x+y2 + 2e2y)j is conservative by finding a potential function f for F, and use f to compute SF F. dr, where is the curve given by r(t) = (2 sinº 1)i +...
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...
please help ! Q1-Q6 1. Let F (3x - 4y +22)i+(4x +2y 3z2)j + (2xz moving once around an 4y zk be a vector field. Co...
please help ! Q1-Q6
1. Let F (3x - 4y +22)i+(4x +2y 3z2)j + (2xz moving once around an 4y zk be a vector field. Consider a particle ellipse C given by parametrization r= 4 cos ti +3 sin tj. Find the work done. 3 3 = 3, y=-- and 2 1 2. Let D be the region in the first quadrant bounded by the lines y=-r1, y 4 + 1. Use the transformation u 3 2y, v r +...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = yzi - yj + xk and the surface S the part of the paraboloid z= 4 a2 ythat lies above the plane z = 3, oriented upwards. curl FdS To verify Stokes' Theorem we will compute the expression on each side. First compute S curl F = Σ <0,y-1,-z> curl F.dS Σ dy dπ (y-1)-2y)+z where 3 -sqrt(9-x^2) Σ 3 sqrt(9-x^2) curl F...
Question 6 6 pts Suppose that f(x, y, z) is a scalar-valued function and F(x, y, z) = (P(x, y, z), Q(2,y,z), R(x, y, z)) is a vector field. If P, Q, R, and f all have continuous partial derivatives, then which of the following equations is invalid? O curl (aF) N21 = a curl F for any positive integer Q. REC o div (fF) = fdiv F+FVF Odiv curl F = 0 O grad div f = div grad...
(2 pts) Calculate the circulation, rF dr, in two ways, directly and using Stokes' Theorem. The vector field F (8x-8y+62)(i + j) and C is the triangle with vertices (0,0,0), (8, 0, 0), (8,2,0), traversed in that order. Calculating directly, we break C into three paths. For each, give a parameterization r (t) that traverses the path from start to end for 0sts 1 On Ci from (0,0, 0) to (8,0,0), r(t) = <8t,0,0> On C2 from (8, 0, 0)...
Verify that Stokes' Theorem is true for the vector field
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F -yi+ zj + xkand the surface S the hemisphere x2 + y2 + z2-25, y > 0oriented in the direction of the positive y- axis To verify Stokes' Theorem we will compute the expression on each side. First compute curl F dS curl F The surface S can be parametrized by S(s, t) -...
Consider the vector field F(x, y) = (ey – ysin x + 2x, xey + cos x) (a) (4pts) Compute curl F. (b) (2pts) Is F conservative? Clearly indicate yes or no. (c) (8pts) Suppose C is the curve parameterized by r(t) = (t3 + 1, t– 2t) 0<t< 2 Compute ( F. dr.
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
(1 point) Determine whether the vector field is conservative and, if so, find the general potential function. F = (cos z, 2y!}, -x sin z) Q= +c Note: if the vector field is not conservative, write "DNE". (1 point) Show F(x, y) = (8xy + 4)i + (12x+y2 + 2e2y)j is conservative by finding a potential function f for F, and use f to compute SF F. dr, where is the curve given by r(t) = (2 sinº 1)i +...
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...
please help ! Q1-Q6
1. Let F (3x - 4y +22)i+(4x +2y 3z2)j + (2xz moving once around an 4y zk be a vector field. Consider a particle ellipse C given by parametrization r= 4 cos ti +3 sin tj. Find the work done. 3 3 = 3, y=-- and 2 1 2. Let D be the region in the first quadrant bounded by the lines y=-r1, y 4 + 1. Use the transformation u 3 2y, v r +...
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