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PROBLEM 3 Calculate the line integral of the function from the origin to the point (2,2,2)...
(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a pot...
(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a potential function for the field. Find the work the field does on an object that follows the path consisting of the line segment from (0,0,0) to (1,2,2), followed by the line segment from (1,2,2) to (2,4,3) Find the work done by the field ß-(x, 3y,-5z) along...
Find the line integral along the curve from the origin along the x-axis to the point...
Find the line integral along the curve from the origin along the x-axis to the point (4.0) and then counterclockwise around the circumference of the circle x+y? - 16 to the point 4/24/2) A7-vx + 13-17 + n(x + 175
Problem #7: Let R = r \ {(0,0,0)) and F is a vector field defined on...
Problem #7: Let R = r \ {(0,0,0)) and F is a vector field defined on R satisfying curl(F) = 0. Which of the following statements are correct? [2 marks] (1) All vector fields on R are conservative. (ii) All vector fields on Rare not conservative. (iii) There exists a differentiable function / such that F - Vf. (iv) The line integral of Falong any path which goes from (1,1,1) to (-2,3,-5) and does not pass through the origin, yields...
Q4 please and thank you (3) You are given that the vector field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2. (4) Conside...
Q4 please and thank you
(3) You are given that the vector field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2. (4) Consider the vector field F(x, y) -ryi - 2j (-Fii F2j) and let C be the closed curve consisting of three segments: the straight line from (0, 0) to (1,0) followed by the circular arc from (1,0) to (0,1) followed by the straight line from...
Consider a particle conned to the xy-plane under the inuence of the force given by: Fx...
Consider a particle conned to the xy-plane under the inuence of the force given by: Fx = -ky Fy = kx where k is a constant and x & y are the coordinates of the particle. Assume the particle is initially at the origin. We wish to move the particle in a closed counter-clockwise loop, consisting of four straight segments: Segment A - { [0,0] to [a,0] } B - { [a,0] to [a,b] } C = { [a,b] to...
q4 please thanks (1) Let A - (0,0), B- (1,1) and consider the veetor field f(r,...
q4 please thanks
(1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
Suppose F⃗(x,y)=(x+6)i⃗+(5y+5)j⃗. Use the fundamental theorem of line integrals to calculate the following (a) The line integral of F⃗→ along the line segment C from the point P=(1,0) to the point Q=(...
Suppose F⃗(x,y)=(x+6)i⃗+(5y+5)j⃗. Use the fundamental theorem of line integrals to calculate the following (a) The line integral of F⃗→ along the line segment C from the point P=(1,0) to the point Q=(4,2). ∫CF⃗⋅dr⃗∫= (b) The line integral of F⃗→ along the triangle C from the origin to the point P=(1,0) to the point Q=(4,2) and back to the origin. ∫CF⃗⋅dr⃗∫=
Question 3 (2 points) ✓ Saved Match the following statements that are true for all vector...
Question 3 (2 points) ✓ Saved Match the following statements that are true for all vector fields, and those that are true only for conservative vector fields. 1 The line integral along a path from P to Q does not depend on which path is chosen. 2 The line integral changes sign if the orientation is reversed. The line integral along a path from P to Q does not depend on how the path is parameterized. 1. All vector fields....
Determine whether the following assertions are true or false 1. The double integral JJDy2dA, wher...
Can you do 3 and 6
Determine whether the following assertions are true or false 1. The double integral JJDy2dA, where D is the disk x2 +y2く1, is equal to π/3 2. The iterated integral J^S 4drdy is equal to 3. The center of mass of the triangular lamina that occupies the region D- 10 4. The triple integral of a function f over the solid tetrahedron with vertices (0,0,0), x < 3,0 < y < 3-2) and has a...
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 +...
(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a potential function for the field. Find the work the field does on an object that follows the path consisting of the line segment from (0,0,0) to (1,2,2), followed by the line segment from (1,2,2) to (2,4,3) Find the work done by the field ß-(x, 3y,-5z) along...
Find the line integral along the curve from the origin along the x-axis to the point (4.0) and then counterclockwise around the circumference of the circle x+y? - 16 to the point 4/24/2) A7-vx + 13-17 + n(x + 175
Problem #7: Let R = r \ {(0,0,0)) and F is a vector field defined on R satisfying curl(F) = 0. Which of the following statements are correct? [2 marks] (1) All vector fields on R are conservative. (ii) All vector fields on Rare not conservative. (iii) There exists a differentiable function / such that F - Vf. (iv) The line integral of Falong any path which goes from (1,1,1) to (-2,3,-5) and does not pass through the origin, yields...
Q4 please and thank you
(3) You are given that the vector field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2. (4) Consider the vector field F(x, y) -ryi - 2j (-Fii F2j) and let C be the closed curve consisting of three segments: the straight line from (0, 0) to (1,0) followed by the circular arc from (1,0) to (0,1) followed by the straight line from...
q4 please thanks
(1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
Question 3 (2 points) ✓ Saved Match the following statements that are true for all vector fields, and those that are true only for conservative vector fields. 1 The line integral along a path from P to Q does not depend on which path is chosen. 2 The line integral changes sign if the orientation is reversed. The line integral along a path from P to Q does not depend on how the path is parameterized. 1. All vector fields....
Can you do 3 and 6
Determine whether the following assertions are true or false 1. The double integral JJDy2dA, where D is the disk x2 +y2く1, is equal to π/3 2. The iterated integral J^S 4drdy is equal to 3. The center of mass of the triangular lamina that occupies the region D- 10 4. The triple integral of a function f over the solid tetrahedron with vertices (0,0,0), x < 3,0 < y < 3-2) and has a...
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 +...
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