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4. Stoke's Theorem: Consider a vector field F = (1,1)+(1,0) + (0,0). tyle +rin the unit...
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...
Consider the following region R and the vector field F. a. Compute the two-dimensional curl of...
Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency. F = (3y, - 3x); R is the triangle with vertices (0,0), (1,0), and (0,2). . a. The two-dimensional curl is (Type an exact answer.) b. Set up the integral over the region R. JO dy dx 0 0 (Type exact answers.) Set up the line integral for the line...
Consider the following region R and vector field a. Evaluate both integrals in Green's Theorem - Circulation Form and check for consistency. b. Is the vector field conservative? 7) (16 points) F...
Consider the following region R and vector field a. Evaluate both integrals in Green's Theorem - Circulation Form and check for consistency. b. Is the vector field conservative? 7) (16 points) F = 〈x4, xy〉, R is the triangular region with vertices (0,0), (1,0) and (0,1).
Consider the following region R and vector field a. Evaluate both integrals in Green's Theorem - Circulation Form and check for consistency. b. Is the vector field conservative? 7) (16 points) F = 〈x4,...
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 +...
Compute the Curl V x F = Qx-P, of the vector field F = (x4, xy),...
Compute the Curl V x F = Qx-P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) fcx* dx + xy dy cow around the triangle with vertices (0,0), (1,0) and (0,1).
Consider the following region R and the vector field F a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in the circulation form of Green's Theorem and check for...
Consider the following region R and the vector field F a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in the circulation form of Green's Theorem and check for consistency. c. State whether the vector field is conservative. F-3y,3x); R is the triangle with vertices (0, 0), (1, 0), and (0, 1) a. The two-dimensional curl is D (Type an exact answer, using π as needed.) b. Set up the integral over the region R. dy...
#3 Consider the vector field F- Mi+ Nj Pk defined by: F- ysinzi+sinjry cos z k. Compute the line ...
#3 Consider the vector field F- Mi+ Nj Pk defined by: F- ysinzi+sinjry cos z k. Compute the line integral ScF dr over a unit circle. Compute the line integral ysin z dr+ r sin z dy + ry cos zdz (0,0,0) #3 Use Green's Theorem to evaluate the line integral along the given positively orientated curve C. e2*t d e" dy, C is the triangle with vertices (0,0), (1,0), and (1,1)
#3 Consider the vector field F- Mi+ Nj...
Q3 6 Points Let F be the vector field represented in the figure: P(-1,1) toyIX Q3.1...
Q3 6 Points Let F be the vector field represented in the figure: P(-1,1) toyIX Q3.1 3 Points O2d-Curl F(0,0) > 0 O2d-Curl F(0,0) = 0 O2d-Curl F(0,0) <0 Q3.2 3 Points OV. F(0,0) > 0 OV. F(0,0) = 0 OV. F(0,0) < 0
6 Points Let F be the vector field represented in the figure: P(-1,1) 1907/1X X Q3.1...
6 Points Let F be the vector field represented in the figure: P(-1,1) 1907/1X X Q3.1 3 Points O2d-Curl F(0,0) > 0 O2d-Curl F(0,0) = 0 O2d-Curl F(0,0) < 0 Q3.2 3 Points OV.F(0,0) > 0 OV.F(0,0) = 0 OV.F(0,0) < 0
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as...
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as Use the definition of electric potential to find the potential difference between the origin and r = x + y + 27, V(r) - V(O) = - Ed. As the line integral is independent of path, choose whatever path you find to be con- vertient Taking V(0) = 0, what is V(r)? Finally, confirm that taking the gradient of the potential recovers our original...
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...
Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency. F = (3y, - 3x); R is the triangle with vertices (0,0), (1,0), and (0,2). . a. The two-dimensional curl is (Type an exact answer.) b. Set up the integral over the region R. JO dy dx 0 0 (Type exact answers.) Set up the line integral for the line...
Consider the following region R and vector field a. Evaluate both integrals in Green's Theorem - Circulation Form and check for consistency. b. Is the vector field conservative? 7) (16 points) F = 〈x4, xy〉, R is the triangular region with vertices (0,0), (1,0) and (0,1).
Consider the following region R and vector field a. Evaluate both integrals in Green's Theorem - Circulation Form and check for consistency. b. Is the vector field conservative? 7) (16 points) F = 〈x4,...
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 +...
Compute the Curl V x F = Qx-P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) fcx* dx + xy dy cow around the triangle with vertices (0,0), (1,0) and (0,1).
Consider the following region R and the vector field F a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in the circulation form of Green's Theorem and check for consistency. c. State whether the vector field is conservative. F-3y,3x); R is the triangle with vertices (0, 0), (1, 0), and (0, 1) a. The two-dimensional curl is D (Type an exact answer, using π as needed.) b. Set up the integral over the region R. dy...
#3 Consider the vector field F- Mi+ Nj Pk defined by: F- ysinzi+sinjry cos z k. Compute the line integral ScF dr over a unit circle. Compute the line integral ysin z dr+ r sin z dy + ry cos zdz (0,0,0) #3 Use Green's Theorem to evaluate the line integral along the given positively orientated curve C. e2*t d e" dy, C is the triangle with vertices (0,0), (1,0), and (1,1)
#3 Consider the vector field F- Mi+ Nj...
Q3 6 Points Let F be the vector field represented in the figure: P(-1,1) toyIX Q3.1 3 Points O2d-Curl F(0,0) > 0 O2d-Curl F(0,0) = 0 O2d-Curl F(0,0) <0 Q3.2 3 Points OV. F(0,0) > 0 OV. F(0,0) = 0 OV. F(0,0) < 0
6 Points Let F be the vector field represented in the figure: P(-1,1) 1907/1X X Q3.1 3 Points O2d-Curl F(0,0) > 0 O2d-Curl F(0,0) = 0 O2d-Curl F(0,0) < 0 Q3.2 3 Points OV.F(0,0) > 0 OV.F(0,0) = 0 OV.F(0,0) < 0
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as Use the definition of electric potential to find the potential difference between the origin and r = x + y + 27, V(r) - V(O) = - Ed. As the line integral is independent of path, choose whatever path you find to be con- vertient Taking V(0) = 0, what is V(r)? Finally, confirm that taking the gradient of the potential recovers our original...
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