Consider ? =< ? , 3?? + ? >.
Let ?1 be the line from (1,0) to (0,0), ?2 be the line from (0,0) to (0,1), and ?3 be the counterclockwise unit circular arc from (1, 0) to (0, 1).
(A) Sketch all the oriented curves on the same window. Include the orientations.
(B) Find curl?.
(C) Find the domain of ?.
(E) Is there any potential function of ? ? If yes, find one. If not, explain why not.
(F) Can you use the result in (E) above to determine whether ? is a gradient vector field or not.
Explain why or why not.
Homework Answers
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Please show all the work to complete the question and explain each step, please. Thank you! Let F(x, y) e*y (y cos x -...
Please show all the work to complete the question and explain
each step, please. Thank you!
Let F(x, y) e*y (y cos x - centered at (1,0) in the first quadrant, traced clockwise from (0,0) to (2, 0). And suppose that C2 is the line from (0,0) to (2,0). sin x) xexy cos xj. Suppose that C1 is the half of the unit circle (A) Use the curl test to determine whether F is a gradient vector field or not....
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q4 please thanks
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Problem 3. For e 0,7), let Le CRP be the line that makes angle with the...
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Please help solve the following question with steps. Thank
you!
6. Compute JF . T ds where F (-y,z) and (a) C is the line segment from (1,0) to (0,0) followed by the line segment from (0,0) to (0, 1) (b) C is the line segment from (1,0) to (0, 1) (c) C is the part of the unit circle in the first quadrant, moving from
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5. Consider Sc 2xydx + (x + y)dy, where C is the path moving from (0,0)...
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(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t
(1)...
please solve all thank you so much :) Let C be the curve consisting of line...
please solve all thank you so
much :)
Let C be the curve consisting of line segments from (0, 0) to (3, 3) to (0, 3) and back to (0,0). Use Green's theorem to find the value of [ xy dx + xy dx + y2 + 3 dy. Use Green's theorem to evaluate line integral fc2x e2x sin(2y) dx + 2x cos(2) dy, where is ellipse 16(x - 3)2 + 9(y – 5)2 = 144 oriented counterclockwise. Use Green's...
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(x) from (0,0) to (π, 0) and the line segment from (π,0) to (0,0). 4 3 3. (2 points) Evaluate F di where F.y,(ry, 2:,3) and C is the curve of intersection of 5 and y29. going...
Please show all the work to complete the question and explain
each step, please. Thank you!
Let F(x, y) e*y (y cos x - centered at (1,0) in the first quadrant, traced clockwise from (0,0) to (2, 0). And suppose that C2 is the line from (0,0) to (2,0). sin x) xexy cos xj. Suppose that C1 is the half of the unit circle (A) Use the curl test to determine whether F is a gradient vector field or not....
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...
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...
(1 point) If C is the line segment from (7,4) to, (0,0), find the value of the line integral: Sc(3y2 7 + 2x1).dñ = ī (1 point) Find Sc((x2 + 3y)i + 5y37) . • dr where C consists of the three line segments from (1,0,0) to (1,1,0) to (0,1,0) to (0,1, 3). Sc((x2 + 3y)ī + 5y37). . dr =
Problem 3. For e 0,7), let Le CRP be the line that makes angle with the positive c-axis. Let To: R2 → R2 be the reflection about Le. Let Ao e R2,2 be the matrix representation of To. a) Find A0, A1/2, and Af/4. For each answer, justify by drawing the images of ēj = (1,0) and ē, = (0,1) under the corresponding reflection. b) Find an orthonormal basis B = (v1, U2) such that To = CT1/ 6C Justify...
Please help solve the following question with steps. Thank
you!
6. Compute JF . T ds where F (-y,z) and (a) C is the line segment from (1,0) to (0,0) followed by the line segment from (0,0) to (0, 1) (b) C is the line segment from (1,0) to (0, 1) (c) C is the part of the unit circle in the first quadrant, moving from
6. Compute JF . T ds where F (-y,z) and (a) C is the...
5. Consider Sc 2xydx + (x + y)dy, where C is the path moving from (0,0) to (1, 1) along the graph of y = x3 and from (1, 1) to (0,0) along the graph of y = x oriented in the counterclockwise direction. a) Calculate the line integral using Green's Theorem. b) Calculate the same line integral using definition.
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(1)...
please solve all thank you so
much :)
Let C be the curve consisting of line segments from (0, 0) to (3, 3) to (0, 3) and back to (0,0). Use Green's theorem to find the value of [ xy dx + xy dx + y2 + 3 dy. Use Green's theorem to evaluate line integral fc2x e2x sin(2y) dx + 2x cos(2) dy, where is ellipse 16(x - 3)2 + 9(y – 5)2 = 144 oriented counterclockwise. Use Green's...
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