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Calculus
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13 Nov 2019
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15.2 a. Evaluate the line integral f (3x 1y2-4z)ds where C is the line segment from (1, 0, -3) to (3, 2, -6). -5x2yz k ! b. Find the work done by the force: F(xyz) = xy i + 3xzj along the curve given by: r(t) = t i + t2 j + t-k , o
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Sixta Kovacek
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13 Nov 2019
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Related questions
b. Find the work done by the force : F(x,y,z)= xy i + 3xzj - 5x92 k along the curve given by: r() tj3k, 0sts1.
15.3 a. For the force field F(x, y, z) y In z i + x Inzj + xy k , calculate the work done by F on an object moving along a curve from (1. 1 e)to (1, 2, e2) Evaluate the line integral F dr where C is the curve parameterized by r(t) = (t + snG t) ) i + (t + cos(f t) ) j , 0-t-1 , and F(x,y) = xy i + x"y j b.
dA R is the region bounded by the graphs xy- 1, xy 4, x 1, x 4 R 1+x2y2 15.1 Vector Fields 19. Consider F(x, y,z) . Find a. curl(F) b. div(F) 15.2 Line Integrals 20. J xy ds where c(t)0sts1 21. h x2 + y2 + z2 ds where c(t) 0 t 22. Evaluate J x +4Vy ds over a. C: traverse the x-axis from (0,0) to (1,0), then along the line y-x 1 from 1,0) to (2,1) C: counterclockwise around the square with vertices (0,0), (2,0), (0,2), (2,2) b. 23. Evaluate the work done by F(x,y) along the curve c(t) - cos(t) 1+ sin(t) 24. Evaluate f (2x-y)da (x + 3y)dy over the arc C: y 1-x2 from (0,1) to (1,0) 15.3 Conservative fields 25. Determine if the following are conservative b. F(x,y) 2xyi (x2 - y)j c. F(x,y) 2xyi (x - y2)j d. F(x,y,z) 2xy(x2z2))2yz k
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dA R is the region bounded by the graphs xy- 1, xy 4, x 1, x 4 R 1+x2y2 15.1 Vector Fields 19. Consider F(x, y,z) . Find a. curl(F) b. div(F) 15.2 Line Integrals 20. J xy ds where c(t)0sts1 21. h x2 + y2 + z2 ds where c(t) 0 t 22. Evaluate J x +4Vy ds over a. C: traverse the x-axis from (0,0) to (1,0), then along the line y-x 1 from 1,0) to (2,1) C: counterclockwise around the square with vertices (0,0), (2,0), (0,2), (2,2) b. 23. Evaluate the work done by F(x,y) along the curve c(t) - cos(t) 1+ sin(t) 24. Evaluate f (2x-y)da (x + 3y)dy over the arc C: y 1-x2 from (0,1) to (1,0) 15.3 Conservative fields 25. Determine if the following are conservative b. F(x,y) 2xyi (x2 - y)j c. F(x,y) 2xyi (x - y2)j d. F(x,y,z) 2xy(x2z2))2yz k
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