3. Consider the vector Field & and thecurveC below.²(x,y) = (3 + 4xy²³) Î + 4x³² yĵ₁C is the are of the hyperbola y=1/xfrom (1,1) to (2, 1/2)evaluateof drf.Calong the given curve c.

Answered: Image /qna-images/answer/f9355cf4-c6b1-4cbb-9a46-28756b541ab8.jpg

Answered: Consider the vector Field 7 and the…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 12P

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1).Evaluate ∮CF•dr, whereF=⟨e^x−y^3,cosy+x^3⟩, and C is a circle of radius 2, centered at the origin, traversed once counterclockwise. 2).Let F(x, y, z) =⟨3x^2y+az, x^3,3x+ 3z^2⟩ be a vector field. For what values of a is F conservative?
8.1 If C is the curve given by r(t)=(1+5sint)i+(1+3sin2t)j+(1+3sin3t)kr(t)=(1+5sin⁡t)i+(1+3sin2⁡t)j+(1+3sin3⁡t)k, 0≤t≤π20≤t≤π2 and F is the radial vector field F(x,y,z)=xi+yj+zkF(x,y,z)=xi+yj+zk, compute the work done by F on a particle moving along C.
Consider the following system dx = x(1-x-y) dy = y(0.5-0.25-0.75x) 1. Use XPPAUT dt di to plot nullclines, determine stability, and draw vector fields with \epsi 0.0001 (submit printed figures ).
Consider I = ∫CF⋅dr, where (img17) is a conservative vector field and curve C is parameterized by:α (t): = ((2 − cos (5t)) cost, (2 − cos (5t)) synt, sin (5t)) with 0≤t≤π. We have that the value of I is equal to: (img18)
1) Consider the conservative vector field given by: F(x, y) = (exy3 + 2e2xy, e2x + 3exy2) A potential function that generates the vector field F corresponds to: A) f(x, y) = exy + exy3 B) f(x, y) = 3exy2 +(e2x/2)+(exy4)/4 C) f(x, y) = e2xy + exy3 D) f(x, y) = exy + e2xy3 2) Consider the vector field F(x, y, z) = (y - z sinx, x, 2z + cosx). The work that performs the F field to displace a body, from point A (3π, −1, 1) to point B (π, 2, 0) corresponds approximately to: A) 28, 45 JB) 32, 42 JC) 15, 71 JD) 13, 72 J
Let C, V, and£, be the oriented curves in Figure 16, and let F = V f be a gradient vector field such that fc F • dr = 4. What are the values of the following integrals? (a) fv F • dr (b) L F. dr
Show that F is a conservative vector field and use this fact to evaluate F. dr along the given curve F(x,y) = x^2i + y^2j C is the arc of the parabola y = 2x^2 from (-1,2) to (2,8)

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Consider the vector Field 7 and the curve C below. F(x,y) = (3 +4 ху?) 1 + 4x²yј, C is the arc of the hyperbola y=¹/x from (1,1) to (2/2)