How do you solve c)? (a) Compute fxdx + ydy + (x + y – 1)dz where C is the line segment from (1, 1, 1) to (2, 3, 4).C1(b) Let F be the vector field F(x, y) =1and let C be the curve with parametrization 7 (t) = (t,t²)xy' x + ywith 1

The objective of the question is determine the gradient field of the given function f(x,y,z) .

Answered: (a) Compute Sædæ + ydy + (x + y – 1)dz…

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 18P

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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.
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
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1. Consider the vector field F(x, y) =⟨2xy3,1 + 3x2y2⟩ in R2. (a) Show that F is conservative. (b) Find a function f such that ∇f=F. (c) Evaluate the line integral ∫CF•dr where C is given by r(t) =⟨t+ 1,2−t2⟩ when 0≤t≤2.
Show that the vector field F(x,y,z)=yz^2i+xz^2j+2xyzk is conservative, find a potential function f, and evaluate ∫C F⋅dR where C is a smooth path from (1,0,1) to (2,2,3).
A path C is defined by the parametric equations: x (t) = t, y (t) = t2, 0 ≤ t ≤ 1, and a vector field is defined by the equation F = y2i + xj What is the value of the line integral ∫C F • ds

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(a) Compute Sædæ + ydy + (x + y – 1)dz where C' is the line segment from (1, 1, 1) to (2, 3, 4). C 1 (b) Let F be the vector field F'(x, y) 1 and let C be the curve with parametrization 7 (t) = (t,t²) xy'x +y with 1