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 + exy3B) f(x, y) = 3exy2 +(e2x/2)+(exy4)/4C) f(x, y) = e2xy + exy3D) f(x, y) = exy + e2xy32) 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 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

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

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 11P

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Question

1) Consider the conservative vector field given by:

F(x, y) = (e^xy³ + 2e^2xy, e^2x + 3e^xy²)

A potential function that generates the vector field F corresponds to:

A) f(x, y) = e^xy + e^xy³

B) f(x, y) = 3e^xy² +(e^2x/2)+(e^xy⁴)/4

C) f(x, y) = e^2xy + e^xy³

D) f(x, y) = e^xy + e^2xy³

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 J
B) 32, 42 J
C) 15, 71 J
D) 13, 72 J

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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