Answered: (a) Use Green's Theorem to prove that… | bartleby

Algebra and Trigonometry (MindTap Course List)

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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Question

(a) Use Green's Theorem to prove that
LA dr + 8(y)dy = 0
if f and g are differentiable functions and C is a simple,
closed, piecewise smooth curve.
(b) What does this tell you about the vector field F(x, y) =
f(x)i + g(y)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 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
Consider the conservative vector field given by:F (x, y) = (x - ycos (x), y - sin (x))A potential function that generates the vector field F corresponds to:
5. Find a potential function corresponding to the vector field F(x, y, z) = (2x, 3Y, 4z).
Calculate the circulation of the field F around the closed curve C. Circulation means line integralF = x 3y 2 i + x 3y 2 j; curve C is the counterclockwise path around the rectangle with vertices at (0,0),(3,0).(3,2) and (0.2) , and a) 0 b) 153 c) -108 d) - 9
use Green’s Theorem to find the counterclockwisecirculation and outward flux for the field F and the curve C. F = (x - y)i + ( y - x)j C: The square bounded by x = 0, x = 1, y = 0, and y = 1
1. Let F =i+y^2j +z^4k. Find the general flow lines for this vector field. Present the flow line through the origin.
Let f (x, y) be a harmonic function such that ∇f (1, 1) = (−1, −3). Showthat the point P (1, 1) is a sink for the vector field G = (fxe^(xy) , fy e^(xy) ).

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