Answered: (b) If F(x, y) = (4x + 4y)i + (4x +…

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(b) If F(x, y) = (4x + 4y)i + (4x + 4y)j, then f(x, y) =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Determine whether each of the following vector fields ~F is path
independent (conservative) or not. If it is path independent, enter a potential function for it, that is, a function f(x, y) so that∇ f = ~F. If it is path dependent, enter NONE.

(b) If F(x, y) = (4x + 4y)i + (4x + 4y)j, then
f(x, y) =

(d) If F(x, y) = (4x² - y², -2xy), then
-0
f(x, y) =
(e) If F(x, y)
f(x,
y) =
2y
x + 6
f(x, y) =
i+2ln(x + 6)j, then
(f) If F(x, y) = 5y sin(xy)i + 5x sin(xy)j, then
0

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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