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(d) If F(x, y) = (5x² - y², -2xy), then f(x, y) = (e) If F(x, y) = 6y z+5 -ỉ +6 ln(x+5)j, then f(x, y) = (f) If F¹(x, y) = 4y sin(ry)i + 4x sin(ry)j, then f(x, y) =

(d) If F(x, y) = (5x² - y², -2xy), then f(x, y) = (e) If F(x, y) = 6y z+5 -ỉ +6 ln(x+5)j, then f(x, y) = (f) If F¹(x, y) = 4y sin(ry)i + 4x sin(ry)j, then f(x, y) =

Advanced Engineering Mathematics
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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(d) If F(x, y) = (5æ² – y², –2xy), then f(x, y) = (e) If F (x, y) = 6y + 6 In(x + 5)j, then a + 5 f(x, y) = (1) If F (x, y) = 4y sin(xy)i + 4x sin(æy)j, then f(x, y) =
Transcribed Image Text:(d) If F(x, y) = (5æ² – y², –2xy), then f(x, y) = (e) If F (x, y) = 6y + 6 In(x + 5)j, then a + 5 f(x, y) = (1) If F (x, y) = 4y sin(xy)i + 4x sin(æy)j, then f(x, y) =
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 Vf = F. If it is path dependent, enter NONE.
Transcribed Image Text: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 Vf = F. If it is path dependent, enter NONE.
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