Determine which of these vector fields are conservative. If a vector field is not conservative, justify why it is not conservative. F = (2x³ + 2xe¯¹)i + (y² − x²e¯³)j G = x²yi - xy²j Ĥ = ey cos(x)i + ey sin(y)] K = (e²² - 2x cos(y))i + (x² sin(y) - 2e ¹)j

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 12E
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Determine which of these vector fields are conservative. If a vector field is not
conservative, justify why it is not conservative.
F = (2x3 +2æe=")i+(ỷ — re )j
G = x²yi - xy²j
Ĥ = e¹y cos(x)i + ey sin(y)]
K = (e²² - 2x cos(y))i + (x² sin(y) - 2e ¹)j
Transcribed Image Text:Determine which of these vector fields are conservative. If a vector field is not conservative, justify why it is not conservative. F = (2x3 +2æe=")i+(ỷ — re )j G = x²yi - xy²j Ĥ = e¹y cos(x)i + ey sin(y)] K = (e²² - 2x cos(y))i + (x² sin(y) - 2e ¹)j
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