2. Let F(x, y, z) = (P(x, y, z), Q(x, y, z), R(x, y, z)) = (y cos(x) — y, sin x + 2yz — x, y² + 1) bea vector field on R³ with continuously differentiable components.(a) Show that F is a conservative vector field by showing that² = ( ²/curl F = V x F =ᎧᎡдуƏR ƏQ ӘРӘQ ӘРƏz' əz əx' əx=(b) Find all possible potential functions (x, y, z) for the conservative vector fieldF(x, y, z) (c.f. Exercise 13.2.2).

Given , F(x,y,z)=(P(x,y,z),Q(x,y,z),R(x,y,z))

2. Let F(x, y, z) = (P(x, y, z), Q(x, y, z), R(x, y, z)) = (y cos(x) — y, sin x + 2yz — x, y² + 1) be a vector field on R³ with continuously differentiable components. (a) Show that F is a conservative vector field by showing that curl F = V x F = ( ƏR ƏQ ӘР o. Əx' əx ду functions (x, y, z) for the conservative vector field ƏR ду (b) Find all possible potential F(x, y, z) (c.f. Exercise 13.2.2). ƏQ ƏP Əz' Əz

2. Let F(x, y, z) = (P(x, y, z), Q(x, y, z), R(x, y, z)) = (y cos(x) — y, sin x + 2yz — x, y² + 1) be a vector field on R³ with continuously differentiable components. (a) Show that F is a conservative vector field by showing that curl F = V x F = ( ƏR ƏQ ӘР o. Əx' əx ду functions (x, y, z) for the conservative vector field ƏR ду (b) Find all possible potential F(x, y, z) (c.f. Exercise 13.2.2). ƏQ ƏP Əz' Əz

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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