Explanation Given information : F = f ( ρ ) ( x , y , z ) for some function f ( ρ ) , where ρ = x 2 + y 2 + z 2 . Formula used : c u r l ( f v ) = | i j k ∂ ∂ x ∂ ∂ y ∂ ∂ z x . f y . f z . f | Chain rule: d d t f ( x , y ) = d f d x . d x d t + d f d y . d y d t Proof: Let v = 〈 x , y , z 〉 We need to show that c u r l ( F ) = 0 or c u r l ( f v ) = 0 . We have c u r l ( f v ) = | i j k ∂ ∂ x ∂ ∂ y ∂ ∂ z x . f y . f z . f | = 〈 ∂ ∂ y ( z . f ) − ∂ ∂ z ( y . f ) , − ∂ ∂ z ( x . f ) + ∂ ∂ x ( z . f ) , ∂ ∂ x ( y . f ) − ∂ ∂ y ( x

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Chapter 18.2, Problem 32E

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To show: curl(F)=0 if F is radial.

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Chapter 18.2, Problem 31E

Chapter 18.2, Problem 33E

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Chapter 18 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 18.1 - Prob. 1PQ Ch. 18.1 - Prob. 2PQ Ch. 18.1 - Prob. 3PQ Ch. 18.1 - Prob. 4PQ Ch. 18.1 - Prob. 5PQ Ch. 18.1 - Prob. 1E Ch. 18.1 - Prob. 2E Ch. 18.1 - Prob. 3E Ch. 18.1 - Prob. 4E Ch. 18.1 - Prob. 5E

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c u r l ( F ) = 0 if F is radial .

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Chapter 18 Solutions