Explanation Proof: It is given that if F is conservative in the region then ∂ f ∂ y = ∂ g ∂ x , ∂ f ∂ z = ∂ h ∂ x , ∂ g ∂ z = ∂ h ∂ y in that region. Also, it is known that the curl of a vector field F x , y , z = f x , y , z i + g x , y , z j + h x , y , z k is given by curl F = ∂ h ∂ y − ∂ g ∂ z i + ∂ f ∂ z − ∂ h ∂ x j + ∂ g ∂ x − ∂ f ∂ y k Evaluate the curl of the vector field F x , y , z = f x , y , z

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ISBN: 9781119244912

Author: Anton

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Chapter 15, Problem 33RE

To determine

To prove: The curl F of a conservative vector field Fx,y,z=fx,y,zi+gx,y,zj+hx,y,zk , f,g and h has continuous first order partial derivatives, in an open spherical region is zero.

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Chapter 15, Problem 32RE

Chapter 15, Problem 34RE

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Chapter 15 Solutions

EBK CALCULUS:EARLY TRANSCENDENTALS

Ch. 15.1 - The function (x,y,z)=xy+yz+xz is a potential for...Ch. 15.1 - The vector field F(x,y,z)=, defined for...Ch. 15.1 - An inverse-square field is one that can be written...Ch. 15.1 - The vector field has divergence and curl Ch. 15.1 - Match the vector field F(x,y) with one of the...Ch. 15.1 - Match the vector field F(x,y) with one of the...Ch. 15.1 - Determine whether the statement about the vector...Ch. 15.1 - Determine whether the statement about the vector...Ch. 15.1 - Sketch the vector field by drawing some...Ch. 15.1 - Sketch the vector field by drawing some...

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To prove: The curl F of a conservative vector field F x , y , z = f x , y , z i + g x , y , z j + h x , y , z k , f , g and h has continuous first order partial derivatives, in an open spherical region is zero.

Solution Summary: The author explains that the curl of a vector field F(x,y,z) is given by ccurlF.

To prove: The curl F of a conservative vector field Fx,y,z=fx,y,zi+gx,y,zj+hx,y,zk , f,g and h has continuous first order partial derivatives, in an open spherical region is zero.

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Chapter 15 Solutions