Rotation fields are usually not conservative (-y,x) a. Prove that the rotation field F = where r = (x, y), is not conservative for p + 2. b. For p = 2, show that F is conservative on any region not containing the origin. c. Find a potential function for F when p = 2.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Rotation fields are usually not conservative
(-y,x)
a. Prove that the rotation field F =
where r = (x, y),
is not conservative for p + 2.
b. For p = 2, show that F is conservative on any region not
containing the origin.
c. Find a potential function for F when p = 2.
Transcribed Image Text:Rotation fields are usually not conservative (-y,x) a. Prove that the rotation field F = where r = (x, y), is not conservative for p + 2. b. For p = 2, show that F is conservative on any region not containing the origin. c. Find a potential function for F when p = 2.
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