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Calculus / Calculus: Early Transcendentals 1 / Chapter 14.3 / Problem 54AE

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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Radial fields in 3 are conservative Prove that the radial

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QUESTION:

Prove that the radial field \(\mathbf{F}=\frac{\mathbf{r}}{|\mathbf{r}|^{p}}\), where \(\mathbf{r}=\langle x, y, z\rangle\) and p is a real number, is conservative on any region not containing the origin. For what values of p is F conservative on a region that contains the origin.

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QUESTION:

Prove that the radial field \(\mathbf{F}=\frac{\mathbf{r}}{|\mathbf{r}|^{p}}\), where \(\mathbf{r}=\langle x, y, z\rangle\) and p is a real number, is conservative on any region not containing the origin. For what values of p is F conservative on a region that contains the origin.

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Solution 54

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