Finding potential functions Determine whether

Chapter 13, Problem 26E

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QUESTION:

Determine whether the following vector fields are conservative on the specified region. If so, determine a potential function. Let \(R^{*}\) and \(D^{*}\) be open regions of \(\mathbf{R}^{2}\) and \(\mathbf{R}^{3}\), respectively, that do not include the origin.

\(\mathbf{F}=\left\langle x^{3}, 2 y,-z^{3}\right\rangle \text { on } \mathbf{R}^{3}\)

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QUESTION:

Determine whether the following vector fields are conservative on the specified region. If so, determine a potential function. Let \(R^{*}\) and \(D^{*}\) be open regions of \(\mathbf{R}^{2}\) and \(\mathbf{R}^{3}\), respectively, that do not include the origin.

\(\mathbf{F}=\left\langle x^{3}, 2 y,-z^{3}\right\rangle \text { on } \mathbf{R}^{3}\)

ANSWER:

Solution 26EThe give

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