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Solution: Conservative vector fields and potentials
Chapter 13, Problem 22RE(choose chapter or problem)
QUESTION:
Conservative vector fields and potentials Determine whether the following vector fields are conservative on their domains. If so, find a potential function.
\(\mathbf{F}=\left\langle e^{x} \cos y,-e^{x} \sin y\right\rangle\)
Text Transcription:
F = langle e^x cos y, -e^x sin y rangle
Questions & Answers
QUESTION:
Conservative vector fields and potentials Determine whether the following vector fields are conservative on their domains. If so, find a potential function.
\(\mathbf{F}=\left\langle e^{x} \cos y,-e^{x} \sin y\right\rangle\)
Text Transcription:
F = langle e^x cos y, -e^x sin y rangle
ANSWER:Solution 22RE
Step 1
Consider the vector function
So that
Observe that
Therefore the given vector function is conservative.