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Solved: Gradient fields Find the gradient field F = for
Chapter 14, Problem 30E(choose chapter or problem)
QUESTION:
Gradient fields Find the gradient field \(\mathbf{F}=\nabla \varphi\) for the following potential functions \(\varphi\).
\(\varphi(x, y, z)=\ln \left(1+x^{2}+y^{2}+z^{2}\right)\)
Text Transcription:
varphi(x, y, z) = ln 1+x^2+y^2+z^2
Questions & Answers
QUESTION:
Gradient fields Find the gradient field \(\mathbf{F}=\nabla \varphi\) for the following potential functions \(\varphi\).
\(\varphi(x, y, z)=\ln \left(1+x^{2}+y^{2}+z^{2}\right)\)
Text Transcription:
varphi(x, y, z) = ln 1+x^2+y^2+z^2
ANSWER:Solution 30EStep 1:Given that(x,y,z) = In (1 + x2 + y2 + z2)