Polar coordinates and second derivatives Introducing polar
Chapter , Problem 94PE(choose chapter or problem)
Polar coordinates and second derivatives Introducing polar coordinates \(x=r \cos \theta\) and \(y=r \sin \theta\) changes \(f(x, y)\) to \(g(r, \theta)\) Find the value of \(\partial^{2} g / \partial \theta^{2}\) at the point \((r, \theta)=(2, \pi / 2)\), given that
\(\frac{\partial f}{\partial x}=\frac{\partial f}{\partial y}=\frac{\partial^{2} f}{\partial x^{2}}=\frac{\partial^{2} f}{\partial y^{2}}=1\)
at that point.
Equation Transcription:
Text Transcription:
x = r cos theta
y = r sin theta
f(x, y)
g(r, theta )
partial ^2g/ partial theta^2
(r, theta ) = (2, pi/2)
partialƒ/partial x = partial ƒ/partial y = partial^2 ƒ/ partial x^2 = partial^2 ƒ/ partial y^2 = 1
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