Function with saddle at the origin If you did Exercise 60
Chapter , Problem 1AAE(choose chapter or problem)
Function with saddle at the origin If you did Exercise 60 in Section , you know that the function
\(f(x, y)=\left\{\begin{array}{ll} x y \frac{x^{2}-y^{2}}{x^{2}+y^{2}}, & (x, y) \neq(0,0) \\ 0, & (x, y)=(0,0) \end{array}\right.\)
(see the accompanying figure) is continuous at . Find \(f_{x y}(0,0) \text { and } f_{y x}(0,0)\).
Equation Transcription:
Text Transcription:
f(x, y)={ xy x^2 -y^2 /x^2 + y^2 , (x, y) neq (0, 0) 0, (x, y) = (0, 0)
f_xy (0, 0) and f_yx (0, 0)
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