In Exercises 45 and 46, use the function to show that and both exist, but that is not
Chapter 13, Problem 45(choose chapter or problem)
In Exercises 45 and 46, use the function to show that \(f_{x}(0,0)\) and \(f_{y}(0,0)\) both exist, but that is not differentiable at (0, 0).
\(f(x, y)=\left\{\begin{array}{ll}
\frac{3 x^{2} y}{x^{4}+y^{2}}, & (x, y) \neq(0,0) \\
0, & (x, y)=(0,0)
\end{array}\right.\)
Text Transcription:
f_x(0,0)
f_y(0,0)
f(x, y)=frac3x^2yx^4+y^2,&(x,y)neq(0,0)0,&(x,y)=(0,0)
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