Question: Use a graphing utility to make a table showing the values of f ( x, y ) at the given points. Use the result to make a conjecture about the limit of f(x, y) as ( x, y ) \(\to \) (0,0). Determine whether the limit exist analytically and discuss the continuity of the function.

\(f(x, y)=\frac{y}{x^{2}+y^{2}}\)

Path: \(y=0\)

Points: \((1,0)\),

\((0.5,0),(0.1,0)\),

\((0.01,0),(0.001,0)\)

Path: \(y=x\)

Points: \((1,1)\),

\((0.5,0.5),(0.1,0.1)\),

\((0.01,0.01),(0.001,0.001)\)

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