Consider the sequence "(x_k, y_k) = (\\frac 1k,\\frac 1{k^2})" : "f(x_k, y_k)=\\frac{\\frac 4{k^4}}{\\frac 5{k^4}} =\\frac 45 \\rightarrow \\frac 45 \\not =0=f(0,0), k \\to \\infin."
Consequently, the function "f(x,y)" is not continuous at "(0,0)" .
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