Answer to Question #273804 in Calculus for Jamailaaa

Question #273804

Give an example of a function of two variables such thatf(0,0) = 0 butfis NOT continuousat (0,0). Explain why the functionfis NOT continuous at (0,0).


1
Expert's answer
2021-12-15T05:09:03-0500

Consider the function "f:\\R\\times\\R\\to\\R,\\ f(x,y)=\\begin{cases}0, \\text { if }(x,y)=(0,0)\\\\ 1, \\text { if }(x,y)\\ne(0,0)\\end{cases}."

Taking into account that "\\lim\\limits_{x\\to 0,\\\\ y\\to 0}f(x,y)=1\\ne 0=f(0,0)," we conclude that the function is not continuous at "(0,0)."

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