Let a function $f :R^2\to R $ so that $\lim_{(x,y)\to (0,0)}f(0,0)=0$ then $f$ is continuous at $(0,0)$. Why is this statement false? I thought the existance of a limit at a point a implied the continuity at that point. What am I missing here?
2026-04-12 14:10:01.1776003001
Why $f$ may not be continuous despite $\lim_{(x,y)\to (0,0)}f(0,0)=0$?
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You are missing that $f(0,0)$ may be different from $0$.