I need to figure out Why wouldn't a limit exist if we got the SAME value on each path? – math.stackexchange.com

I need to figure out Why wouldn't a limit exist if we got the SAME value on each path? – math.stackexchange.com

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When talking about limits for functions of several variables, why isn’t it sufficient to say, $$\lim_{(x,y)\to(0,0)} f(x,y)=L$$ if $f(x,y)$ gets close to $L$ as we approach $(0,0)$ along the $x$-axis ...

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