How can I use the directional derivative of a two variable function to show that the limit does not exist? For example, suppose I have a function f(x,y)=g(x)/f(y) and g(a)=f(b)=0 and the limit as x and y go to a and b is 0. How would I use the directional derivative to show that the limit at (a,b) does not exist.(adsbygoogle = window.adsbygoogle || []).push({});

So far, I have tried to take the directional derivatives of the f(x,y) at points around the (a,b), but I feel this is inconclusive because nothing is known about the function itself, other than the fact that it is undefined at (a,b).

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# Directional Derivatives and Limits

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