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When I plug in values, I get -1/0 which is undefined. My question is, how do I prove that the limit does not exist? I can't set y=mx because y and x do not necessarily follow the same path to the point (1,-1,1) and using polar coordinate substitution does not seem to work here. I tried setting z=x but that still gives me a 0 in the denominator because of the -1 for the y. Finally, multiplying the equation by various values of 1 (such as multiplying y squared to both the numerator and denominator) don't solve the undefined issue.