If f(x, y) ={ 1 if x=0 or y=0 and 0 otherwise } then lim f(x, y) does not exist for limit (x, y) approaches to (0, 0).
Consider the limit of along straight lines , wherea is the slope) as
.We have,
(by definition of the function).And,
(by definition of the function)Thus, since the limit along a straight line depends on the slope of te line. We have that the two-variable limit does not exist.
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