The limit of the function lim(x,y)→(1,0) ((x-y-1)²/(x+y-1)²) can be evaluated using L'Hôpital's Rule, but it requires confirming that the limit is consistent across different paths. Specifically, approaching the limit point along the lines y = x - 1 and y = -x + 1 yields different results, indicating that the limit does not exist. This conclusion is critical for understanding multivariable limits and the application of L'Hôpital's Rule in such contexts.
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For this you need to show that the limit exists (and is the same) along all paths approaching it.brunette15 said:I am trying to find the limit of the following:
lim(x,y)--> (1,0) ((x-y-1)2/(x+y-1)2)
I have had a few attempts trying to use l'hopital's rule but i don't seem to be getting anywhere...