MHB Can the limit of (x,y) at (1,0) be found using l'hopital's rule?

[brunette15]

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...

 

[topsquark]

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...

For this you need to show that the limit exists (and is the same) along all paths approaching it.

Hint: Approach the limit point along the line y = x - 1 and the line y = -x + 1. Is the limit the same in both cases?

-Dan