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## Main Question or Discussion Point

The first one is a mere question. If we are given lim f(x,y) = L, (x,y) -->(∞, u) where u represents an unknown, is it possible to figure out what value u must be so that the limit will in fact, be L?

And the second one:

given:

lim [(x

Thanks!

And the second one:

given:

lim [(x

^{x}/(x-n)^{(x-n)})^{-n}- ((x-n)^{(x-n)})^{-n}]/n = L for (x,n)--->(∞, 0). Is it possible to prove that this limit exists using the δ and ε method? In this case n is merely a dummy variable, and one can view this as y = f(x,n) if you wish with the value of L corresponding to the line y = L.Thanks!