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!