Searching for an asymptotic to exp[0.5]

[tommy1729]

I havent given this much consideration yet but let lim x->+oo :

C = lim ( 1 - ( D exp_a^[b](x) / exp_a^[b](x) ) ) / ( 1 - ( D exp_c^[d](x) / exp_c^[d](x) ) ).

For a,c > eta ( = exp(1/e)) [a and c are bases]
For 0.25 < b,d < 0.5.
(a-c)^2 + (b-d)^2 > 0.
C > 0. (limit exists and is larger than 0).

Is that true ?

Do we know numerical examples of such a,b,c,d,C ?

It seems - at first sight - that l'hopitals rule cannot be used.

regards

tommy1729