let be the function $ ( \epsilon x +1)^{1/\epsilon}=f(x) $, i know that in the limit
$ \epsilon \to 0 $ then $f(x)=e^{x}$ , however i would like to know what happens if i have the function
$ ( \epsilon x +a)^{1/\epsilon}=f(x) $, in the cases $ a >1$ , $a<1$
in the first case if $a>1 $ and 'x' is positive the function is $f(x)=\infty$ , for the other case with $ a<1$ i believe that $ f(x)=0$ , but i am not sure.