Question 1030353
We will use the definition of e to evaluate this: {{{lim(n->infinity, (1+lambda/n)^(n/lambda)) = e}}}
Now let w = x-a.
==> x+a = w+2a, {{{w-> infinity}}} as {{{x->infinity}}}, and 


 {{{lim( x->infinity, ((x+a)/(x-a))^x ) =lim( w->infinity, ((w+2a)/w)^(w+a)) = lim( w->infinity, (1+(2a)/w)^(w+a)) = lim( w->infinity, (1+(2a)/w)^w *(1+(2a)/w)^a) }}}

= {{{lim( w->infinity, (1+(2a)/w)^w )*lim(w->infinity, (1+(2a)/w)^a) = lim( w->infinity, ((1+(2a)/w)^(w/(2a)))^(2a) )*lim(w->infinity, (1+(2a)/w)^a) }}}.

In the very last expression, the second limit {{{lim(w->infinity, (1+(2a)/w)^a) = 1 }}}, because {{{(2a)/w -> 0}}} as w approaches infinity, and a is a fixed constant that doesn't vary with w.

But {{{lim( w->infinity, ((1+(2a)/w)^(w/(2a)))^(2a) ) = (lim( w->infinity, (1+(2a)/w)^(w/(2a))))^(2a)  = e^(2a) = e}}}, and hence 2a = 1, or a = 1/2.