If, lim [(A)/2^y] as y->infinity = (1/2)*[(1/2)^x], what is A(x)?

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If

lim [A(x,y)/2^y] as y->infinity = (1/2)*[(1/2)^x] ,

What is A(x,y)?
 
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You would want to have a term that cancels out the denominator. For example take A(x,y)=C(x)D(y), if we then take D(y)=2^y \lim_{y \to \infty}A(x,y)/2^y=\lim_{y \to \infty}C(x)=C(x).
 
A(x,y) must not be y independent for y<infinity.
 

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