#lim_(x to oo) sqrt(x)(sqrt(x)-sqrt(x-a))#
#= lim_(x to oo) sqrt(x)(sqrt(x)-sqrt(x-a))* (sqrt(x)+sqrt(x-a))/(sqrt(x)+sqrt(x-a))#
#= lim_(x to oo) sqrt(x)* (x-(x-a))/( sqrt(x)+sqrt(x-a))#
#= lim_(x to oo) (a)/( 1+sqrt(1-a/x))#
#= (a)/( 1+ lim_(x to oo) sqrt(1-a/x)) = a/2#