posted by musuma .
lim of x as it approaches infinity for sqrt of x^2 -1/2x+1
x^2 -1/2x+1 = x/2 - 1/4 - 3/(4(2x+1))
as x-->oo, that goes to oo as well.
Discard all of the numerator and denominator except the highest powers. For large x, your function just looks like x/2. Big, big limit.