If limx→∞ x2+1x+1−(ax+b)→∞, then

We have, limx→∞ x2+1x+1−ax−b=∞⇒ limx→∞ x2(1−a)−x(a+b)+1−bx+1=∞The limit of the given expression will be infinity, if degree of numerator is more than that of denominator. ∴ 1−a>0⇒a<1.Hence , a∈(−∞,1)can assume any real value.