∵ lim(x->∞)(x^2+1)/(x+1) -ax-b = 0 ∴ 0=lim(x->∞)[(x^2+1)/(x+1) -ax-b ] / x =lim(x->∞)[(x+1/x)/(x+1) -a-b/x =lim(x->∞)[(1+1/x^2)/(1+1/x) -a-b/x = 1 - a - 0 = 1-a ∴ a = 1 ∴ lim(x->∞)(x^2+1)/(x+1) - x - b =lim(x->∞)(x^2+1 - x^2 - x )/(x+1) - b =lim(x->∞)(1 - x )/(x+1) - b =lim(x->∞)(1/x - 1 )/(1+1/x) - b = -1 - b = 0 ∴ b = -1