解：原式=lim(x->∞){[√(4x^2+x-1)+x+1]/[√(x^2+sinx)]} =lim(x->∞){[√(4+1/x-1/x²)+1+1/x]/[√(1+sinx/x²)]} (分子分母同除x) =[√(4+0-0)+1+0]/[√(1+0)] =3.
趋于负无穷是1 正无穷是3
3
