Question

limx趋向+∞√x²-x+1 -x=?

能写个过程嘛，谢谢，

Answer 1

lim(x->+∞) [√(x^2-x+1) -x ]
分子分母同时乘以 [√(x^2-x+1) +x ]
=lim(x->+∞) [(x^2-x+1) -x^2 ]/[√(x^2-x+1) +x ]
=lim(x->+∞) (-x+1)/[√(x^2-x+1) +x ]
分子分母同时除x

=lim(x->+∞) (-1+1/x)/[√(1-1/x+1/x^2) +1 ]
=-1/(1+1)
=-1/2

Answer 2

x→+∞lim[√(x²-x+1)-x]=lim[(x²-x+1)-x²]/[√(x²-x+1)+x]=lim(-x+1)/[√(x²-x+1)+x]
=lim(-1+1/x)/[√(1-1/x+1/x²)+1]=-1/(1+1)=-1/2