lim(x→∞)x[√(x²+1)-x]=lim(x→∞)x[(x²+1)-x²}/[√(x²+1)-x]=lim(x→∞)x/[√(x²+1)+x]=lim(x→∞)1/[√(1+1/x²)+1]=1/2
答案中怎么会有:lim(x→∞)x[(x²+1)-x²}/[√(x²+1)-x
不好意思,刚才太忙了以至于写错了。现在更正过来lim(x→∞)x[√(x²+1)-x]=lim(x→∞)x[(x²+1)-x²}/[√(x²+1)+x]=lim(x→∞)x/[√(x²+1)+x]=lim(x→∞)1/[√(1+1/x²)+1]=1/2