X乘以[（根号下X的平方-1)-X] 当X趋近于无穷时的极限

Question

如题所述

Answer 1

当X趋近于无穷时,
limx*(根号下(x^2-1)-x])
=limx*(根号下(x^2-1)-x)*(根号下(x^2-1)+x)/(根号下(x^2-1)+x)
=limx*(x^2-1-x^2)/(根号下(x^2-1)+x)
=-limx/[根号下(x^2-1)+x]
=-lim1/[根号下(x^2-1)/x+1]
分子分母同除以x
=-lim1/[根号下(1-1/x^2)+1]
=-1*1/(1+1)
=-1/2