Question

X乘以[（根号下X的平方-1)-X] 当X趋近于无穷时的极限

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