Question

求函数(x/x-1)-(1/lnx)x趋向于1的极限

Answer 1

t=x-1

T=(t+1)/t-1/ln(t+1),t->0

ln(1+t)=t-t^2/2.

T=1+1/t-1/[t-t^2/2+0(t^3)]----通分

=1+[1-t/2+0(t^2)-1]/[t-t^2/2+0(t^3)]

=1+[t/2+0(t^2)]/[t-t^2/2+0(t^3)]

=1+1/2

=3/2