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求函数(x/x-1)-(1/lnx)x趋向于1的极限
题目详情
求函数(x/x-1)-(1/lnx)x趋向于1的极限
▼优质解答
答案和解析
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
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
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