lim(1+tanx/1+sinx)^1/sinx x趋近于0
来源：学生作业帮助网 编辑：六六作业网 时间：2024/05/10 02:01:54
lim(1+tanx/1+sinx)^1/sinxx趋近于0lim(1+tanx/1+sinx)^1/sinxx趋近于0lim(1+tanx/1+sinx)^1/sinxx趋近于0原式=lim(x->
lim(1+tanx/1+sinx)^1/sinx x趋近于0
lim(1+tanx/1+sinx)^1/sinx x趋近于0
lim(1+tanx/1+sinx)^1/sinx x趋近于0
原式=lim(x->0){[1+(tanx-sinx)/(1+sinx)]^[((1+sinx)/(tanx-sinx))*((tanx-sinx)/(sinx+sin²x))]}
=e^{lim(x->0)[(tanx-sinx)/(sinx+sin²x)]} (应用重要极限lim(z->0)[(1+z)^(1/z)]=e)
=e^{lim(x->0)[(1/cosx-1)/(1+sinx)]}
=e^[(1-1)/(1+0)]
=e^0
=1.