Sinx的tanx次方当x趋近于二分之派时的极限是 - 知识问答

Sinx的tanx次方当x趋近于二分之派时的极限是多少啊?

2个回答

原式=lim(x→π/2) (1+sinx-1)^{[1/(sinx-1)](tanx)(sinx-1)}
=lim(x→π/2) e^[(tanx)(sinx-1)]
=e^ lim(x→π/2) (sinx-1)/cotx
=e^ lim(x→π/2) cosx/(- csc²x)
=e^0
=1

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