Question

高数中,如何证明arctanx和x是等价无穷小函数

Answer 1

,如何证明arctanx和x是等价无穷小函数
令arctanx=t,
则x=tant
limarctanx/x
=limt/tant
=limt/sint•lim1/cost
=1•1
=1所以，sinx~x

Answer 2

lim(x→0)
arctanx/x
=lim(x→0)
[1/(1+x²)]/1
——0/0型，应用洛必达法则
=lim(x→0)
1/(1+x²)
=1
∴arctanx和x是等价无穷小