X→0时,arctanx～X
变量替换,令arctanx＝y,x＝tany,x趋于0时,y趋于0,因此
lim arctanx/x
＝lim y/tany
＝lim ycosy/siny
=lim cosy/(siny/y)
＝1.即arctanx～x
证明：X→0时,arctanx～X
X→0时,arctanx～X
变量替换,令arctanx＝y,x＝tany,x趋于0时,y趋于0,因此
lim arctanx/x
＝lim y/tany
＝lim ycosy/siny
=lim cosy/(siny/y)
＝1.即arctanx～x