求lim{下面(x属于0）}（x-tanx)/x^3的极限怎么算?
问题描述：
求lim{下面(x属于0）}（x-tanx)/x^3的极限怎么算?
答
lim(x→0)(x-tanx)/x^3
[洛必达法则]
=lim(x→0)(1-(secx)^2)/3x^2
[洛必达法则]
=lim(x→0)(-2secxsecxtgx)/6x
=lim(x→0)tgx/(-3x)*1/(cosx)^2
[tgx和x是等价无穷小量]
=-1/3*1
=-1/3