求极限 limx→0 x-arcsinx/xsinxtan2x

题目

求极限 limx→0 x-arcsinx/xsinxtan2x

答案

x->0时,sinx~x,tan2x~2x
lim x-arcsinx/xsinxtan2x
=lim x-arcsinx/2x^3
=lim [1-1/√(1-x²)]/6x²
=lim [-x(1-x²)^(-3/2)]/12x
=lim [-(1-x²)^(-3/2)]/12
=-1/12