X趋近于零(x-sinx)/(x+sinx)的极限

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X趋近于零(x-sinx)/(x+sinx)的极限X趋近于零(x-sinx)/(x+sinx)的极限X趋近于零(x-sinx)/(x+sinx)的极限lim(x->0)(x-sinx)/(x+sinx

X趋近于零(x-sinx)/(x+sinx)的极限
X趋近于零(x-sinx)/(x+sinx)的极限

X趋近于零(x-sinx)/(x+sinx)的极限
lim(x->0) (x-sinx)/(x+sinx)
= lim(x->0) ( 1 - sinx /x ) / ( 1 + sinx /x)
= (1-1)/(1+1) = 0

上下同除x 可得极限为 0/2 所以最后极限为0

lim(x-sinx)/(x+sinx)(用洛比特法则)
=lim(1-cosx)/(1+cosx)
=limsinx/(-sinx)
=-1